Space-time models based on random fields with local interactions

NASA Astrophysics Data System (ADS)

Hristopulos, Dionissios T.; Tsantili, Ivi C.

2016-08-01

The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

A quantum analogy to the classical gravitomagnetic clock effect

NASA Astrophysics Data System (ADS)

Faruque, S. B.

2018-06-01

We present an approximation to the solution of Dirac equation in Schwarzschild field found through the use of Foldy-Wouthuysen Hamiltonian. We solve the equation for the positive energy states and found the frequencies by which the states oscillate. Difference of the periods of oscillation of the two states with two different total angular momentum quantum number j has an analogical form of the classical clock effect found in general relativity. But unlike the term that appears as clock effect in classical physics, here the term is quantized. Thus, we find a quantum analogue of the classical gravitomagnetic clock effect.

SU(N) affine Toda solitons and breathers from transparent Dirac potentials

NASA Astrophysics Data System (ADS)

Thies, Michael

2017-05-01

Transparent scalar and pseudoscalar potentials in the one-dimensional Dirac equation play an important role as self-consistent mean fields in 1  +  1 dimensional four-fermion theories (Gross-Neveu, Nambu-Jona Lasinio models) and quasi-one dimensional superconductors (Bogoliubov-de Gennes equation). Here, we show that they also serve as seed to generate a large class of classical multi-soliton and multi-breather solutions of su(N) affine Toda field theories, including the Lax representation and the corresponding vector. This generalizes previous findings about the relationship between real kinks in the Gross-Neveu model and classical solitons of the sinh-Gordon equation to complex twisted kinks.

Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories

NASA Astrophysics Data System (ADS)

Román-Roy, Narciso

2009-11-01

This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.

Spectra of turbulently advected scalars that have small Schmidt number

NASA Astrophysics Data System (ADS)

Hill, Reginald J.

2017-09-01

Exact statistical equations are derived for turbulent advection of a passive scalar having diffusivity much larger than the kinematic viscosity, i.e., small Schmidt number. The equations contain all terms needed for precise direct numerical simulation (DNS) quantification. In the appropriate limit, the equations reduce to the classical theory for which the scalar spectrum is proportional to the energy spectrum multiplied by k-4, which, in turn, results in the inertial-diffusive range power law, k-17 /3. The classical theory was derived for the case of isotropic velocity and scalar fields. The exact equations are simplified for less restrictive cases: (1) locally isotropic scalar fluctuations at dissipation scales with no restriction on symmetry of the velocity field, (2) isotropic velocity field with averaging over all wave-vector directions with no restriction on the symmetry of the scalar, motivated by that average being used for DNS, and (3) isotropic velocity field with axisymmetric scalar fluctuations, motivated by the mean-scalar-gradient-source case. The equations are applied to recently published DNSs of passive scalars for the cases of a freely decaying scalar and a mean-scalar-gradient source. New terms in the exact equations are estimated for those cases and are found to be significant; those terms cause the deviations from the classical theory found by the DNS studies. A new formula for the mean-scalar-gradient case explains the variation of the scalar spectra for the DNS of the smallest Schmidt-number cases. Expansion in Legendre polynomials reveals the effect of axisymmetry. Inertial-diffusive-range formulas for both the zero- and second-order Legendre contributions are given. Exact statistical equations reveal what must be quantified using DNS to determine what causes deviations from asymptotic relationships.

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ϕ4-Theory

NASA Astrophysics Data System (ADS)

Finster, Felix; Tolksdorf, Jürgen

2012-05-01

Solutions of the classical ϕ4-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

Spinomotive force induced by a transverse displacement current in a thin metal or doped-semiconductor sheet: Classical and quantum views.

NASA Astrophysics Data System (ADS)

Hu, Chia-Ren

2004-03-01

We present classical macroscopic, microscopic, and quantum mechanical arguments to show that in a metallic or electron/hole-doped semiconducting sheet thinner than the screening length, a displacement current applied normal to it can induce a spinomotive force along it. The magnitude is weak but clearly detectable. The classical arguments are purely electromagnetic. The quantum argument, based on the Dirac equation, shows that the predicted effect originates from the spin-orbit interaction, but not of the usual kind. That is, it relies on an external electric field, whereas the usual S-O interaction involves the electric field generated by the ions. Because the Dirac equation incorporatesThomas precession, which is due to relativistic kinematics, the quantum prediction is a factor of two smaller than the classical prediction. Replacing the displacement current by a charge current, and one obtains a new source for the spin-Hall effect. Classical macroscopic argument also predicts its existence, but the other two views are controversial.

Generalizations of the classical Yang-Baxter equation and O-operators

NASA Astrophysics Data System (ADS)

Bai, Chengming; Guo, Li; Ni, Xiang

2011-06-01

Tensor solutions (r-matrices) of the classical Yang-Baxter equation (CYBE) in a Lie algebra, obtained as the classical limit of the R-matrix solution of the quantum Yang-Baxter equation, is an important structure appearing in different areas such as integrable systems, symplectic geometry, quantum groups, and quantum field theory. Further study of CYBE led to its interpretation as certain operators, giving rise to the concept of {O}-operators. The O-operators were in turn interpreted as tensor solutions of CYBE by enlarging the Lie algebra [Bai, C., "A unified algebraic approach to the classical Yang-Baxter equation," J. Phys. A: Math. Theor. 40, 11073 (2007)], 10.1088/1751-8113/40/36/007. The purpose of this paper is to extend this study to a more general class of operators that were recently introduced [Bai, C., Guo, L., and Ni, X., "Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras," Commun. Math. Phys. 297, 553 (2010)], 10.1007/s00220-010-0998-7 in the study of Lax pairs in integrable systems. Relations between O-operators, relative differential operators, and Rota-Baxter operators are also discussed.

Interaction of the sonic boom with atmospheric turbulence

NASA Technical Reports Server (NTRS)

Rusak, Zvi; Cole, Julian D.

1994-01-01

Theoretical research was carried out to study the effect of free-stream turbulence on sonic boom pressure fields. A new transonic small-disturbance model to analyze the interactions of random disturbances with a weak shock was developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustics equation that describes the propagation of sound beams with narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed type elliptic-hyperbolic flows around the shock wave was also developed. Numerical calculations of shock wave interactions with various deterministic and random fluctuations will be presented in a future report.

Linear and angular coherence momenta in the classical second-order coherence theory of vector electromagnetic fields.

PubMed

Wang, Wei; Takeda, Mitsuo

2006-09-01

A new concept of vector and tensor densities is introduced into the general coherence theory of vector electromagnetic fields that is based on energy and energy-flow coherence tensors. Related coherence conservation laws are presented in the form of continuity equations that provide new insights into the propagation of second-order correlation tensors associated with stationary random classical electromagnetic fields.

Quantum-classical analogies in waveguide arrays: From Fourier transforms to ion-laser interactions

NASA Astrophysics Data System (ADS)

Moya-Cessa, Héctor M.

2018-04-01

By using the fact that infinite and semi-infinite systems of differential equations may be casted as Schrödinger-like equations we show how quantum-classical analogies may be achieved. In particular we show how the analogies of ion-laser, functions of a phase operator and quantised-field-two-level-atom interactions may be emulated. We also show a realization of the fractional discrete Fourier transform.

CLASSICAL AREAS OF PHENOMENOLOGY: Material parameter equation for rotating elliptical spherical cloaks

NASA Astrophysics Data System (ADS)

Ma, Hua; Qu, Shao-Bo; Xu, Zhuo; Zhang, Jie-Qiu; Wang, Jia-Fu

2009-01-01

By using the coordinate transformation method, we have deduced the material parameter equation for rotating elliptical spherical cloaks and carried out simulation as well. The results indicate that the rotating elliptical spherical cloaking shell, which is made of meta-materials whose permittivity and permeability are governed by the equation deduced in this paper, can achieve perfect invisibility by excluding electromagnetic fields from the internal region without disturbing any external field.

Exact treatment of the Jaynes-Cummings model under the action of an external classical field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abdalla, M. Sebawe, E-mail: m.sebaweh@physics.org; Khalil, E.M.; Mathematics Department, College of Science, Taibah University, Al-MaDinah

2011-09-15

We consider the usual Jaynes-Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency {omega}{sub 0} and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strongmore » value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity. - Highlights: > The time-dependent JCM, in the presence of the classical field, is still one of the essential problems in the quantum optics. > A new approach is applied through a certain canonical transformation. > The classical field augments the atomic frequency {omega}{sub 0} and mixes the original atomic states.« less

Electrons in strong electromagnetic fields: spin effects and radiation reaction (Conference Presentation)

NASA Astrophysics Data System (ADS)

Bauke, Heiko; Wen, Meng; Keitel, Christoph H.

2017-05-01

Various different classical models of electrons including their spin degree of freedom are commonly applied to describe the coupled dynamics of relativistic electron motion and spin precession in strong electromagnetic fields. The spin dynamics is usually governed by the Thomas-Bargmann-Michel-Telegdi equation [1, 2] in these models, while the electron's orbital motion follows the (modified) Lorentz force and a spin-dependent Stern-Gerlach force. Various classical models can lead to different or even contradicting predictions how the spin degree of freedom modifies the electron's orbital motion when the electron moves in strong electromagnetic fields. This discrepancy is rooted in the model-specific energy dependency of the spin induced relativistic Stern-Gerlach force acting on the electron. The Frenkel model [3, 4] and the classical Foldy-Wouthuysen model 5 are compared exemplarily against each other and against the quantum mechanical Dirac equation in order to identify parameter regimes where these classical models make different predictions [6, 7]. Our theoretical results allow for experimental tests of these models. In the setup of the longitudinal Stern-Gerlach effect, the Frenkel model and classical Foldy-Wouthuysen model lead in the relativistic limit to qualitatively different spin effects on the electron trajectory. Furthermore, it is demonstrated that in tightly focused beams in the near infrared the effect of the Stern-Gerlach force of the Frenkel model becomes sufficiently large to be potentially detectable in an experiment. Among the classical spin models, the Frenkel model is certainly prominent for its long history and its wide application. Our results, however, suggest that the classical Foldy-Wouthuysen model is superior as it is qualitatively in better agreement with the quantum mechanical Dirac equation. In ultra strong laser setups at parameter regimes where effects of the Stern-Gerlach force become relevant also radiation reaction effects are expected to set in. We incorporate radiation reaction classically via the Landau-Lifshitz equation and demonstrate that although radiation reaction effects can have a significant effect on the electron trajectory, the Frenkel model and the classical Foldy-Wouthuysen model remain distinguishable also if radiation reaction effects are taken into account. Our calculations are also suitable to verify the Landau-Lifshitz equation for the radiation reaction of electrons and other spin one-half particles. 1. Thomas, L. H., "I. The kinematics of an electron with an axis," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 3(13), 1-22 (1927). 2. Bargmann, V., Michel, L., and Telegdi, V. L., "Precession of the polarization of particles moving in a homogeneous electromagnetic field," Phys. Rev. Lett. 2(10), 435-436 (1959). 3. Frenkel, J., "Die Elektrodynamik des rotierenden Elektrons," Z. Phys. 37(4-5), 243-262 (1926). 4. Frenkel, J., "Spinning electrons," Nature (London) 117(2949), 653-654 (1926). 5. Silenko, A. J., "Foldy-Wouthyusen transformation and semiclassical limit for relativistic particles in strong external fields," Phys. Rev. A 77(1), 012116 (2008). 6. Wen, M., Bauke, H., and Keitel, C. H., "Identifying the Stern-Gerlach force of classical electron dynamics," Sci. Rep. 6, 31624 (2016). 7. Wen, M., Keitel, C. H., and Bauke, H., "Spin one-half particles in strong electromagnetic fields: spin effects and radiation reaction," arXiv:1610.08951 (2016).

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE PAGES

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

2017-02-01

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

Gravitational self-interactions of a degenerate quantum scalar field

NASA Astrophysics Data System (ADS)

Chakrabarty, Sankha S.; Enomoto, Seishi; Han, Yaqi; Sikivie, Pierre; Todarello, Elisa M.

2018-02-01

We develop a formalism to help calculate in quantum field theory the departures from the description of a system by classical field equations. We apply the formalism to a homogeneous condensate with attractive contact interactions and to a homogeneous self-gravitating condensate in critical expansion. In their classical descriptions, such condensates persist forever. We show that in their quantum description, parametric resonance causes quanta to jump in pairs out of the condensate into all modes with wave vector less than some critical value. We calculate, in each case, the time scale over which the homogeneous condensate is depleted and after which a classical description is invalid. We argue that the duration of classicality of inhomogeneous condensates is shorter than that of homogeneous condensates.

Motion of small bodies in classical field theory

NASA Astrophysics Data System (ADS)

Gralla, Samuel E.

2010-04-01

I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body’s composition (and, e.g., black holes are allowed). The worldline “left behind” by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the “Bianchi identity” for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the “monopoles” of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of “chameleon” bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.

Superconductor in a weak static gravitational field

NASA Astrophysics Data System (ADS)

Ummarino, Giovanni Alberto; Gallerati, Antonio

2017-08-01

We provide the detailed calculation of a general form for Maxwell and London equations that takes into account gravitational corrections in linear approximation. We determine the possible alteration of a static gravitational field in a superconductor making use of the time-dependent Ginzburg-Landau equations, providing also an analytic solution in the weak field condition. Finally, we compare the behavior of a high-T_ {c} superconductor with a classical low-T_ {c} superconductor, analyzing the values of the parameters that can enhance the reduction of the gravitational field.

Nonextensive Thomas-Fermi model

NASA Astrophysics Data System (ADS)

Shivamoggi, Bhimsen; Martinenko, Evgeny

2007-11-01

Nonextensive Thomas-Fermi model was father investigated in the following directions: Heavy atom in strong magnetic field. following Shivamoggi work on the extension of Kadomtsev equation we applied nonextensive formalism to father generalize TF model for the very strong magnetic fields (of order 10e12 G). The generalized TF equation and the binding energy of atom were calculated which contain a new nonextensive term dominating the classical one. The binding energy of a heavy atom was also evaluated. Thomas-Fermi equations in N dimensions which is technically the same as in Shivamoggi (1998) ,but behavior is different and in interesting 2 D case nonextesivity prevents from becoming linear ODE as in classical case. Effect of nonextensivity on dielectrical screening reveals itself in the reduction of the envelope radius. It was shown that nonextesivity in each case is responsible for new term dominating classical thermal correction term by order of magnitude, which is vanishing in a limit q->1. Therefore it appears that nonextensive term is ubiquitous for a wide range of systems and father work is needed to understand the origin of it.

Efficient solution of the Wigner-Liouville equation using a spectral decomposition of the force field

NASA Astrophysics Data System (ADS)

Van de Put, Maarten L.; Sorée, Bart; Magnus, Wim

2017-12-01

The Wigner-Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner-Liouville kernel both conceptually and numerically as the spectral force Wigner-Liouville equation avoids the numerical evaluation of the highly oscillatory Wigner kernel which is nonlocal in both position and momentum. The quantum mechanical evolution is instead governed by a term local in space and non-local in momentum, where the non-locality in momentum has only a limited range. An interpretation of the time evolution in terms of two processes is presented; a classical evolution under the influence of the averaged driving field, and a probability-preserving quantum-mechanical generation and annihilation term. Using the inherent stability and reduced complexity, a direct deterministic numerical implementation using Chebyshev and Fourier pseudo-spectral methods is detailed. For the purpose of illustration, we present results for the time-evolution of a one-dimensional resonant tunneling diode driven out of equilibrium.

The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-09-01

We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

Derivation of the cut-off length from the quantum quadratic enhancement of a mass in vacuum energy constant Lambda

NASA Astrophysics Data System (ADS)

Fukushima, Kimichika; Sato, Hikaru

2018-04-01

Ultraviolet self-interaction energies in field theory sometimes contain meaningful physical quantities. The self-energies in such as classical electrodynamics are usually subtracted from the rest mass. For the consistent treatment of energies as sources of curvature in the Einstein field equations, this study includes these subtracted self-energies into vacuum energy expressed by the constant Lambda (used in such as Lambda-CDM). In this study, the self-energies in electrodynamics and macroscopic classical Einstein field equations are examined, using the formalisms with the ultraviolet cut-off scheme. One of the cut-off formalisms is the field theory in terms of the step-function-type basis functions, developed by the present authors. The other is a continuum theory of a fundamental particle with the same cut-off length. Based on the effectiveness of the continuum theory with the cut-off length shown in the examination, the dominant self-energy is the quadratic term of the Higgs field at a quantum level (classical self-energies are reduced to logarithmic forms by quantum corrections). The cut-off length is then determined to reproduce today's tiny value of Lambda for vacuum energy. Additionally, a field with nonperiodic vanishing boundary conditions is treated, showing that the field has no zero-point energy.

On integrability of the Killing equation

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

Numeric Solutions of Dirac-Gursey Spinor Field Equation Under External Gaussian White Noise

NASA Astrophysics Data System (ADS)

Aydogmus, Fatma

2016-06-01

In this paper, we consider the Dirac-Gursey spinor field equation that has particle-like solutions derived classical field equations so-called instantons, formed by using Heisenberg ansatz, under the effect of an additional Gaussian white noise term. Our purpose is to understand how the behavior of spinor-type excited instantons in four dimensions can be affected by noise. Thus, we simulate the phase portraits and Poincaré sections of the obtained system numerically both with and without noise. Recurrence plots are also given for more detailed information regarding the system.

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

NASA Astrophysics Data System (ADS)

Austin, Rickey W.

In Einstein's theory of Special Relativity (SR), one method to derive relativistic kinetic energy is via applying the classical work-energy theorem to relativistic momentum. This approach starts with a classical based work-energy theorem and applies SR's momentum to the derivation. One outcome of this derivation is relativistic kinetic energy. From this derivation, it is rather straight forward to form a kinetic energy based time dilation function. In the derivation of General Relativity a common approach is to bypass classical laws as a starting point. Instead a rigorous development of differential geometry and Riemannian space is constructed, from which classical based laws are derived. This is in contrast to SR's approach of starting with classical laws and applying the consequences of the universal speed of light by all observers. A possible method to derive time dilation due to Newtonian gravitational potential energy (NGPE) is to apply SR's approach to deriving relativistic kinetic energy. It will be shown this method gives a first order accuracy compared to Schwarzschild's metric. The SR's kinetic energy and the newly derived NGPE derivation are combined to form a Riemannian metric based on these two energies. A geodesic is derived and calculations compared to Schwarzschild's geodesic for an orbiting test mass about a central, non-rotating, non-charged massive body. The new metric results in high accuracy calculations when compared to Einsteins General Relativity's prediction. The new method provides a candidate approach for starting with classical laws and deriving General Relativity effects. This approach mimics SR's method of starting with classical mechanics when deriving relativistic equations. As a compliment to introducing General Relativity, it provides a plausible scaffolding method from classical physics when teaching introductory General Relativity. A straight forward path from classical laws to General Relativity will be derived. This derivation provides a minimum first order accuracy to Schwarzschild's solution to Einstein's field equations.

Axion as a cold dark matter candidate: analysis to third order perturbation for classical axion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noh, Hyerim; Hwang, Jai-chan; Park, Chan-Gyung, E-mail: hr@kasi.re.kr, E-mail: jchan@knu.ac.kr, E-mail: park.chan.gyung@gmail.com

2015-12-01

We investigate aspects of axion as a coherently oscillating massive classical scalar field by analyzing third order perturbations in Einstein's gravity in the axion-comoving gauge. The axion fluid has its characteristic pressure term leading to an axion Jeans scale which is cosmologically negligible for a canonical axion mass. Our classically derived axion pressure term in Einstein's gravity is identical to the one derived in the non-relativistic quantum mechanical context in the literature. We present the general relativistic continuity and Euler equations for an axion fluid valid up to third order perturbation. Equations for axion are exactly the same as thatmore » of a zero-pressure fluid in Einstein's gravity except for an axion pressure term in the Euler equation. Our analysis includes the cosmological constant.« less

A functional equation for the specular reflection of rays.

PubMed

Le Bot, A

2002-10-01

This paper aims to generalize the "radiosity method" when applied to specular reflection. Within the field of thermics, the radiosity method is also called the "standard procedure." The integral equation for incident energy, which is usually derived for diffuse reflection, is replaced by a more appropriate functional equation. The latter is used to solve some specific problems and it is shown that all the classical features of specular reflection, for example, the existence of image sources, are embodied within this equation. This equation can be solved with the ray-tracing technique, despite the implemented mathematics being quite different. Several interesting features of the energy field are presented.

Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koke, Christian, E-mail: christian.koke@stud.uni-heidelberg.de; Noh, Changsuk, E-mail: changsuk@kias.re.kr; Angelakis, Dimitris G., E-mail: dimitris.angelakis@gmail.com

When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogicalmore » introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.« less

On the self-force in Bopp-Podolsky electrodynamics

NASA Astrophysics Data System (ADS)

Gratus, Jonathan; Perlick, Volker; Tucker, Robin W.

2015-10-01

In the classical vacuum Maxwell-Lorentz theory the self-force of a charged point particle is infinite. This makes classical mass renormalization necessary and, in the special relativistic domain, leads to the Abraham-Lorentz-Dirac equation of motion possessing unphysical run-away and pre-acceleration solutions. In this paper we investigate whether the higher-order modification of classical vacuum electrodynamics suggested by Bopp, Landé, Thomas and Podolsky in the 1940s, can provide a solution to this problem. Since the theory is linear, Green-function techniques enable one to write the field of a charged point particle on Minkowski spacetime as an integral over the particle’s history. By introducing the notion of timelike worldlines that are ‘bounded away from the backward light-cone’ we are able to prescribe criteria for the convergence of such integrals. We also exhibit a timelike worldline yielding singular fields on a lightlike hyperplane in spacetime. In this case the field is mildly singular at the event where the particle crosses the hyperplane. Even in the case when the Bopp-Podolsky field is bounded, it exhibits a directional discontinuity as one approaches the point particle. We describe a procedure for assigning a value to the field on the particle worldline which enables one to define a finite Lorentz self-force. This is explicitly derived leading to an integro-differential equation for the motion of the particle in an external electromagnetic field. We conclude that any worldline solutions to this equation belonging to the categories discussed in the paper have continuous four-velocities.

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

Pressure and Chemical Potential: Effects Hydrophilic Soils Have on Adsorption and Transport

NASA Astrophysics Data System (ADS)

Bennethum, L. S.; Weinstein, T.

2003-12-01

Using the assumption that thermodynamic properties of fluid is affected by its proximity to the solid phase, a theoretical model has been developed based on upscaling and fundamental thermodynamic principles (termed Hybrid Mixture Theory). The theory indicates that Darcy's law and the Darcy-scale chemical potential (which determines the rate of adsorption and diffusion) need to be modified in order to apply to soils containing hydrophilic soils. In this talk we examine the Darcy-scale definition of pressure and chemical potential, especially as it applies to hydrophilic soils. To arrive at our model, we used hybrid mixture theory - first pioneered by Hassanizadeh and Gray in 1979. The technique involves averaging the field equations (i.e. conservation of mass, momentum balance, energy balance, etc.) to obtain macroscopic field equations, where each field variable is defined precisely in terms of its microscale counterpart. To close the system consistently with classical thermodynamics, the entropy inequality is exploited in the sense of Coleman and Noll. With the exceptions that the macroscale field variables are defined precisely in terms of their microscale counterparts and that microscopic interfacial equations can also be treated in a similar manner, the resulting system of equations is consistent with those derived using classical mixture theory. Hence the terminology, Hybrid Mixture Theory.

The effect of air flow, panel curvature, and internal pressurization on field-incidence transmission loss. [acoustic propagation through aircraft fuselage

NASA Technical Reports Server (NTRS)

Koval, L. R.

1975-01-01

In the context of sound transmission through aircraft fuselage panels, equations for the field-incidence transmission loss (TL) of a single-walled panel are derived that include the effects of external air flow, panel curvature, and internal fuselage pressurization. These effects are incorporated into the classical equations for the TL of single panels, and the resulting double integral for field-incidence TL is numerically evaluated for a specific set of parameters.

Tree-level correlations in the strong field regime

NASA Astrophysics Data System (ADS)

Gelis, François

2017-09-01

We consider the correlation function of an arbitrary number of local observables in quantum field theory, in situations where the field amplitude is large. Using a quasi-classical approximation (valid for a highly occupied initial mixed state, or for a coherent initial state if the classical dynamics has instabilities), we show that at tree level these correlations are dominated by fluctuations at the initial time. We obtain a general expression of the correlation functions in terms of the classical solution of the field equation of motion and its derivatives with respect to its initial conditions, that can be arranged graphically as the sum of labeled trees where the nodes are the individual observables, and the links are pairs of derivatives acting on them. For 3-point (and higher) correlation functions, there are additional tree-level terms beyond the quasi-classical approximation, generated by fluctuations in the bulk.

Multiscale modeling and computation of optically manipulated nano devices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bao, Gang, E-mail: baog@zju.edu.cn; Liu, Di, E-mail: richardl@math.msu.edu; Luo, Songting, E-mail: luos@iastate.edu

2016-07-01

We present a multiscale modeling and computational scheme for optical-mechanical responses of nanostructures. The multi-physical nature of the problem is a result of the interaction between the electromagnetic (EM) field, the molecular motion, and the electronic excitation. To balance accuracy and complexity, we adopt the semi-classical approach that the EM field is described classically by the Maxwell equations, and the charged particles follow the Schrödinger equations quantum mechanically. To overcome the numerical challenge of solving the high dimensional multi-component many-body Schrödinger equations, we further simplify the model with the Ehrenfest molecular dynamics to determine the motion of the nuclei, andmore » use the Time-Dependent Current Density Functional Theory (TD-CDFT) to calculate the excitation of the electrons. This leads to a system of coupled equations that computes the electromagnetic field, the nuclear positions, and the electronic current and charge densities simultaneously. In the regime of linear responses, the resonant frequencies initiating the out-of-equilibrium optical-mechanical responses can be formulated as an eigenvalue problem. A self-consistent multiscale method is designed to deal with the well separated space scales. The isomerization of azobenzene is presented as a numerical example.« less

Ultrasonic waves in classical gases

NASA Astrophysics Data System (ADS)

Magner, A. G.; Gorenstein, M. I.; Grygoriev, U. V.

2017-12-01

The velocity and absorption coefficient for the plane sound waves in a classical gas are obtained by solving the Boltzmann kinetic equation, which describes the reaction of the single-particle distribution function to a periodic external field. Within the linear response theory, the nonperturbative dispersion equation valid for all sound frequencies is derived and solved numerically. The results are in agreement with the approximate analytical solutions found for both the frequent- and rare-collision regimes. These results are also in qualitative agreement with the experimental data for ultrasonic waves in dilute gases.

The Initial Flow of Classical Gluon Fields in Heavy Ion Collisions

NASA Astrophysics Data System (ADS)

Fries, Rainer J.; Chen, Guangyao

2015-03-01

Using analytic solutions of the Yang-Mills equations we calculate the initial flow of energy of the classical gluon field created in collisions of large nuclei at high energies. We find radial and elliptic flow which follows gradients in the initial energy density, similar to a simple hydrodynamic behavior. In addition we find a rapidity-odd transverse flow field which implies the presence of angular momentum and should lead to directed flow in final particle spectra. We trace those energy flow terms to transverse fields from the non-abelian generalization of Gauss' Law and Ampere's and Faraday's Laws.

Symmetric solitonic excitations of the (1 + 1)-dimensional Abelian-Higgs classical vacuum.

PubMed

Diakonos, F K; Katsimiga, G C; Maintas, X N; Tsagkarakis, C E

2015-02-01

We study the classical dynamics of the Abelian-Higgs model in (1 + 1) space-time dimensions for the case of strongly broken gauge symmetry. In this limit the wells of the potential are almost harmonic and sufficiently deep, presenting a scenario far from the associated critical point. Using a multiscale perturbation expansion, the equations of motion for the fields are reduced to a system of coupled nonlinear Schrödinger equations. Exact solutions of the latter are used to obtain approximate analytical solutions for the full dynamics of both the gauge and Higgs field in the form of oscillons and oscillating kinks. Numerical simulations of the exact dynamics verify the validity of these solutions. We explore their persistence for a wide range of the model's single parameter, which is the ratio of the Higgs mass (m(H)) to the gauge-field mass (m(A)). We show that only oscillons oscillating symmetrically with respect to the "classical vacuum," for both the gauge and the Higgs field, are long lived. Furthermore, plane waves and oscillating kinks are shown to decay into oscillon-like patterns, due to the modulation instability mechanism.

Kinetic theory molecular dynamics and hot dense matter: theoretical foundations.

PubMed

Graziani, F R; Bauer, J D; Murillo, M S

2014-09-01

Electrons are weakly coupled in hot, dense matter that is created in high-energy-density experiments. They are also mildly quantum mechanical and the ions associated with them are classical and may be strongly coupled. In addition, the dynamical evolution of plasmas under these hot, dense matter conditions involve a variety of transport and energy exchange processes. Quantum kinetic theory is an ideal tool for treating the electrons but it is not adequate for treating the ions. Molecular dynamics is perfectly suited to describe the classical, strongly coupled ions but not the electrons. We develop a method that combines a Wigner kinetic treatment of the electrons with classical molecular dynamics for the ions. We refer to this hybrid method as "kinetic theory molecular dynamics," or KTMD. The purpose of this paper is to derive KTMD from first principles and place it on a firm theoretical foundation. The framework that KTMD provides for simulating plasmas in the hot, dense regime is particularly useful since current computational methods are generally limited by their inability to treat the dynamical quantum evolution of the electronic component. Using the N-body von Neumann equation for the electron-proton plasma, three variations of KTMD are obtained. Each variant is determined by the physical state of the plasma (e.g., collisional versus collisionless). The first variant of KTMD yields a closed set of equations consisting of a mean-field quantum kinetic equation for the electron one-particle distribution function coupled to a classical Liouville equation for the protons. The latter equation includes both proton-proton Coulombic interactions and an effective electron-proton interaction that involves the convolution of the electron density with the electron-proton Coulomb potential. The mean-field approach is then extended to incorporate equilibrium electron-proton correlations through the Singwi-Tosi-Land-Sjolander (STLS) ansatz. This is the second variant of KTMD. The STLS contribution produces an effective electron-proton interaction that involves the electron-proton structure factor, thereby extending the usual mean-field theory to correlated but near equilibrium systems. Finally, a third variant of KTMD is derived. It includes dynamical electrons and their correlations coupled to a MD description for the ions. A set of coupled equations for the one-particle electron Wigner function and the electron-electron and electron-proton correlation functions are coupled to a classical Liouville equation for the protons. This latter variation has both time and momentum dependent correlations.

Tsallis’ quantum q-fields

NASA Astrophysics Data System (ADS)

Plastino, A.; Rocca, M. C.

2018-05-01

We generalize several well known quantum equations to a Tsallis’ q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schródinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601 (2011), EPL 118, 61004 (2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle. These q-fields are meaningful at very high energies (TeV scale) for q = 1.15, high energies (GeV scale) for q = 1.001, and low energies (MeV scale) for q = 1.000001 [Nucl. Phys. A 955 (2016) 16 and references therein]. (See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields’ logarithms.

Quantum spatial propagation of squeezed light in a degenerate parametric amplifier

NASA Technical Reports Server (NTRS)

Deutsch, Ivan H.; Garrison, John C.

1992-01-01

Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.

Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

NASA Astrophysics Data System (ADS)

Karagiorgos, A.; Pailas, T.; Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.

2018-03-01

We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.

Quantization and Quantum-Like Phenomena: A Number Amplitude Approach

NASA Astrophysics Data System (ADS)

Robinson, T. R.; Haven, E.

2015-12-01

Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.

Cascading and local-field effects in non-linear optics revisited: a quantum-field picture based on exchange of photons.

PubMed

Bennett, Kochise; Mukamel, Shaul

2014-01-28

The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N(2).

Time evolution of linearized gauge field fluctuations on a real-time lattice

NASA Astrophysics Data System (ADS)

Kurkela, A.; Lappi, T.; Peuron, J.

2016-12-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss' law.

Quantum localization of classical mechanics

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.

2016-07-01

Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.

Potential theory of radiation

NASA Technical Reports Server (NTRS)

Chiu, Huei-Huang

1989-01-01

A theoretical method is being developed by which the structure of a radiation field can be predicted by a radiation potential theory, similar to a classical potential theory. The introduction of a scalar potential is justified on the grounds that the spectral intensity vector is irrotational. The vector is also solenoidal in the limits of a radiation field in complete radiative equilibrium or in a vacuum. This method provides an exact, elliptic type equation that will upgrade the accuracy and the efficiency of the current CFD programs required for the prediction of radiation and flow fields. A number of interesting results emerge from the present study. First, a steady state radiation field exhibits an optically modulated inverse square law distribution character. Secondly, the unsteady radiation field is structured with two conjugate scalar potentials. Each is governed by a Klein-Gordon equation with a frictional force and a restoring force. This steady potential field structure and the propagation of radiation potentials are consistent with the well known results of classical electromagnetic theory. The extension of the radiation potential theory for spray combustion and hypersonic flow is also recommended.

Scalar field as a Bose-Einstein condensate?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Castellanos, Elías; Escamilla-Rivera, Celia; Macías, Alfredo

We discuss the analogy between a classical scalar field with a self-interacting potential, in a curved spacetime described by a quasi-bounded state, and a trapped Bose-Einstein condensate. In this context, we compare the Klein-Gordon equation with the Gross-Pitaevskii equation. Moreover, the introduction of a curved background spacetime endows, in a natural way, an equivalence to the Gross-Pitaevskii equation with an explicit confinement potential. The curvature also induces a position dependent self-interaction parameter. We exploit this analogy by means of the Thomas-Fermi approximation, commonly used to describe the Bose-Einstein condensate, in order to analyze the quasi bound scalar field distribution surroundingmore » a black hole.« less

Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

NASA Astrophysics Data System (ADS)

Colmenares, Pedro J.

2018-05-01

This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.

Basic results on the equations of magnetohydrodynamics of partially ionized inviscid plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nunez, Manuel

2009-10-15

The equations of evolution of partially ionized plasmas have been far more studied in one of their many simplifications than in its original form. They present a relation between the velocity of each species, plus the magnetic and electric fields, which yield as an analog of Ohm's law a certain elliptic equation. Therefore, the equations represent a functional evolution system, not a classical one. Nonetheless, a priori estimates and theorems of existence may be obtained in appropriate Sobolev spaces.

Mean-field approximation for spacing distribution functions in classical systems

NASA Astrophysics Data System (ADS)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

Non-classical and potential symmetry analysis of Richard's equation for moisture flow in soil

NASA Astrophysics Data System (ADS)

Wiltshire, Ron; El-Kafri, Manal

2004-01-01

This paper focuses upon the derivation of the non-classical symmetries of Bluman and Cole as they apply to Richard's equation for water flow in an unsaturated uniform soil. It is shown that the determining equations for the non-classical case lead to four highly non-linear equations which have been solved in five particular cases. In each case the corresponding similarity ansatz has been derived and Richard's equation is reduced to an ordinary differential equation. Explicit solutions are produced when possible. Richard's equation is also expressed as a potential system and in reviewing the classical Lie solutions a new symmetry is derived together with its similarity ansatz. Determining equations are then produced for the potential system using the non-classical algorithm. This results in an under-determined set of equations and an example symmetry that reveals a missing classical case is presented. An example of a classical and a non-classical symmetry reduction applied to the infiltration of moisture in soil is presented. The condition for surface invariance is used to demonstrate the equivalence of a classical Lie and a potential symmetry.

Magnetic Bianchi type II string cosmological model in loop quantum cosmology

NASA Astrophysics Data System (ADS)

Rikhvitsky, Victor; Saha, Bijan; Visinescu, Mihai

2014-07-01

The loop quantum cosmology of the Bianchi type II string cosmological model in the presence of a homogeneous magnetic field is studied. We present the effective equations which provide modifications to the classical equations of motion due to quantum effects. The numerical simulations confirm that the big bang singularity is resolved by quantum gravity effects.

Force, torque, linear momentum, and angular momentum in classical electr odynamics

NASA Astrophysics Data System (ADS)

Mansuripur, Masud

2017-10-01

The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic (EM) field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and by the Lorentz force law. Whereas Maxwell's equations relate the fields to their material sources, Poynting's theorem governs the flow of EM energy and its exchange between fields and material media, while the Lorentz law regulates the back-and-forth transfer of momentum between the media and the fields. An alternative force law, first proposed by Einstein and Laub, exists that is consistent with Maxwell's equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetized medium, the Einstein-Laub (E-L) formulation of EM force and torque does not invoke hidden entities under such circumstances. Moreover, total force/torque exerted by EM fields on any given object turns out to be independent of whether the density of force/torque is evaluated using the law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions inside matter. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.

Scalar/Vector potential formulation for compressible viscous unsteady flows

NASA Technical Reports Server (NTRS)

Morino, L.

1985-01-01

A scalar/vector potential formulation for unsteady viscous compressible flows is presented. The scalar/vector potential formulation is based on the classical Helmholtz decomposition of any vector field into the sum of an irrotational and a solenoidal field. The formulation is derived from fundamental principles of mechanics and thermodynamics. The governing equations for the scalar potential and vector potential are obtained, without restrictive assumptions on either the equation of state or the constitutive relations or the stress tensor and the heat flux vector.

Transport processes in magnetically confined plasmas in the nonlinear regime.

PubMed

Sonnino, Giorgio

2006-06-01

A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.

Bose–Einstein condensates and scalar fields; exploring the similitudes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Castellanos, E.; Macías, A.; Núñez, D.

We analyze the the remarkable analogy between the classical Klein–Gordon equation for a test scalar field in a flat and also in a curved background, and the Gross–Pitaevskii equation for a Bose–Einstein condensate trapped by an external potential. We stress here that the solution associated with the Klein–Gordon equation (KG) in a flat space time has the same mathematical structure, under certain circumstances, to those obtained for the Gross–Pitaevskii equation, that is, a static soliton solution. Additionally, Thomas–Fermi approximation is applied to the 3–dimensional version of this equation, in order to calculate some thermodynamical properties of the system in curvedmore » a space–time back ground. Finally, we stress the fact that a gravitational background provides, in some cases, a kind of confining potential for the scalar field, allowing us to remarks even more the possible connection between scalar fields and the phenomenon of Bose–Einstein condensation.« less

Convective flows of generalized time-nonlocal nanofluids through a vertical rectangular channel

NASA Astrophysics Data System (ADS)

Ahmed, Najma; Vieru, Dumitru; Fetecau, Constantin; Shah, Nehad Ali

2018-05-01

Time-nonlocal generalized model of the natural convection heat transfer and nanofluid flows through a rectangular vertical channel with wall conditions of the Robin type are studied. The generalized mathematical model with time-nonlocality is developed by considering the fractional constitutive equations for the shear stress and thermal flux defined with the time-fractional Caputo derivative. The Caputo power-law non-local kernel provides the damping to the velocity and temperature gradient; therefore, transport processes are influenced by the histories at all past and present times. Analytical solutions for dimensionless velocity and temperature fields are obtained by using the Laplace transform coupled with the finite sine-cosine Fourier transform which is suitable to problems with boundary conditions of the Robin type. Particularizing the fractional thermal and velocity parameters, solutions for three simplified models are obtained (classical linear momentum equation with damped thermal flux; fractional shear stress constitutive equation with classical Fourier's law for thermal flux; classical shear stress and thermal flux constitutive equations). It is found that the thermal histories strongly influence the thermal transport for small values of time t. Also, the thermal transport can be enhanced if the thermal fractional parameter decreases or by increasing the nanoparticles' volume fraction. The velocity field is influenced on the one hand by the temperature of the fluid and on the other by the damping of the velocity gradient introduced by the fractional derivative. Also, the transport motions of the channel walls influence the motion of the fluid layers located near them.

The Reliability and Precision of Total Scores and IRT Estimates as a Function of Polytomous IRT Parameters and Latent Trait Distribution

ERIC Educational Resources Information Center

Culpepper, Steven Andrew

2013-01-01

A classic topic in the fields of psychometrics and measurement has been the impact of the number of scale categories on test score reliability. This study builds on previous research by further articulating the relationship between item response theory (IRT) and classical test theory (CTT). Equations are presented for comparing the reliability and…

A rigorous solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Aksu, H.; Spehert, T.

1975-01-01

A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.

Quantum-mechanical transport equation for atomic systems.

NASA Technical Reports Server (NTRS)

Berman, P. R.

1972-01-01

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

The quantum realm of the ''Little Sibling'' of the Big Rip singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Albarran, Imanol; Bouhmadi-López, Mariam; Cabral, Francisco

We analyse the quantum behaviour of the ''Little Sibling'' of the Big Rip singularity (LSBR) [1]. The quantisation is carried within the geometrodynamical approach given by the Wheeler-DeWitt (WDW) equation. The classical model is based on a Friedmann-Lemaître-Robertson-Walker Universe filled by a perfect fluid that can be mapped to a scalar field with phantom character. We analyse the WDW equation in two setups. In the first step, we consider the scale factor as the single degree of freedom, which from a classical perspective parametrises both the geometry and the matter content given by the perfect fluid. We then solve themore » WDW equation within a WKB approximation, for two factor ordering choices. On the second approach, we consider the WDW equation with two degrees of freedom: the scale factor and a scalar field. We solve the WDW equation, with the Laplace-Beltrami factor-ordering, using a Born-Oppenheimer approximation. In both approaches, we impose the DeWitt (DW) condition as a potential criterion for singularity avoidance. We conclude that in all the cases analysed the DW condition can be verified, which might be an indication that the LSBR can be avoided or smoothed in the quantum approach.« less

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.

Hamiltonian approach to GR - Part 1: covariant theory of classical gravity

NASA Astrophysics Data System (ADS)

Cremaschini, Claudio; Tessarotto, Massimo

2017-05-01

A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor \\widehat{g}(r)≡ { \\widehat{g}_{μ ν }(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields x≡ { g,π } obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations.

Effective dynamics of a classical point charge

DOE Office of Scientific and Technical Information (OSTI.GOV)

Polonyi, Janos, E-mail: polonyi@iphc.cnrs.fr

2014-03-15

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-polemore » of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out. -- Highlights: •Extension of the classical action principle for dissipative systems. •New derivation of the Abraham–Lorentz force for a point charge. •Absence of a runaway solution of the Abraham–Lorentz force. •Acausality in classical electrodynamics. •Renormalization of classical electrodynamics of point charges.« less

Mixed Quantum/Classical Theory for Molecule-Molecule Inelastic Scattering: Derivations of Equations and Application to N2 + H2 System.

PubMed

Semenov, Alexander; Babikov, Dmitri

2015-12-17

The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward.

Mean-field approximation for spacing distribution functions in classical systems.

PubMed

González, Diego Luis; Pimpinelli, Alberto; Einstein, T L

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed. © 2012 American Physical Society

Modifiying shallow-water equations as a model for wave-vortex turbulence

NASA Astrophysics Data System (ADS)

Mohanan, A. V.; Augier, P.; Lindborg, E.

2017-12-01

The one-layer shallow-water equations is a simple two-dimensional model to study the complex dynamics of the oceans and the atmosphere. We carry out forced-dissipative numerical simulations, either by forcing medium-scale wave modes, or by injecting available potential energy (APE). With pure wave forcing in non-rotating cases, a statistically stationary regime is obtained for a range of forcing Froude numbers Ff = ɛ /(kf c), where ɛ is the energy dissipation rate, kf the forcing wavenumber and c the wave speed. Interestingly, the spectra scale as k-2 and third and higher order structure functions scale as r. Such statistics is a manifestation of shock turbulence or Burgulence, which dominate the flow. Rotating cases exhibit some inverse energy cascade, along with a stronger forward energy cascade, dominated by wave-wave interactions. We also propose two modifications to the classical shallow-water equations to construct a toy model. The properties of the model are explored by forcing in APE at a small and a medium wavenumber. The toy model simulations are then compared with results from shallow-water equations and a full General Circulation Model (GCM) simulation. The most distinctive feature of this model is that, unlike shallow-water equations, it avoids shocks and conserves quadratic energy. In Fig. 1, for the shallow-water equations, shocks appear as thin dark lines in the divergence (∇ .{u}) field, and as discontinuities in potential temperature (θ ) field; whereas only waves appear in the corresponding fields from toy model simulation. Forward energy cascade results in a wave field with k-5/3 spectrum, along with equipartition of KE and APE at small scales. The vortical field develops into a k-3 spectrum. With medium forcing wavenumber, at large scales, energy converted from APE to KE undergoes inverse cascade as a result of nonlinear fluxes composed of vortical modes alone. Gradually, coherent vortices emerge with a strong preference for anticyclonic motion. The model can serve as a closer representation of real geophysical turbulence than the classical shallow-water equations. Fig 1. Divergence and potential temperature fields of shallow-water (top row) and toy model (bottom row) simulations.

Analogy between electromagnetic potentials and wave-like dynamic variables with connections to quantum theory

NASA Astrophysics Data System (ADS)

Yang, Chen

2018-05-01

The transitions from classical theories to quantum theories have attracted many interests. This paper demonstrates the analogy between the electromagnetic potentials and wave-like dynamic variables with their connections to quantum theory for audiences at advanced undergraduate level and above. In the first part, the counterpart relations in the classical electrodynamics (e.g. gauge transform and Lorenz condition) and classical mechanics (e.g. Legendre transform and free particle condition) are presented. These relations lead to similar governing equations of the field variables and dynamic variables. The Lorenz gauge, scalar potential and vector potential manifest a one-to-one similarity to the action, Hamiltonian and momentum, respectively. In the second part, the connections between the classical pictures of electromagnetic field and particle to quantum picture are presented. By characterising the states of electromagnetic field and particle via their (corresponding) variables, their evolution pictures manifest the same algebraic structure (isomorphic). Subsequently, pictures of the electromagnetic field and particle are compared to the quantum picture and their interconnections are given. A brief summary of the obtained results are presented at the end of the paper.

Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ho, Choon-Lin, E-mail: hcl@mail.tku.edu.tw

2011-04-15

Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it ismore » also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.« less

On One Possible Generalization of the Regression Theorem

NASA Astrophysics Data System (ADS)

Bogolubov, N. N.; Soldatov, A. V.

2018-03-01

A general approach to derivation of formally exact closed time-local or time-nonlocal evolution equations for non-equilibrium multi-time correlations functions made of observables of an open quantum system interacting simultaneously with external time-dependent classical fields and dissipative environment is discussed. The approach allows for the subsequent treatment of these equations within a perturbative scheme assuming that the system-environment interaction is weak.

A note on powers in finite fields

NASA Astrophysics Data System (ADS)

Aabrandt, Andreas; Lundsgaard Hansen, Vagn

2016-08-01

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom.

Model for Ultrafast Carrier Scattering in Semiconductors

DTIC Science & Technology

2012-11-14

energy transfer between semi-classical carrier drift-diffusion under an electric field and quantum kinetics of interband /intersubband transitions...from an electron during each phonon-emission event. The net rate of phonon emission is determined by the Boltzmann scattering equation which depends ...energy-drift term under a strong dc field was demonstrated to reduce the field- dependent drift velocity and mobility. The Doppler shift in the energy

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

NASA Astrophysics Data System (ADS)

Rivera, R.; Villarroel, D.

2002-10-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

Electromagnetic potential vectors and the Lagrangian of a charged particle

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

Maxwell's equations can be shown to imply the existence of two independent three-dimensional potential vectors. A comparison between the potential vectors and the electric and magnetic field vectors, using a spatial Fourier transformation, reveals six independent potential components but only four independent electromagnetic field components for each mode. Although the electromagnetic fields determined by Maxwell's equations give a complete description of all possible classical electromagnetic phenomena, potential vectors contains more information and allow for a description of such quantum mechanical phenomena as the Aharonov-Bohm effect. A new result is that a charged particle Lagrangian written in terms of potential vectors automatically contains a 'spontaneous symmetry breaking' potential.

Dipole Relaxation in an Electric Field.

ERIC Educational Resources Information Center

Neumann, Richard M.

1980-01-01

Derives an expression for the orientational entropy of a rigid rod (electric dipole) from Boltzmann's equation. Subsequent application of Newton's second law of motion produces Debye's classical expression for the relaxation of an electric dipole in a viscous medium. (Author/GS)

Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Tsung-Wei; Chiou, Dah-Wei; Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 106, Taiwan

The classical dynamics for a charged point particle with intrinsic spin is governed by a relativistic Hamiltonian for the orbital motion and by the Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is natural to ask whether the classical Hamiltonian (with both the orbital and spin parts) is consistent with that in the relativistic quantum theory for a spin-1/2 charged particle, which is described by the Dirac equation. In the low-energy limit, up to terms of the seventh order in 1/E{sub g} (E{sub g}=2mc{sup 2} and m is the particle mass), we investigate the Foldy-Wouthuysen (FW) transformation of themore » Dirac Hamiltonian in the presence of homogeneous and static electromagnetic fields and show that it is indeed in agreement with the classical Hamiltonian with the gyromagnetic ratio being equal to 2. Through electromagnetic duality, this result can be generalized for a spin-1/2 dyon, which has both electric and magnetic charges and thus possesses both intrinsic electric and magnetic dipole moments. Furthermore, the relativistic quantum theory for a spin-1/2 dyon with arbitrary values of the gyromagnetic and gyroelectric ratios can be described by the Dirac-Pauli equation, which is the Dirac equation with augmentation for the anomalous electric and anomalous magnetic dipole moments. The FW transformation of the Dirac-Pauli Hamiltonian is shown, up to the seventh-order again, to be in accord with the classical Hamiltonian as well.« less

Theorem: A Static Magnetic N-pole Becomes an Oscillating Electric N-pole in a Cosmic Axion Field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hill, Christopher T.

We show for the classical Maxwell equations, including the axion electromagnetic anomaly source term, that a cosmic axion field induces an oscillating electric N-moment for any static magnetic N-moment. This is a straightforward result, accessible to anyone who has taken a first year graduate course in electrodynamics.

Analytical and numerical solutions of the equation for the beam propagation in a photovoltaic-photorefractive media

NASA Astrophysics Data System (ADS)

Lin, Ji; Wang, Hou

2013-07-01

We use the classical Lie-group method to study the evolution equation describing a photovoltaic-photorefractive media with the effects of diffusion process and the external electric field. We reduce it to some similarity equations firstly, and then obtain some analytically exact solutions including the soliton solution, the exponential solution and the oscillatory solution. We also obtain the numeric solitons from these similarity equations. Moreover, We show theoretically that these solutions have two types of trajectories. One type is a straight line. The other is a parabolic curve, which indicates these solitons have self-deflection.

Quark and gluon production from a boost-invariantly expanding color electric field

NASA Astrophysics Data System (ADS)

Taya, Hidetoshi

2017-07-01

Particle production from an expanding classical color electromagnetic field is extensively studied, motivated by the early stage dynamics of ultrarelativistic heavy ion collisions. We develop a formalism at one-loop order to compute the particle spectra by canonically quantizing quark, gluon, and ghost fluctuations under the presence of such an expanding classical color background field; the canonical quantization is done in the τ -η coordinates in order to take into account manifestly the expanding geometry. As a demonstration, we model the expanding classical color background field by a boost-invariantly expanding homogeneous color electric field with lifetime T , for which we obtain analytically the quark and gluon production spectra by solving the equations of motion of QCD nonperturbatively with respect to the color electric field. In this paper we study (i) the finite lifetime effect, which is found to modify significantly the particle spectra from those expected from the Schwinger formula; (ii) the difference between the quark and gluon production; and (iii) the quark mass dependence of the production spectra. Implications of these results to ultrarelativistic heavy ion collisions are also discussed.

Simulation of the effects of sub-breakdown electric fields on the chemical kinetics in nonpremixed counterflow methane/air flames

NASA Astrophysics Data System (ADS)

Belhi, Memdouh; Im, Hong; Computational Reacting Flows Laboratory, Clean Combustion Research Center Team

2017-11-01

The effects of an electric field on the combustion kinetics in nonpremixed counterflow methane/air flames were investigated via one-dimensional numerical simulations. A classical fluid model coupling Poison's equation with transport equations for combustion species and electric field-induced particles was used. A methane-air reaction mechanism accounting for the natural ionization in flames was combined with a set of reactions that describe the formation of active particles induced by the electric field. Kinetic parameters for electron-impact reactions and transport coefficients of electrons were modeled as functions of reduced electric field via solutions to the Boltzmann kinetic equation using the BOLSIG code. Mobility of ions was computed based on the (n,6,4) and coulomb interaction potentials, while the diffusion coefficient was approximated from the mobility using Einstein relation. Contributions of electron dissociation, excitation and ionization processes were characterized quantitatively. An analysis to identify the plasma regime where the electric field can alter the combustion kinetic was proposed.

Semi-classical approach to compute RABBITT traces in multi-dimensional complex field distributions.

PubMed

Lucchini, M; Ludwig, A; Kasmi, L; Gallmann, L; Keller, U

2015-04-06

We present a semi-classical model to calculate RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) traces in the presence of a reference infrared field with a complex two-dimensional (2D) spatial distribution. The evolution of the electron spectra as a function of the pump-probe delay is evaluated starting from the solution of the classical equation of motion and incorporating the quantum phase acquired by the electron during the interaction with the infrared field. The total response to an attosecond pulse train is then evaluated by a coherent sum of the contributions generated by each individual attosecond pulse in the train. The flexibility of this model makes it possible to calculate spectrograms from non-trivial 2D field distributions. After confirming the validity of the model in a simple 1D case, we extend the discussion to describe the probe-induced phase in photo-emission experiments on an ideal metallic surface.

Dissipative tunnelling by means of scaled trajectories

NASA Astrophysics Data System (ADS)

Mousavi, S. V.; Miret-Artés, S.

2018-06-01

Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schrödinger-Langevin or Kostin quantum-classical transition wave equation is used and applied resulting in a scaled differential equation of motion. A Gaussian wave packet solution to the resulting scaled Kostin nonlinear equation is assumed and compared to the same solution for the scaled linear Caldirola-Kanai equation. The resulting scaled trajectories are obtained at different dynamical regimes and friction cases, showing the gradual decoherence process in this open dynamics. Theoretical results show that the transmission probabilities are always higher in the Kostin approach than in the Caldirola-Kanai approach in the presence or not of an external electric field. This discrepancy should be understood due to the presence of an environment since the corresponding open dynamics should be governed by nonlinear quantum equations, whereas the second approach is issued from an effective Hamiltonian within a linear theory.

Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zampeli, Adamantia; Pailas, Theodoros; Terzis, Petros A.

2016-05-01

In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries onmore » the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.« less

Loop quantum cosmology of Bianchi IX: effective dynamics

NASA Astrophysics Data System (ADS)

Corichi, Alejandro; Montoya, Edison

2017-03-01

We study solutions to the effective equations for the Bianchi IX class of spacetimes within loop quantum cosmology (LQC). We consider Bianchi IX models whose matter content is a massless scalar field, by numerically solving the loop quantum cosmology effective equations, with and without inverse triad corrections. The solutions are classified using certain geometrically motivated classical observables. We show that both effective theories—with lapse N  =  V and N  =  1—resolve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the positive spatial curvature, there is an infinite number of bounces and recollapses. We study the limit of large field momentum and show that both effective theories reproduce the same dynamics, thus recovering general relativity. We implement a procedure to identify amongst the Bianchi IX solutions, those that behave like k  =  0,1 FLRW as well as Bianchi I, II, and VII0 models. The effective solutions exhibit Bianchi I phases with Bianchi II transitions and also Bianchi VII0 phases, which had not been studied before. We comment on the possible implications of these results for a quantum modification to the classical BKL behaviour.

A family of nonlinear Schrödinger equations admitting q-plane wave solutions

NASA Astrophysics Data System (ADS)

Nobre, F. D.; Plastino, A. R.

2017-08-01

Nonlinear Schrödinger equations with power-law nonlinearities have attracted considerable attention recently. Two previous proposals for these types of equations, corresponding respectively to the Gross-Pitaievsky equation and to the one associated with nonextensive statistical mechanics, are here unified into a single, parameterized family of nonlinear Schrödinger equations. Power-law nonlinear terms characterized by exponents depending on a real index q, typical of nonextensive statistical mechanics, are considered in such a way that the Gross-Pitaievsky equation is recovered in the limit q → 1. A classical field theory shows that, due to these nonlinearities, an extra field Φ (x → , t) (besides the usual one Ψ (x → , t)) must be introduced for consistency. The new field can be identified with Ψ* (x → , t) only when q → 1. For q ≠ 1 one has a pair of coupled nonlinear wave equations governing the joint evolution of the complex valued fields Ψ (x → , t) and Φ (x → , t). These equations reduce to the usual pair of complex-conjugate ones only in the q → 1 limit. Interestingly, the nonlinear equations obeyed by Ψ (x → , t) and Φ (x → , t) exhibit a common, soliton-like, traveling solution, which is expressible in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics.

Stellar Equilibrium in Semiclassical Gravity.

PubMed

Carballo-Rubio, Raúl

2018-02-09

The phenomenon of quantum vacuum polarization in the presence of a gravitational field is well understood and is expected to have a physical reality, but studies of its backreaction on the dynamics of spacetime are practically nonexistent outside of the specific context of homogeneous cosmologies. Building on previous results of quantum field theory in curved spacetimes, in this Letter we first derive the semiclassical equations of stellar equilibrium in the s-wave Polyakov approximation. It is highlighted that incorporating the polarization of the quantum vacuum leads to a generalization of the classical Tolman-Oppenheimer-Volkoff equation. Despite the complexity of the resulting field equations, it is possible to find exact solutions. Aside from being the first known exact solutions that describe relativistic stars including the nonperturbative backreaction of semiclassical effects, these are identified as a nontrivial combination of the black star and gravastar proposals.

High-order integral equation methods for problems of scattering by bumps and cavities on half-planes.

PubMed

Pérez-Arancibia, Carlos; Bruno, Oscar P

2014-08-01

This paper presents high-order integral equation methods for the evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced in this paper apply to eight classical scattering problems, namely, scattering by a dielectric bump on a perfectly conducting or a dielectric half-plane, and scattering by a filled, overfilled, or void dielectric cavity on a perfectly conducting or a dielectric half-plane. In all cases field representations based on single-layer potentials for appropriately chosen Green functions are used. The numerical far fields and near fields exhibit excellent convergence as discretizations are refined-even at and around points where singular fields and infinite currents exist.

Induced Angular Momentum

ERIC Educational Resources Information Center

Parker, G. W.

1978-01-01

Discusses, classically and quantum mechanically, the angular momentum induced in the bound motion of an electron by an external magnetic field. Calculates the current density and its magnetic moment, and then uses two methods to solve the first-order perturbation theory equation for the required eigenfunction. (Author/GA)

Quantum propagation in single mode fiber

NASA Technical Reports Server (NTRS)

Joneckis, Lance G.; Shapiro, Jeffrey H.

1994-01-01

This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.

Non-Abelian Yang-Mills analogue of classical electromagnetic duality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chan, Hong-Mo; Faridani, J.; Tsun, T.S.

The classic question of non-Abelian Yang-Mills analogue to electromagnetic duality is examined here in a minimalist fashion at the strictly four-dimensional, classical field, and point charge level. A generalization of the Abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the Abelian theory. For example, there is a dual potential, but it is a two-indexed tensor {ital T}{sub {mu}{nu}} of the Freedman-Townsend-type. Though not itself functioning as such, {ital T}{sub {mu}{nu}} gives rise to a dual parallel transport {ital {tilde A}}{sub {mu}} for the phase of themore » wave function of the color magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard color (electric) charge itself is found to be a monpole of {ital {tilde A}}{sub {mu}}. At the same time, the gauge symmetry is found doubled from say SU({ital N}) to SU({ital N}){times}SU({ital N}). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a ``universal`` principle, namely, the Wu-Yang criterion for monpoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov.« less

1/f Noise Inside a Faraday Cage

NASA Astrophysics Data System (ADS)

Handel, Peter H.; George, Thomas F.

2009-04-01

We show that quantum 1/f noise does not have a lower frequency limit given by the lowest free electromagnetic field mode in a Faraday cage, even in an ideal cage. Indeed, quantum 1/f noise comes from the infrared-divergent coupling of the field with the charges, in their joint nonlinear system, where the charges cause the field that reacts back on the charges, and so on. This low-frequency limitation is thus not applicable for the nonlinear system of matter and field in interaction. Indeed, this nonlinear system is governed by Newton's laws, Maxwell's equations, in general also by the diffusion equations for particles and heat, or reaction kinetics given by quantum matrix elements. Nevertheless, all the other quantities can be eliminated in principle, resulting in highly nonlinear integro-differential equations for the electromagnetic field only, which no longer yield a fundamental frequency. Alternatively, we may describe this through the presence of an infinite system of subharmonics. We show how this was proven early in the classical and quantum domains, adding new insight.

Rigorous derivation of electromagnetic self-force

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gralla, Samuel E.; Harte, Abraham I.; Wald, Robert M.

2009-07-15

During the past century, there has been considerable discussion and analysis of the motion of a point charge in an external electromagnetic field in special relativity, taking into account 'self-force' effects due to the particle's own electromagnetic field. We analyze the issue of 'particle motion' in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density J{sup a}({lambda}) and stress-energy tensor T{sub ab}({lambda}) scale to zero size in an asymptotically self-similar manner about a worldline {gamma} as {lambda}{yields}0. In thismore » limit, the charge, q, and total mass, m, of the body go to zero, and q/m goes to a well-defined limit. The Maxwell field F{sub ab}({lambda}) is assumed to be the retarded solution associated with J{sup a}({lambda}) plus a homogeneous solution (the 'external field') that varies smoothly with {lambda}. We prove that the worldline {gamma} must be a solution to the Lorentz force equations of motion in the external field F{sub ab}({lambda}=0). We then obtain self-force, dipole forces, and spin force as first-order perturbative corrections to the center-of-mass motion of the body. We believe that this is the first rigorous derivation of the complete first-order correction to Lorentz force motion. We also address the issue of obtaining a self-consistent perturbative equation of motion associated with our perturbative result, and argue that the self-force equations of motion that have previously been written down in conjunction with the 'reduction of order' procedure should provide accurate equations of motion for a sufficiently small charged body with negligible dipole moments and spin. (There is no corresponding justification for the non-reduced-order equations.) We restrict consideration in this paper to classical electrodynamics in flat spacetime, but there should be no difficulty in extending our results to the motion of a charged body in an arbitrary globally hyperbolic curved spacetime.« less

Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

NASA Astrophysics Data System (ADS)

Ray, S. Saha

2018-04-01

In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.

On the theory of Brownian motion with the Alder-Wainwright effect

NASA Astrophysics Data System (ADS)

Okabe, Yasunori

1986-12-01

The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.

A Stationary One-Equation Turbulent Model with Applications in Porous Media

NASA Astrophysics Data System (ADS)

de Oliveira, H. B.; Paiva, A.

2018-06-01

A one-equation turbulent model is studied in this work in the steady-state and with homogeneous Dirichlet boundary conditions. The considered problem generalizes two distinct approaches that are being used with success in the applications to model different flows through porous media. The novelty of the problem relies on the consideration of the classical Navier-Stokes equations with a feedback forces field, whose presence in the momentum equation will affect the equation for the turbulent kinetic energy (TKE) with a new term that is known as the production and represents the rate at which TKE is transferred from the mean flow to the turbulence. By assuming suitable growth conditions on the feedback forces field and on the function that describes the rate of dissipation of the TKE, as well as on the production term, we will prove the existence of the velocity field and of the TKE. The proof of their uniqueness is made by assuming monotonicity conditions on the feedback forces field and on the turbulent dissipation function, together with a condition of Lipschitz continuity on the production term. The existence of a unique pressure, will follow by the application of a standard version of de Rham's lemma.

JOURNAL SCOPE GUIDELINES: Paper classification scheme

NASA Astrophysics Data System (ADS)

2005-06-01

This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org). 1. Statistical physics numerical and computational methods statistical mechanics, phase transitions and critical phenomena quantum condensed matter theory Bose-Einstein condensation strongly correlated electron systems exactly solvable models in statistical mechanics lattice models, random walks and combinatorics field-theoretical models in statistical mechanics disordered systems, spin glasses and neural networks nonequilibrium systems network theory 2. Chaotic and complex systems nonlinear dynamics and classical chaos fractals and multifractals quantum chaos classical and quantum transport cellular automata granular systems and self-organization pattern formation biophysical models 3. Mathematical physics combinatorics algebraic structures and number theory matrix theory classical and quantum groups, symmetry and representation theory Lie algebras, special functions and orthogonal polynomials ordinary and partial differential equations difference and functional equations integrable systems soliton theory functional analysis and operator theory inverse problems geometry, differential geometry and topology numerical approximation and analysis geometric integration computational methods 4. Quantum mechanics and quantum information theory coherent states eigenvalue problems supersymmetric quantum mechanics scattering theory relativistic quantum mechanics semiclassical approximations foundations of quantum mechanics and measurement theory entanglement and quantum nonlocality geometric phases and quantum tomography quantum tunnelling decoherence and open systems quantum cryptography, communication and computation theoretical quantum optics 5. Classical and quantum field theory quantum field theory gauge and conformal field theory quantum electrodynamics and quantum chromodynamics Casimir effect integrable field theory random matrix theory applications in field theory string theory and its developments classical field theory and electromagnetism metamaterials 6. Fluid and plasma theory turbulence fundamental plasma physics kinetic theory magnetohydrodynamics and multifluid descriptions strongly coupled plasmas one-component plasmas non-neutral plasmas astrophysical and dusty plasmas

A hybrid approach for nonlinear computational aeroacoustics predictions

NASA Astrophysics Data System (ADS)

Sassanis, Vasileios; Sescu, Adrian; Collins, Eric M.; Harris, Robert E.; Luke, Edward A.

2017-01-01

In many aeroacoustics applications involving nonlinear waves and obstructions in the far-field, approaches based on the classical acoustic analogy theory or the linearised Euler equations are unable to fully characterise the acoustic field. Therefore, computational aeroacoustics hybrid methods that incorporate nonlinear wave propagation have to be constructed. In this study, a hybrid approach coupling Navier-Stokes equations in the acoustic source region with nonlinear Euler equations in the acoustic propagation region is introduced and tested. The full Navier-Stokes equations are solved in the source region to identify the acoustic sources. The flow variables of interest are then transferred from the source region to the acoustic propagation region, where the full nonlinear Euler equations with source terms are solved. The transition between the two regions is made through a buffer zone where the flow variables are penalised via a source term added to the Euler equations. Tests were conducted on simple acoustic and vorticity disturbances, two-dimensional jets (Mach 0.9 and 2), and a three-dimensional jet (Mach 1.5), impinging on a wall. The method is proven to be effective and accurate in predicting sound pressure levels associated with the propagation of linear and nonlinear waves in the near- and far-field regions.

Star-disk interaction in Herbig Ae/Be stars

NASA Astrophysics Data System (ADS)

Speights, Christa Marie

2012-09-01

The question of the mechanism of certain types of stars is important. Classical T Tauri (CTTS) stars accrete magnetospherically, and Herbig Ae/Be stars (higher-mass analogs to CTTS) are thought to also accrete magnetospherically, but the source of a kG magnetic field is unknown, since these stars have radiative interiors. For magnetospheric accretion, an equation has been derived (Hartmann, 2001) which relates the truncation radius, stellar radius, stellar mass, mass accretion rate and magnetic field strength. Currently the magnetic field of Herbig stars is known to be somewhere between 0.1 kG and 10 kG. One goal of this research is to further constrain the magnetic field. In order to do that, I use the magnetospheric accretion equation. For CTTS, all of the variables used in the equation can be measured, so I gather this data from the literature and test the equation and find that it is consistent. Then I apply the equation to Herbig Ae stars and find that the error introduced from using random inclinations is too large to lower the current upper limit of the magnetic field range. If Herbig Ae stars are higher-mass analogs to CTTS, then they should have a similar magnetic field distribution. I compare the calculated Herbig Ae magnetic field distribution to several typical magnetic field distributions using the Kolmogorov-Smirnov test, and find that the data distribution does not match any of the distributions used. This means that Herbig Ae stars do not have well ordered kG fields like CTTS.

Scalar field quantum cosmology: A Schrödinger picture

NASA Astrophysics Data System (ADS)

Vakili, Babak

2012-11-01

We study the classical and quantum models of a scalar field Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time problem in quantum cosmology. We introduce a canonical transformation on the scalar field sector of the action such that the momentum conjugate to the new canonical variable appears linearly in the transformed Hamiltonian. Using this canonical transformation, we show that, it may lead to the identification of a time parameter for the corresponding dynamical system. In the cases of flat, closed and open FRW universes the classical cosmological solutions are obtained in terms of the introduced time parameter. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave functions in order to investigate the possible corrections to the classical cosmologies due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.

Differential Galois theory and non-integrability of planar polynomial vector fields

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo B.; Lázaro, J. Tomás; Morales-Ruiz, Juan J.; Pantazi, Chara

2018-06-01

We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular solution it is obtained a necessary condition for the existence of a rational first integral. The method is systematic starting with the first order variational equation. We illustrate this result with several families of examples. A key point is to check whether a suitable primitive is elementary or not. Using a theorem by Liouville, the problem is equivalent to the existence of a rational solution of a certain first order linear equation, the Risch equation. This is a classical problem studied by Risch in 1969, and the solution is given by the "Risch algorithm". In this way we point out the connection of the non integrability with some higher transcendent functions, like the error function.

Wave chaos in the elastic disk.

PubMed

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

Modeling the Gross-Pitaevskii Equation Using the Quantum Lattice Gas Method

NASA Astrophysics Data System (ADS)

Oganesov, Armen

We present an improved Quantum Lattice Gas (QLG) algorithm as a mesoscopic unitary perturbative representation of the mean field Gross Pitaevskii (GP) equation for Bose-Einstein Condensates (BECs). The method employs an interleaved sequence of unitary collide and stream operators. QLG is applicable to many different scalar potentials in the weak interaction regime and has been used to model the Korteweg-de Vries (KdV), Burgers and GP equations. It can be implemented on both quantum and classical computers and is extremely scalable. We present results for 1D soliton solutions with positive and negative internal interactions, as well as vector solitons with inelastic scattering. In higher dimensions we look at the behavior of vortex ring reconnection. A further improvement is considered with a proper operator splitting technique via a Fourier transformation. This is great for quantum computers since the quantum FFT is exponentially faster than its classical counterpart which involves non-local data on the entire lattice (Quantum FFT is the backbone of the Shor algorithm for quantum factorization). We also present an imaginary time method in which we transform the Schrodinger equation into a diffusion equation for recovering ground state initial conditions of a quantum system suitable for the QLG algorithm.

Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.

PubMed

Li, Yu-Qi; Pan, Xiao-Yin; Sahni, Viraht

2013-09-21

The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.

Soliton switching in a site-dependent ferromagnet

NASA Astrophysics Data System (ADS)

Senjudarvannan, R.; Sathishkumar, P.; Vijayalakshmi, S.

2017-02-01

Switching of soliton in a ferromagnetic medium offers the possibility of developing a new innovative approach for information storage technologies. The nonlinear spin dynamics of a site-dependent Heisenberg ferromagnetic spin chain with Gilbert damping under the influence of external magnetic field is expressed in the form of the Landau-Lifshitz-Gilbert equation in the classical continuum limit. The corresponding evolution equation is developed through stereographic projection technique by projecting the unit sphere of spin onto a complex plane. The exact soliton solutions are constructed by solving the associated evolution equation through the modified extended tanh-function method. The impact of damping and external magnetic field on the magnetic soliton under the invariant inhomogeneity is investigated and finally, the magnetization switching in the form of shape changing solitons are demonstrated.

Photon exchange and entanglement formation during transmission through a rectangular quantum barrier.

PubMed

Sulyok, Georg; Durstberger-Rennhofer, Katharina; Summhammer, Johann

2015-09-04

When a quantum particle traverses a rectangular potential created by a quantum field both photon exchange and entanglement between particle and field take place. We present the full analytic solution of the Schrödinger equation of the composite particle-field system allowing investigation of these phenomena in detail and comparison to the results of a classical field treatment. Besides entanglement formation, remarkable differences also appear with respect to the symmetry between energy emission and absorption, resonance effects and if the field initially occupies the vacuum state.

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaofeng, E-mail: xfyang@math.sc.edu; Han, Daozhi, E-mail: djhan@iu.edu

2017-02-01

In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank–Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposedmore » schemes.« less

Bouncing cosmologies from quantum gravity condensates

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Sindoni, Lorenzo; Wilson-Ewing, Edward

2017-02-01

We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.

Phantom of the Hartle–Hawking instanton: Connecting inflation with dark energy

DOE PAGES

Chen, Pisin; Qiu, Taotao; Yeom, Dong -han

2016-02-20

If the Hartle–Hawking wave function is the correct boundary condition of our universe, the history of our universe will be well approximated by an instanton. Although this instanton should be classicalized at infinity, as long as we are observing a process of each history, we may detect a non-classicalized part of field combinations. When we apply it to a dark energy model, this non-classicalized part of fields can be well embedded to a quintessence and a phantom model, i.e., a quintom model. Because of the property of complexified instantons, the phantomness will be naturally free from a big rip singularity.more » This phantomness does not cause perturbative instabilities, as it is an effect emergent from the entire wave function. Lastly, our work may thus provide a theoretical basis for the quintom models, whose equation of state can cross the cosmological constant boundary phenomenologically.« less

Phantom of the Hartle-Hawking instanton: connecting inflation with dark energy

NASA Astrophysics Data System (ADS)

Chen, Pisin; Qiu, Taotao; Yeom, Dong-han

2016-02-01

If the Hartle-Hawking wave function is the correct boundary condition of our universe, the history of our universe will be well approximated by an instanton. Although this instanton should be classicalized at infinity, as long as we are observing a process of each history, we may detect a non-classicalized part of field combinations. When we apply it to a dark energy model, this non-classicalized part of fields can be well embedded to a quintessence and a phantom model, i.e., a quintom model. Because of the property of complexified instantons, the phantomness will be naturally free from a big rip singularity. This phantomness does not cause perturbative instabilities, as it is an effect emergent from the entire wave function. Our work may thus provide a theoretical basis for the quintom models, whose equation of state can cross the cosmological constant boundary phenomenologically.

Exhaustive Classification of the Invariant Solutions for a Specific Nonlinear Model Describing Near Planar and Marginally Long-Wave Unstable Interfaces for Phase Transition

NASA Astrophysics Data System (ADS)

Ahangari, Fatemeh

2018-05-01

Problems of thermodynamic phase transition originate inherently in solidification, combustion and various other significant fields. If the transition region among two locally stable phases is adequately narrow, the dynamics can be modeled by an interface motion. This paper is devoted to exhaustive analysis of the invariant solutions for a modified Kuramoto-Sivashinsky equation in two spatial and one temporal dimensions is presented. This nonlinear partial differential equation asymptotically characterizes near planar interfaces, which are marginally long-wave unstable. For this purpose, by applying the classical symmetry method for this model the classical symmetry operators are attained. Moreover, the structure of the Lie algebra of symmetries is discussed and the optimal system of subalgebras, which yields the preliminary classification of group invariant solutions is constructed. Mainly, the Lie invariants corresponding to the infinitesimal symmetry generators as well as associated similarity reduced equations are also pointed out. Furthermore, the nonclassical symmetries of this nonlinear PDE are also comprehensively investigated.

Synergies from using higher order symplectic decompositions both for ordinary differential equations and quantum Monte Carlo methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matuttis, Hans-Georg; Wang, Xiaoxing

Decomposition methods of the Suzuki-Trotter type of various orders have been derived in different fields. Applying them both to classical ordinary differential equations (ODEs) and quantum systems allows to judge their effectiveness and gives new insights for many body quantum mechanics where reference data are scarce. Further, based on data for 6 × 6 system we conclude that sampling with sign (minus-sign problem) is probably detrimental to the accuracy of fermionic simulations with determinant algorithms.

Book Review:

NASA Astrophysics Data System (ADS)

Poisson, E.

2006-09-01

The motion of a charged particle interacting with its own electromagnetic field is an area of research that has a long history; this problem has never ceased to fascinate its investigators. On the one hand the theory ought to be straightforward to formulate: one has Maxwell's equations that tell the field how to behave (given the motion of the particle), and one has the Lorentz-force law that tells the particle how to move (given the field). On the other hand the theory is fundamentally ambiguous because of the field singularities that necessarily come with a point particle. While each separate sub-problem can easily be solved, to couple the field to the particle in a self-consistent treatment turns out to be tricky. I believe it is this dilemma (the theory is straightforward but tricky) that has been the main source of the endless fascination. For readers of Classical and Quantum Gravity, the fascination does not end there. For them it is also rooted in the fact that the electromagnetic self-force problem is deeply analogous to the gravitational self-force problem, which is of direct relevance to future gravitational wave observations. The motion of point particles in curved spacetime has been the topic of a recent Topical Review [1], and it was the focus of a recent Special Issue [2]. It is surprising to me that radiation reaction is a subject that continues to be poorly covered in the standard textbooks, including Jackson's bible [3]. Exceptions are Rohrlich's excellent text [4], which makes a very useful introduction to radiation reaction, and the Landau and Lifshitz classic [5], which contains what is probably the most perfect summary of the foundational ideas (presented in characteristic terseness). It is therefore with some trepidation that I received Herbert Spohn's book, which covers both the classical and quantum theories of a charged particle coupled to its own field (the presentation is limited to flat spacetime). Is this the text that graduate students and researchers should turn to in order to get a complete and accessible education in radiation reaction? My answer is that while the book does indeed contain a lot of useful material, it is not a very accessible source of information, and it is certainly not a student-friendly textbook. Instead, the book presents a technical account of the author's personal take on the theory, and represents a culminating summary of the author's research contributions over more than a decade. The book is written in a fairly mathematical style (the author is Professor of Mathematical Physics at the Technische Universitat in Munich), and it very much emphasises mathematical rigour. This makes the book less accessible than I would wish it to be, but this is perhaps less a criticism than a statement about my taste, expectation, and attitude. The presentation of the classical theory begins with a point particle, but Spohn immediately smears the charge distribution to eliminate the vexing singularities of the retarded field. He considers both the nonrelativistic Abraham model (in which the extended particle is spherically symmetric in the laboratory frame) and the relativistic Lorentz model (in which the particle is spherical in its rest frame). In Spohn's work, the smearing of the charge distribution is entirely a mathematical procedure, and I would have wished for a more physical discussion. A physically extended body, held together against electrostatic repulsion by cohesive forces (sometimes called Poincaré stresses) would make a sound starting point for a classical theory of charged particles, and would have nicely (and physically) motivated the smearing operation adopted in the book. Spohn goes on to derive energy momentum relations for the extended objects, and to obtain their equations of motion. A compelling aspect of his presentation is that he formally introduces the 'adiabatic limit', the idea that the external fields acting on the charged body should have length and time scales that are long compared with the particle's internal scales (respectively the electrostatic classical radius and its associated time scale). As a consequence, the equations of motion do not involve a differentiated acceleration vector (as is the case for the Abraham Lorentz Dirac equations) but are proper second-order differential equations for the position vector. In effect, the correct equations of motion are obtained from the Abraham Lorentz Dirac equations by a reduction-of-order procedure that was first proposed (as far as I know) by Landau and Lifshitz [5]. In Spohn's work this procedure is not {\\it ad hoc}, but a natural consequence of the adiabatic approximation. An aspect of the classical portion of the book that got me particularly excited is Spohn's proposal for an experimental test of the predictions of the Landau Lifshitz equations. His proposed experiment involves a Penning trap, a device that uses a uniform magnetic field and a quadrupole electric field to trap an electron for very long times. Without radiation reaction, the motion of an electron in the trap is an epicycle that consists of a rapid (and small) cyclotron orbit superposed onto a slow (and large) magnetron orbit. Spohn shows that according to the Landau Lifshitz equations, the radiation reaction produces a damping of the cyclotron motion. For reasonable laboratory situations this damping occurs over a time scale of the order of 0.1 second. This experiment might well be within technological reach. The presentation of the quantum theory is based on the nonrelativistic Abraham model, which upon quantization leads to the well-known Pauli-Fierz Hamiltonian of nonrelativistic quantum electrodynamics. This theory, an approximation to the fully relativistic version of QED, has a wide domain of validity that includes many aspects of quantum optics and laser-matter interactions. As I am not an expert in this field, my ability to review this portion of Spohn's book is limited, and I will indeed restrict myself to a few remarks. I first admit that I found Spohn's presentation to be tough going. Unlike the pair of delightful books by Cohen-Tannoudji, Dupont-Roc, and Grynberg [6, 7], this is not a gentle introduction to the quantum theory of a charged particle coupled to its own electromagnetic field. Instead, Spohn proceeds rather quickly through the formulation of the theory (defining the Hamiltonian and the Hilbert space) and then presents some applications (for example, he constructs the ground states of the theory, he examines radiation processes, and he explores finite-temperature aspects). There is a lot of material in the eight chapters devoted to the quantum theory, but my insufficient preparation and the advanced nature of Spohn's presentation were significant obstacles; I was not able to draw much appreciation for this material. One of the most useful resources in Spohn's book are the historical notes and literature reviews that are inserted at the end of each chapter. I discovered a wealth of interesting articles by reading these, and I am grateful that the author made the effort to collect this information for the benefit of his readers. References [1] Poisson E 2004 Radiation reaction of point particles in curved spacetime Class. Quantum Grav 21 R153 R232 [2] Lousto C O 2005 Special issue: Gravitational Radiation from Binary Black Holes: Advances in the Perturbative Approach, Class. Quantum Grav22 S543 S868 [3] Jackson J D 1999 Classical Electrodynamics Third Edition (New York: Wiley) [4] Rohrlich F 1990 Classical Charged Particles (Redwood City, CA: Addison Wesley) [5] Landau L D and Lifshitz E M 2000 The Classical Theory of Fields Fourth Edition (Oxford: Butterworth Heinemann) [6] Cohen-Tannoudji C Dupont-Roc J and Grynberg G 1997 Photons and Atoms - Introduction to Quantum Electrodynamics (New York: Wiley-Interscience) [7] Cohen-Tannoudji C, Dupont-Roc J and G Grynberg G 1998 Atom Photon Interactions: Basic Processes and Applications (New York: Wiley-Interscience)

Vakonomic Constraints in Higher-Order Classical Field Theory

NASA Astrophysics Data System (ADS)

Campos, Cédric M.

2010-07-01

We propose a differential-geometric setting for the dynamics of a higher-order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both, the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher-order jet bundle and the canonical multisymplectic form on its affine dual. The result is that we obtain a unique and global intrinsic description of the dynamics. The case of vakonomic constraints is also studied within this formalism.

Microscopic description of exciton polaritons in direct two-band semiconductors

NASA Astrophysics Data System (ADS)

Nguyen, Van Trong; Mahler, Günter

1999-07-01

Based on a quantum electrodynamical formulation, a microscopic description of exciton polaritons in a two-band semiconductor is presented. We show that the interband exchange Coulomb interaction, responsible for the coupling of the exciton with the longitudinal part of the induced field, should be treated on equal footing together with the coupling to the transverse part of the induced field (the photon field). The constitutive relation is established to connect the current density with the total electric field of polaritons. The classical Maxwell equations are derived from the quantum representation of photons to get a closed system of equations. The temporal evolution for an initial excited exciton state is studied in detail and an anisotropic polariton vacuum Rabi splitting is shown to occur. A number of up-to-now unresolved discrepancies in the literature are clarified.

An extended approach for computing the critical properties in the two-and three-dimensional lattices within the effective-field renormalization group method

NASA Astrophysics Data System (ADS)

de Albuquerque, Douglas F.; Santos-Silva, Edimilson; Moreno, N. O.

2009-10-01

In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.

Inflation and acceleration of the universe by nonlinear magnetic monopole fields

NASA Astrophysics Data System (ADS)

Övgün, A.

2017-02-01

Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields.

Semi-classical Reissner-Nordstrom model for the structure of charged leptons

NASA Technical Reports Server (NTRS)

Rosen, G.

1980-01-01

The lepton self-mass problem is examined within the framework of the quantum theory of electromagnetism and gravity. Consideration is given to the Reissner-Nordstrom solution to the Einstein-Maxwell classical field equations for an electrically charged mass point, and the WKB theory for a semiclassical system with total energy zero is used to obtain an expression for the Einstein-Maxwell action factor. The condition obtained is found to account for the observed mass values of the three charged leptons, and to be in agreement with the correspondence principle.

Effect of surface bilayer charges on the magnetic field around ionic channels

NASA Astrophysics Data System (ADS)

Gomes Soares, Marília Amável; Cortez, Celia Martins; Oliveira Cruz, Frederico Alan de; Silva, Dilson

2017-01-01

In this work, we present a physic-mathematical model for representing the ion transport through membrane channels, in special Na+ and K+-channels, and discuss the influence of surface bilayer charges on the magnetic field behavior around the ionic current. The model was composed of a set of equations, including: a nonlinear differential Poisson-Boltzmann equation which usually allows to estimate the surface potentials and electric potential profile across membrane; equations for the ionic flux through channel and the ionic current density based on Armstrong's model for Na+ and K+ permeability and other Physics concepts; and a magnetic field expression derived from the classical Ampère equation. Results from computational simulations using the finite element method suggest that the ionic permeability is strongly dependent of surface bilayer charges, the current density through a K+-channel is very less sensible to temperature changes than the current density through a Na+- channel, active Na+-channels do not directly interfere with the K+-channels around, and vice-versa, since the magnetic perturbation generated by an active channel is of short-range.

Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Unver, O.; Gurtug, O.

2010-10-15

Quantum singularities considered in the 3D Banados-Teitelboim-Zanelli (BTZ) spacetime by Pitelli and Letelier [Phys. Rev. D 77, 124030 (2008)] is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurrence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and nonlinear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analyzed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields, the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence,more » the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying the Klein-Gordon equation but nonsingular for fermions obeying the Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes does not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.« less

Comparison of exact pupil astigmatism conditions with Seidel approximations

NASA Astrophysics Data System (ADS)

Zhao, Chunyu; Burge, James H.

2002-12-01

The aberrations of axisymmetric imaging systems can be calculated to third order by use of the Seidel formulas. The Coddington equations give aberrations that have quadratic dependence on the pupil, for all field points. The pupil astigmatism conditions were recently developed to predict and control aberrations that have quadratic field dependence and arbitrary pupil dependence. We investigate the relationship between the exact pupil astigmatism conditions and the classical Seidel treatment of pupil aberrations.

Why Trees Migrate So Fast: Confronting Theory with Dispersal Biology and the Paleorecord

Treesearch

James S. Clark

1998-01-01

Reid's paradox describes the fact that classical models cannot account for the rapid (102-103 yr-1) spread of trees at the end of the Pleistocene. I use field estimates of seed dispersal with an integrodifference equation and simulation models of population growth to show that dispersal data are...

Turbulent Chemically Reacting Flows According to a Kinetic Theory. Ph.D. Thesis; [statistical analysis/gas flow

NASA Technical Reports Server (NTRS)

Hong, Z. C.

1975-01-01

A review of various methods of calculating turbulent chemically reacting flow such as the Green Function, Navier-Stokes equation, and others is presented. Nonequilibrium degrees of freedom were employed to study the mixing behavior of a multiscale turbulence field. Classical and modern theories are discussed.

Matter-antimatter asymmetry and dark matter from torsion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Poplawski, Nikodem J.

2011-04-15

We propose a simple scenario which explains the observed matter-antimatter imbalance and the origin of dark matter in the Universe. We use the Einstein-Cartan-Sciama-Kibble theory of gravity which naturally extends general relativity to include the intrinsic spin of matter. Spacetime torsion produced by spin generates, in the classical Dirac equation, the Hehl-Datta term which is cubic in spinor fields. We show that under a charge-conjugation transformation this term changes sign relative to the mass term. A classical Dirac spinor and its charge conjugate therefore satisfy different field equations. Fermions in the presence of torsion have higher energy levels than antifermions,more » which leads to their decay asymmetry. Such a difference is significant only at extremely high densities that existed in the very early Universe. We propose that this difference caused a mechanism, according to which heavy fermions existing in such a Universe and carrying the baryon number decayed mostly to normal matter, whereas their antiparticles decayed mostly to hidden antimatter which forms dark matter. The conserved total baryon number of the Universe remained zero.« less

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

Gravitational decoherence, alternative quantum theories and semiclassical gravity

NASA Astrophysics Data System (ADS)

Hu, B. L.

2014-04-01

In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity. 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not 3) Gravitational Decoherence: derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schrödinger Equations in relation to SCG; b) Master equation of gravity-induced effects serving as discriminator of 2); and c) Role of gravity in macroscopic quantum phenomena.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shao Xiaoqiang; Wang Hongfu; Zhang Shou

We present an approach for implementation of a 1->3 orbital state quantum cloning machine based on the quantum Zeno dynamics via manipulating three rf superconducting quantum interference device (SQUID) qubits to resonantly interact with a superconducting cavity assisted by classical fields. Through appropriate modulation of the coupling constants between rf SQUIDs and classical fields, the quantum cloning machine can be realized within one step. We also discuss the effects of decoherence such as spontaneous emission and the loss of cavity in virtue of master equation. The numerical simulation result reveals that the quantum cloning machine is especially robust against themore » cavity decay, since all qubits evolve in the decoherence-free subspace with respect to cavity decay due to the quantum Zeno dynamics.« less

Generation of long-living entanglement between two distant three-level atoms in non-Markovian environments.

PubMed

Li, Chuang; Yang, Sen; Song, Jie; Xia, Yan; Ding, Weiqiang

2017-05-15

In this paper, a scheme for the generation of long-living entanglement between two distant Λ-type three-level atoms separately trapped in two dissipative cavities is proposed. In this scheme, two dissipative cavities are coupled to their own non-Markovian environments and two three-level atoms are driven by the classical fields. The entangled state between the two atoms is produced by performing Bell state measurement (BSM) on photons leaving the dissipative cavities. Using the time-dependent Schördinger equation, we obtain the analytical results for the evolution of the entanglement. It is revealed that, by manipulating the detunings of classical field, the long-living stationary entanglement between two atoms can be generated in the presence of dissipation.

Stability of flow of a thermoviscoelastic fluid between rotating coaxial circular cylinders

NASA Technical Reports Server (NTRS)

Ghandour, N. N.; Narasimhan, M. N. L.

1976-01-01

The stability problem of thermoviscoelastic fluid flow between rotating coaxial cylinders is investigated using nonlinear thermoviscoelastic constitutive equations due to Eringen and Koh. The velocity field is found to be identical with that of the classical viscous case and the case of the viscoelastic fluid, but the temperature and pressure fields are found to be different. By imposing some physically reasonable mechanical and geometrical restrictions on the flow, and by a suitable mathematical analysis, the problem is reduced to a characteristic value problem. The resulting problem is solved and stability criteria are obtained in terms of critical Taylor numbers. In general, it is found that thermoviscoelastic fluids are more stable than classical viscous fluids and viscoinelastic fluids under similar conditions.

Forces on nuclei moving on autoionizing molecular potential energy surfaces.

PubMed

Moiseyev, Nimrod

2017-01-14

Autoionization of molecular systems occurs in diatomic molecules and in small biochemical systems. Quantum chemistry packages enable calculation of complex potential energy surfaces (CPESs). The imaginary part of the CPES is associated with the autoionization decay rate, which is a function of the molecular structure. Molecular dynamics simulations, within the framework of the Born-Oppenheimer approximation, require the definition of a force field. The ability to calculate the forces on the nuclei in bio-systems when autoionization takes place seems to rely on an understanding of radiative damages in RNA and DNA arising from the release of slow moving electrons which have long de Broglie wavelengths. This work addresses calculation of the real forces on the nuclei moving on the CPES. By using the transformation of the time-dependent Schrödinger equation, previously used by Madelung, we proved that the classical forces on nuclei moving on the CPES correlated with the gradient of the real part of the CPES. It was proved that the force on the nuclei of the metastable molecules is time independent although the probability to detect metastable molecules exponentially decays. The classical force is obtained from the transformed Schrödinger equation when ℏ=0 and the Schrödinger equation is reduced to the classical (Newtonian) equations of motion. The forces on the nuclei regardless on what potential energy surface they move (parent CPES or product real PESs) vary in time due to the autoionization process.

Ψ-model of micro- and macrosystems

NASA Astrophysics Data System (ADS)

Perepelkin, E. E.; Sadovnikov, B. I.; Inozemtseva, N. G.

2017-08-01

A mathematical model (referred as Ψ-model for convenience) has been developed, which allows describing certain class of micro- and macrosystems. Ψ-model is based on quantum mechanics and classical mechanics of continuous media. Ψ-model describes micro- and macrosystems, in which vector field of velocities of probability flows, charge, mass has specific spiral structure. The field of velocities has spiral structure on concentric spherical surfaces. The velocity field is not defined and has a characteristic property on the poles of sphere and on the axis and tends to zero at infinity. The behavior of Ψ-model can be described in the general case with time-dependent periodic singular solution of the Schrödinger equation. The goal of this paper is to choose a particular probability flux in the continuity equation which we solve in this paper and deduce from it the solution of the Schrödinger equation. For example, in the frame of approach the problem with modified Coulomb potential was considered.

Hamiltonian and Thermodynamic Modeling of Quantum Turbulence

NASA Astrophysics Data System (ADS)

Grmela, Miroslav

2010-10-01

The state variables in the novel model introduced in this paper are the fields playing this role in the classical Landau-Tisza model and additional fields of mass, entropy (or temperature), superfluid velocity, and gradient of the superfluid velocity, all depending on the position vector and another tree dimensional vector labeling the scale, describing the small-scale structure developed in 4He superfluid experiencing turbulent motion. The fluxes of mass, momentum, energy, and entropy in the position space as well as the fluxes of energy and entropy in scales, appear in the time evolution equations as explicit functions of the state variables and of their conjugates. The fundamental thermodynamic relation relating the fields to their conjugates is left in this paper undetermined. The GENERIC structure of the equations serves two purposes: (i) it guarantees that solutions to the governing equations, independently of the choice of the fundamental thermodynamic relation, agree with the observed compatibility with thermodynamics, and (ii) it is used as a guide in the construction of the novel model.

An Elliptic PDE Approach for Shape Characterization

PubMed Central

Haidar, Haissam; Bouix, Sylvain; Levitt, James; McCarley, Robert W.; Shenton, Martha E.; Soul, Janet S.

2009-01-01

This paper presents a novel approach to analyze the shape of anatomical structures. Our methodology is rooted in classical physics and in particular Poisson's equation, a fundamental partial differential equation [1]. The solution to this equation and more specifically its equipotential surfaces display properties that are useful for shape analysis. We present a numerical algorithm to calculate the length of streamlines formed by the gradient field of the solution to this equation for 2D and 3D objects. The length of the streamlines along the equipotential surfaces was used to build a new function which can characterize the shape of objects. We illustrate our method on 2D synthetic and natural shapes as well as 3D medical data. PMID:17271986

Inertial effects in systems with magnetic charge

NASA Astrophysics Data System (ADS)

Armitage, N. P.

2018-05-01

This short article sets out some of the basic considerations that go into detecting the mass of quasiparticles with effective magnetic charge in solids. Effective magnetic charges may be appear as defects in particular magnetic textures. A magnetic monopole is a defect in this texture and as such these are not monopoles in the actual magnetic field B, but instead in the auxiliary field H. They may have particular properties expected for such quasiparticles such as magnetic charge and mass. This effective mass may-in principle-be detected in the same fashion that the mass is detected of other particles classically e.g. through their inertial response to time-dependent electromagnetic fields. I discuss this physics in the context of the "simple" case of the quantum spin ices, but aspects are broadly applicable. Based on extensions to Ryzkhin's model for classical spin ice, a hydrodynamic formulation can be given that takes into account inertial and entropic forces. Ultimately, a form for the susceptibility is obtained that is equivalent to the Rocard equation, which is a classic form used to account for inertial effects in the context of Debye-like relaxation.

Nonlinear Fluid Model Of 3-D Field Effects In Tokamak Plasmas

NASA Astrophysics Data System (ADS)

Callen, J. D.; Hegna, C. C.; Beidler, M. T.

2017-10-01

Extended MHD codes (e.g., NIMROD, M3D-C1) are beginning to explore nonlinear effects of small 3-D magnetic fields on tokamak plasmas. To facilitate development of analogous physically understandable reduced models, a fluid-based dynamic nonlinear model of these added 3-D field effects in the base axisymmetric tokamak magnetic field geometry is being developed. The model incorporates kinetic-based closures within an extended MHD framework. Key 3-D field effects models that have been developed include: 1) a comprehensive modified Rutherford equation for the growth of a magnetic island that includes the classical tearing and NTM perturbed bootstrap current drives, externally applied magnetic field and current drives, and classical and neoclassical polarization current effects, and 2) dynamic nonlinear evolution of the plasma toroidal flow (radial electric field) in response to the 3-D fields. An application of this model to RMP ELM suppression precipitated by an ELM crash will be discussed. Supported by Office of Fusion Energy Sciences, Office of Science, Dept. of Energy Grants DE-FG02-86ER53218 and DE-FG02-92ER54139.

Rota-Baxter operators on sl (2,C) and solutions of the classical Yang-Baxter equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pei, Jun, E-mail: peitsun@163.com; Bai, Chengming, E-mail: baicm@nankai.edu.cn; Guo, Li, E-mail: liguo@rutgers.edu

2014-02-15

We explicitly determine all Rota-Baxter operators (of weight zero) on sl (2,C) under the Cartan-Weyl basis. For the skew-symmetric operators, we give the corresponding skew-symmetric solutions of the classical Yang-Baxter equation in sl (2,C), confirming the related study by Semenov-Tian-Shansky. In general, these Rota-Baxter operators give a family of solutions of the classical Yang-Baxter equation in the six-dimensional Lie algebra sl (2,C)⋉{sub ad{sup *}} sl (2,C){sup *}. They also give rise to three-dimensional pre-Lie algebras which in turn yield solutions of the classical Yang-Baxter equation in other six-dimensional Lie algebras.

Quantum Dynamics in the HMF Model

NASA Astrophysics Data System (ADS)

Plestid, Ryan; O'Dell, Duncan

2017-04-01

The Hamiltonian Mean Field (HMF) model represents a paradigm in the study of long-range interactions but has never been realized in a lab. Recently Shutz and Morigi (PRL 113) have come close but ultimately fallen short. Their proposal relied on cavity-induced interactions between atoms. If a design using cold atoms is to be successful, an understanding of quantum effects is essential. I will outline the natural quantum generalization of the HMF assuming a BEC by using a generalized Gross-Pitaevskii equation (gGPE). I will show how quantum effects modify features which are well understood in the classical model. More specifically, by working in the semi-classical regime (strong interparticle interactions) we can identify the universal features predicted by catastrophe theory dressed with quantum interference effects. The stationary states of gGPE can be solved exactly and are found to be described by self-consistent Mathieu functions. Finally, I will discuss the connection between the classical description of the dynamics in terms of the Vlassov equation, and the gGPE. We would like to thank the Government of Ontario's OGS program, NSERC, and the Perimeter Institute of Theoretical Physics.

Soliton Gases and Generalized Hydrodynamics

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Yoshimura, Takato; Caux, Jean-Sébastien

2018-01-01

We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.

Absorbing Boundary Conditions in Quantum Relativistic Mechanics for Spinless Particles Subject to a Classical Electromagnetic Field

NASA Astrophysics Data System (ADS)

Sater, Julien

The theory of Artificial Boundary Conditions described by Antoine et al. [2,4-6] for the Schrodinger equation is applied to the Klein-Gordon (KG) in two-dimensions (2-D) for spinless particles subject to electromagnetic fields. We begin by providing definitions for a basic understanding of the theory of operators, differential geometry and wave front sets needed to discuss the factorization theorem thanks to Nirenberg and Hormander [14, 16]. The laser-free Klein-Gordon equation in 1-D is then discussed, followed by the case including electrodynamics potentials, concluding with the KG equation in 2-D space with electrodynamics potentials. We then consider numerical simulations of the laser-particle KG equation, which includes a brief analysis of a finite difference scheme. The conclusion integrates a discussion of the numerical results, the successful completion of the objective set forth, a declaration of the unanswered encountered questions and a suggestion of subjects for further research.

A field theory approach to the evolution of canonical helicity and energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

You, S.

A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems.more » For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.« less

Holography as a highly efficient renormalization group flow. I. Rephrasing gravity

NASA Astrophysics Data System (ADS)

Behr, Nicolas; Kuperstein, Stanislav; Mukhopadhyay, Ayan

2016-07-01

We investigate how the holographic correspondence can be reformulated as a generalization of Wilsonian renormalization group (RG) flow in a strongly interacting large-N quantum field theory. We first define a highly efficient RG flow as one in which the Ward identities related to local conservation of energy, momentum and charges preserve the same form at each scale. To achieve this, it is necessary to redefine the background metric and external sources at each scale as functionals of the effective single-trace operators. These redefinitions also absorb the contributions of the multitrace operators to these effective Ward identities. Thus, the background metric and external sources become effectively dynamical, reproducing the dual classical gravity equations in one higher dimension. Here, we focus on reconstructing the pure gravity sector as a highly efficient RG flow of the energy-momentum tensor operator, leaving the explicit constructive field theory approach for generating such RG flows to the second part of the work. We show that special symmetries of the highly efficient RG flows carry information through which we can decode the gauge fixing of bulk diffeomorphisms in the corresponding gravity equations. We also show that the highly efficient RG flow which reproduces a given classical gravity theory in a given gauge is unique provided the endpoint can be transformed to a nonrelativistic fixed point with a finite number of parameters under a universal rescaling. The results obtained here are used in the second part of this work, where we do an explicit field-theoretic construction of the RG flow and obtain the dual classical gravity theory.

Nonclassical acoustics

NASA Technical Reports Server (NTRS)

Kentzer, C. P.

1976-01-01

A statistical approach to sound propagation is considered in situations where, due to the presence of large gradients of properties of the medium, the classical (deterministic) treatment of wave motion is inadequate. Mathematical methods for wave motions not restricted to small wavelengths (analogous to known methods of quantum mechanics) are used to formulate a wave theory of sound in nonuniform flows. Nonlinear transport equations for field probabilities are derived for the limiting case of noninteracting sound waves and it is postulated that such transport equations, appropriately generalized, may be used to predict the statistical behavior of sound in arbitrary flows.

Discrete dynamical laser equation for the critical onset of bistability, entanglement and disappearance

NASA Astrophysics Data System (ADS)

Abdul, M.; Farooq, U.; Akbar, Jehan; Saif, F.

2018-06-01

We transform the semi-classical laser equation for single mode homogeneously broadened lasers to a one-dimensional nonlinear map by using the discrete dynamical approach. The obtained mapping, referred to as laser logistic mapping (LLM), characteristically exhibits convergent, cyclic and chaotic behavior depending on the control parameter. Thus, the so obtained LLM explains stable, bistable, multi-stable, and chaotic solutions for output field intensity. The onset of bistability takes place at a critical value of the effective gain coefficient. The obtained analytical results are confirmed through numerical calculations.

Purely cubic action for string field theory

NASA Technical Reports Server (NTRS)

Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.

1986-01-01

It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.

Predicting the Rotor-Stator Interaction Acoustics of a Ducted Fan Engine

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Rumsey, Christopher L.; Podboy, Gary G.; Dunn, M. H.

2001-01-01

A Navier-Stokes computation is performed for a ducted-fan configuration with the goal of predicting rotor-stator noise generation without having to resort to heuristic modeling. The calculated pressure field in the inlet region is decomposed into classical infinite-duct modes, which are then used in either a hybrid finite-element/Kirchhoff surface method or boundary integral equation method to calculate the far field noise. Comparisons with experimental data are presented, including rotor wake surveys and far field sound pressure levels for two blade passage frequency (BPF) tones.

Susceptible-infected-susceptible epidemics on networks with general infection and cure times.

PubMed

Cator, E; van de Bovenkamp, R; Van Mieghem, P

2013-06-01

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.

Susceptible-infected-susceptible epidemics on networks with general infection and cure times

NASA Astrophysics Data System (ADS)

Cator, E.; van de Bovenkamp, R.; Van Mieghem, P.

2013-06-01

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Angular momentum and torque described with the complex octonion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weng, Zi-Hua, E-mail: xmuwzh@xmu.edu.cn

2014-08-15

The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum (or torque, force) to combine some physics contents, which were considered to be independent of each other in the past. J. C. Maxwell used simultaneously two methods, the vector terminology and quaternion analysis, to depict the electromagnetic theory. It motivates the paper to introduce the quaternion space into the field theory, describing the physical feature of electromagnetic and gravitational fields. The spaces of electromagnetic field andmore » of gravitational field can be chosen as the quaternion spaces, while the coordinate component of quaternion space is able to be the complex number. The quaternion space of electromagnetic field is independent of that of gravitational field. These two quaternion spaces may compose one octonion space. Contrarily, one octonion space can be separated into two subspaces, the quaternion space and S-quaternion space. In the quaternion space, it is able to infer the field potential, field strength, field source, angular momentum, torque, and force etc in the gravitational field. In the S-quaternion space, it is capable of deducing the field potential, field strength, field source, current continuity equation, and electric (or magnetic) dipolar moment etc in the electromagnetic field. The results reveal that the quaternion space is appropriate to describe the gravitational features, including the torque, force, and mass continuity equation etc. The S-quaternion space is proper to depict the electromagnetic features, including the dipolar moment and current continuity equation etc. In case the field strength is weak enough, the force and the continuity equation etc can be respectively reduced to that in the classical field theory.« less

High-order rogue wave solutions of the classical massive Thirring model equations

NASA Astrophysics Data System (ADS)

Guo, Lijuan; Wang, Lihong; Cheng, Yi; He, Jingsong

2017-11-01

The nth-order solutions of the classical massive Thirring model (MTM) equations are derived by using the n-fold Darboux transformation. These solutions are expressed by the ratios of the two determinants consisted of 2n eigenfunctions under the reduction conditions. Using this method, rogue waves are constructed explicitly up to the third-order. Three patterns, i.e., fundamental, triangular and circular patterns, of the rogue waves are discussed. The parameter μ in the MTM model plays the role of the mass in the relativistic field theory while in optics it is related to the medium periodic constant, which also results in a significant rotation and a remarkable lengthening of the first-order rogue wave. These results provide new opportunities to observe rouge waves by using a combination of electromagnetically induced transparency and the Bragg scattering four-wave mixing because of large amplitudes.

Insight into the Li2CO3-K2CO3 eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics

NASA Astrophysics Data System (ADS)

Corradini, Dario; Coudert, François-Xavier; Vuilleumier, Rodolphe

2016-03-01

We use molecular dynamics simulations to study the thermodynamics, structure, and dynamics of the Li2CO3-K2CO3 (62:38 mol. %) eutectic mixture. We present a new classical non-polarizable force field for this molten salt mixture, optimized using experimental and first principles molecular dynamics simulations data as reference. This simple force field allows efficient molecular simulations of phenomena at long time scales. We use this optimized force field to describe the behavior of the eutectic mixture in the 900-1100 K temperature range, at pressures between 0 and 5 GPa. After studying the equation of state in these thermodynamic conditions, we present molecular insight into the structure and dynamics of the melt. In particular, we present an analysis of the temperature and pressure dependence of the eutectic mixture's self-diffusion coefficients, viscosity, and ionic conductivity.

Insight into the Li2CO3-K2CO3 eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics.

PubMed

Corradini, Dario; Coudert, François-Xavier; Vuilleumier, Rodolphe

2016-03-14

We use molecular dynamics simulations to study the thermodynamics, structure, and dynamics of the Li2CO3-K2CO3 (62:38 mol. %) eutectic mixture. We present a new classical non-polarizable force field for this molten salt mixture, optimized using experimental and first principles molecular dynamics simulations data as reference. This simple force field allows efficient molecular simulations of phenomena at long time scales. We use this optimized force field to describe the behavior of the eutectic mixture in the 900-1100 K temperature range, at pressures between 0 and 5 GPa. After studying the equation of state in these thermodynamic conditions, we present molecular insight into the structure and dynamics of the melt. In particular, we present an analysis of the temperature and pressure dependence of the eutectic mixture's self-diffusion coefficients, viscosity, and ionic conductivity.

Optical analogue of relativistic Dirac solitons in binary waveguide arrays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tran, Truong X., E-mail: truong.tran@mpl.mpg.de; Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen; Longhi, Stefano

2014-01-15

We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An opticalmore » analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.« less

Relativistic quantum chaos-An emergent interdisciplinary field.

PubMed

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Relativistic quantum chaos—An emergent interdisciplinary field

NASA Astrophysics Data System (ADS)

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics—all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Classical electromagnetic radiation of the Dirac electron

NASA Technical Reports Server (NTRS)

Lanyi, G.

1973-01-01

A wave-function-dependent four-vector potential is added to the Dirac equation in order to achieve conservation of energy and momentum for a Dirac electron and its emitted electromagnetic field. The resultant equation contains solutions which describe transitions between different energy states of the electron. As a consequence it is possible to follow the space-time evolution of such a process. This evolution is shown in the case of the spontaneous emission of an electromagnetic field by an electron bound in a hydrogen-like atom. The intensity of the radiation and the spectral distribution are calculated for transitions between two eigenstates. The theory gives a self-consistent deterministic description of some simple radiation processes without using quantum electrodynamics or the correspondence principle.

Analysis of scattering by a linear chain of spherical inclusions in an optical fiber

NASA Astrophysics Data System (ADS)

Chremmos, Ioannis D.; Uzunoglu, Nikolaos K.

2006-12-01

The scattering by a linear chain of spherical dielectric inclusions, embedded along the axis of an optical fiber, is analyzed using a rigorous integral equation formulation, based on the dyadic Green's function theory. The coupled electric field integral equations are solved by applying the Galerkin technique with Mie-type expansion of the field inside the spheres in terms of spherical waves. The analysis extends the previously studied case of a single spherical inhomogeneity inside a fiber to the multisphere-scattering case, by utilizing the classic translational addition theorems for spherical waves in order to analytically extract the direct-intersphere-coupling coefficients. Results for the transmitted and reflected power, on incidence of the fundamental HE11 mode, are presented for several cases.

Electromagnetic scattering and emission by a fixed multi-particle object in local thermal equilibrium: General formalism.

PubMed

Mishchenko, Michael I

2017-10-01

The majority of previous studies of the interaction of individual particles and multi-particle groups with electromagnetic field have focused on either elastic scattering in the presence of an external field or self-emission of electromagnetic radiation. In this paper we apply semi-classical fluctuational electrodynamics to address the ubiquitous scenario wherein a fixed particle or a fixed multi-particle group is exposed to an external quasi-polychromatic electromagnetic field as well as thermally emits its own electromagnetic radiation. We summarize the main relevant axioms of fluctuational electrodynamics, formulate in maximally rigorous mathematical terms the general scattering-emission problem for a fixed object, and derive such fundamental corollaries as the scattering-emission volume integral equation, the Lippmann-Schwinger equation for the dyadic transition operator, the multi-particle scattering-emission equations, and the far-field limit. We show that in the framework of fluctuational electrodynamics, the computation of the self-emitted component of the total field is completely separated from that of the elastically scattered field. The same is true of the computation of the emitted and elastically scattered components of quadratic/bilinear forms in the total electromagnetic field. These results pave the way to the practical computation of relevant optical observables.

Gravitational Wave in Linear General Relativity

NASA Astrophysics Data System (ADS)

Cubillos, D. J.

2017-07-01

General relativity is the best theory currently available to describe the interaction due to gravity. Within Albert Einstein's field equations this interaction is described by means of the spatiotemporal curvature generated by the matter-energy content in the universe. Weyl worked on the existence of perturbations of the curvature of space-time that propagate at the speed of light, which are known as Gravitational Waves, obtained to a first approximation through the linearization of the field equations of Einstein. Weyl's solution consists of taking the field equations in a vacuum and disturbing the metric, using the Minkowski metric slightly perturbed by a factor ɛ greater than zero but much smaller than one. If the feedback effect of the field is neglected, it can be considered as a weak field solution. After introducing the disturbed metric and ignoring ɛ terms of order greater than one, we can find the linearized field equations in terms of the perturbation, which can then be expressed in terms of the Dalambertian operator of the perturbation equalized to zero. This is analogous to the linear wave equation in classical mechanics, which can be interpreted by saying that gravitational effects propagate as waves at the speed of light. In addition to this, by studying the motion of a particle affected by this perturbation through the geodesic equation can show the transversal character of the gravitational wave and its two possible states of polarization. It can be shown that the energy carried by the wave is of the order of 1/c5 where c is the speed of light, which explains that its effects on matter are very small and very difficult to detect.

Algebraic aspects of the driven dynamics in the density operator and correlation functions calculation for multi-level open quantum systems

NASA Astrophysics Data System (ADS)

Bogolubov, Nikolai N.; Soldatov, Andrey V.

2017-12-01

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level quantum system with finite number N of quantum eigenstates interacting with arbitrary external classical fields and dissipative environment simultaneously. It was shown that the structure of these equations can be simplified significantly if the free Hamiltonian driven dynamics of an arbitrary quantum multi-level system under the influence of the external driving fields as well as its Markovian and non-Markovian evolution, stipulated by the interaction with the environment, are described in terms of the SU(N) algebra representation. As a consequence, efficient numerical methods can be developed and employed to analyze these master equations for real problems in various fields of theoretical and applied physics. It was also shown that literally the same master equations hold not only for the reduced density operator but also for arbitrary nonequilibrium multi-time correlation functions as well under the only assumption that the system and the environment are uncorrelated at some initial moment of time. A calculational scheme was proposed to account for these lost correlations in a regular perturbative way, thus providing additional computable terms to the correspondent master equations for the correlation functions.

Coherent distributions for the rigid rotator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grigorescu, Marius

2016-06-15

Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions localized on the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum. The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite “zero point” energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville equation, the related quantum wave function should satisfy the time-dependent Schrödingermore » equation.« less

Fractional Diffusion Analysis of the Electromagnetic Field In Fractured Media Part II: 2.5-D Approach

NASA Astrophysics Data System (ADS)

Ge, J.; Everett, M. E.; Weiss, C. J.

2012-12-01

A 2.5D finite difference (FD) frequency-domain modeling algorithm based on the theory of fractional diffusion of electromagnetic (EM) fields generated by a loop source lying above a fractured geological medium is addressed in this paper. The presence of fractures in the subsurface, usually containing highly conductive pore fluids, gives rise to spatially hierarchical flow paths of induced EM eddy currents. The diffusion of EM eddy currents in such formations is anomalous, generalizing the classical Gaussian process described by the conventional Maxwell equations. Based on the continuous time random walk (CTRW) theory, the diffusion of EM eddy currents in a rough medium is governed by the fractional Maxwell equations. Here, we model the EM response of a 2D subsurface containing fractured zones, with a 3D loop source, which results the so-called 2.5D model geometry. The governing equation in the frequency domain is converted using Fourier transform into k domain along the strike direction (along which the model conductivity doesn't vary). The resulting equation system is solved by the multifrontal massively parallel solver (MUMPS). The data obtained is then converted back to spatial domain and the time domain. We find excellent agreement between the FD and analytic solutions for a rough halfspace model. Then FD solutions are calculated for a 2D fault zone model with variable conductivity and roughness. We compare the results with responses from several classical models and explore the relationship between the roughness and the spatial density of the fracture distribution.

Hyperbolic polaritons in nanoparticles

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Rubio, Angel; Guinea, Francisco; Basov, Dimitri; Fogler, Michael

2015-03-01

Hyperbolic optical materials (HM) are characterized by permittivity tensor that has both positive and negative principal values. Collective electromagnetic modes (polaritons) of HM have novel properties promising for various applications including subdiffractional imaging and on-chip optical communication. Hyperbolic response is actively investigated in the context of metamaterials, anisotropic polar insulators, and layered superconductors. We study polaritons in spheroidal HM nanoparticles using Hamiltonian optics. The field equations are mapped to classical dynamics of fictitious particles (wave packets) of an indefinite Hamiltonian. This dynamics is quantized using the Einstein-Brillouin-Keller quantization rule. The eigenmodes are classified as either bulk or surface according to whether their transverse momenta are real or imaginary. To model how such hyperbolic polaritons can be probed by near-field experiments, we compute the field distribution induced inside and outside the spheroid by an external point dipole. At certain magic frequencies the field shows striking geometric patterns whose origin is traced to the classical periodic orbits. The theory is applied to natural hyperbolic materials hexagonal boron nitride and superconducting LaSrCuO.

Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donker, H.C., E-mail: h.donker@science.ru.nl; Katsnelson, M.I.; De Raedt, H.

2016-09-15

The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds. - Highlights: • Logical inference applied to relativistic, massive, charged, and spinless particle experiments leads to the Klein–Gordon equation. • The relativistic Hamilton–Jacobi is scrutinized by employing a field description formore » the four-velocity. • Logical inference allows analysis of experiments with uncertainty in detection events and experimental conditions.« less

Laguerre-Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two

NASA Astrophysics Data System (ADS)

Hounga, C.; Hounkonnou, M. N.; Ronveaux, A.

2006-10-01

In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.

Thermal noise due to surface-charge effects within the Debye layer of endogenous structures in dendrites.

PubMed

Poznanski, Roman R

2010-02-01

An assumption commonly used in cable theory is revised by taking into account electrical amplification due to intracellular capacitive effects in passive dendritic cables. A generalized cable equation for a cylindrical volume representation of a dendritic segment is derived from Maxwell's equations under assumptions: (i) the electric-field polarization is restricted longitudinally along the cable length; (ii) extracellular isopotentiality; (iii) quasielectrostatic conditions; and (iv) homogeneous medium with constant conductivity and permittivity. The generalized cable equation is identical to Barenblatt's equation arising in the theory of infiltration in fissured strata with a known analytical solution expressed in terms of a definite integral involving a modified Bessel function and the solution to a linear one-dimensional classical cable equation. Its solution is used to determine the impact of thermal noise on voltage attenuation with distance at any particular time. A regular perturbation expansion for the membrane potential about the linear one-dimensional classical cable equation solution is derived in terms of a Green's function in order to describe the dynamics of free charge within the Debye layer of endogenous structures in passive dendritic cables. The asymptotic value of the first perturbative term is explicitly evaluated for small values of time to predict how the slowly fluctuating (in submillisecond range) electric field attributed to intracellular capacitive effects alters the amplitude of the membrane potential. It was found that capacitive effects are almost negligible for cables with electrotonic lengths L>0.5 , contributes up to 10% of the signal for cables with electrotonic lengths in the range between 0.25

The classical limit of minimal length uncertainty relation: revisit with the Hamilton-Jacobi method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Xiaobo; Wang, Peng; Yang, Haitang, E-mail: guoxiaobo@swust.edu.cn, E-mail: pengw@scu.edu.cn, E-mail: hyanga@scu.edu.cn

2016-05-01

The existence of a minimum measurable length could deform not only the standard quantum mechanics but also classical physics. The effects of the minimal length on classical orbits of particles in a gravitation field have been investigated before, using the deformed Poisson bracket or Schwarzschild metric. In this paper, we first use the Hamilton-Jacobi method to derive the deformed equations of motion in the context of Newtonian mechanics and general relativity. We then employ them to study the precession of planetary orbits, deflection of light, and time delay in radar propagation. We also set limits on the deformation parameter bymore » comparing our results with the observational measurements. Finally, comparison with results from previous papers is given at the end of this paper.« less

Conserved Quantities in General Relativity: From the Quasi-Local Level to Spatial Infinity

NASA Astrophysics Data System (ADS)

Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung

2015-08-01

We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in Wang and Yau (Commun Math Phys 288(3):919-942, 2009) to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each optimal isometric embedding, a dual element of the Lie algebra of the Lorentz group is assigned. Quasi-local angular momentum and quasi-local center of mass correspond to pairing this element with rotation Killing fields and boost Killing fields, respectively. They obey classical transformation laws under the action of the Poincaré group. We further justify these definitions by considering their limits as the total angular momentum and the total center of mass of an isolated system. These expressions were derived from the Hamilton-Jacobi analysis of the gravitational action and thus satisfy conservation laws. As a result, we obtained an invariant total angular momentum theorem in the Kerr spacetime. For a vacuum asymptotically flat initial data set of order 1, it is shown that the limits are always finite without any extra assumptions. We also study these total conserved quantities on a family of asymptotically flat initial data sets evolving by the vacuum Einstein evolution equation. It is shown that the total angular momentum is conserved under the evolution. For the total center of mass, the classical dynamical formula relating the center of mass, energy, and linear momentum is recovered, in the nonlinear context of initial data sets evolving by the vacuum Einstein evolution equation. The definition of quasi-local angular momentum provides an answer to the second problem in classical general relativity on Penrose's list (Proc R Soc Lond Ser A 381(1780):53-63, 1982).

Finite difference methods for transient signal propagation in stratified dispersive media

NASA Technical Reports Server (NTRS)

Lam, D. H.

1975-01-01

Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.

Global Solutions to Repulsive Hookean Elastodynamics

NASA Astrophysics Data System (ADS)

Hu, Xianpeng; Masmoudi, Nader

2017-01-01

The global existence of classical solutions to the three dimensional repulsive Hookean elastodynamics around an equilibrium is considered. By linearization and Hodge's decomposition, the compressible part of the velocity, the density, and the compressible part of the transpose of the deformation gradient satisfy Klein-Gordon equations with speed {√{2}}, while the incompressible parts of the velocity and of the transpose of the deformation gradient satisfy wave equations with speed one. The space-time resonance method combined with the vector field method is used in a novel way to obtain the decay of the solution and hence global existence.

Conceptual Foundations of Soliton Versus Particle Dualities Toward a Topological Model for Matter

NASA Astrophysics Data System (ADS)

Kouneiher, Joseph

2016-06-01

The idea that fermions could be solitons was actually confirmed in theoretical models in 1975 in the case when the space-time is two-dimensional and with the sine-Gordon model. More precisely S. Coleman showed that two different classical models end up describing the same fermions particle, when the quantum theory is constructed. But in one model the fermion is a quantum excitation of the field and in the other model the particle is a soliton. Hence both points of view can be reconciliated.The principal aim in this paper is to exhibit a solutions of topological type for the fermions in the wave zone, where the equations of motion are non-linear field equations, i.e. using a model generalizing sine- Gordon model to four dimensions, and describe the solutions for linear and circular polarized waves. In other words, the paper treat fermions as topological excitations of a bosonic field.

Covariance and Quantum Cosmology: A Comparison of Two Matter Clocks

NASA Astrophysics Data System (ADS)

Halnon, Theodore; Bojowald, Martin

2017-01-01

In relativity, time is relative between reference frames. However, quantum mechanics requires a specific time coordinate in order to write an evolution equation for wave functions. This difference between the two theories leads to the problem of time in quantum gravity. One method to study quantum relativity is to interpret the dynamics of a matter field as a clock. In order to test the relationship between different reference frames, an isotropic cosmological model with two matter ingredients is introduced. One is given by a scalar field and one by vacuum energy or a cosmological constant. There are two matter fields, and thus two different Hamiltonians are derived from the respective clock rates. Semi-classical solutions are found for these equations and a comparison is made of the physical predictions that they imply. Partial funding from the Ronald E. McNair Postbaccalaureate Achievement Program.

Simplified derivation of the gravitational wave stress tensor from the linearized Einstein field equations.

PubMed

Balbus, Steven A

2016-10-18

A conserved stress energy tensor for weak field gravitational waves propagating in vacuum is derived directly from the linearized general relativistic wave equation alone, for an arbitrary gauge. In any harmonic gauge, the form of the tensor leads directly to the classical expression for the outgoing wave energy. The method described here, however, is a much simpler, shorter, and more physically motivated approach than is the customary procedure, which involves a lengthy and cumbersome second-order (in wave-amplitude) calculation starting with the Einstein tensor. Our method has the added advantage of exhibiting the direct coupling between the outgoing wave energy flux and the work done by the gravitational field on the sources. For nonharmonic gauges, the directly derived wave stress tensor has an apparent index asymmetry. This coordinate artifact may be straightforwardly removed, and the symmetrized (still gauge-invariant) tensor then takes on its widely used form. Angular momentum conservation follows immediately. For any harmonic gauge, however, the stress tensor found is manifestly symmetric from the start, and its derivation depends, in its entirety, on the structure of the linearized wave equation.

Electromagnetic fields with vanishing quantum corrections

NASA Astrophysics Data System (ADS)

Ortaggio, Marcello; Pravda, Vojtěch

2018-04-01

We show that a large class of null electromagnetic fields are immune to any modifications of Maxwell's equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any generalized classical electrodynamics containing both non-linear terms and higher derivatives, including, e.g., non-linear electrodynamics as well as QED- and string-motivated effective theories. This result holds not only in a flat or (anti-)de Sitter background, but also in a larger subset of Kundt spacetimes, which allow for the presence of aligned gravitational waves and pure radiation.

Phantom behavior bounce with tachyon and non-minimal derivative coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banijamali, A.; Fazlpour, B., E-mail: a.banijamali@nit.ac.ir, E-mail: b.fazlpour@umz.ac.ir

2012-01-01

The bouncing cosmology provides a successful solution of the cosmological singularity problem. In this paper, we study the bouncing behavior of a single scalar field model with tachyon field non-minimally coupled to itself, its derivative and to the curvature. By utilizing the numerical calculations we will show that the bouncing solution can appear in the universe dominated by such a quintom matter with equation of state crossing the phantom divide line. We also investigate the classical stability of our model using the phase velocity of the homogeneous perturbations of the tachyon scalar field.

A quantum Rosetta Stone for the information paradox

NASA Astrophysics Data System (ADS)

Pando Zayas, Leopoldo A.

2014-11-01

The black hole information loss paradox epitomizes the contradictions between general relativity and quantum field theory. The AdS/conformal field theory (CFT) correspondence provides an implicit answer for the information loss paradox in black hole physics by equating a gravity theory with an explicitly unitary field theory. Gravitational collapse in asymptotically AdS spacetimes is generically turbulent. Given that the mechanism to read out the information about correlations functions in the field theory side is plagued by deterministic classical chaos, we argue that quantum chaos might provide the true Rosetta Stone for answering the information paradox in the context of the AdS/CFT correspondence.

Completed Beltrami-Michell Formulation for Analyzing Radially Symmetrical Bodies

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Saigal, Sunil; Hopkins, Dale A.; Patnaik, Surya N.

1994-01-01

A force method formulation, the completed Beltrami-Michell formulation (CBMF), has been developed for analyzing boundary value problems in elastic continua. The CBMF is obtained by augmenting the classical Beltrami-Michell formulation with novel boundary compatibility conditions. It can analyze general elastic continua with stress, displacement, or mixed boundary conditions. The CBMF alleviates the limitations of the classical formulation, which can solve stress boundary value problems only. In this report, the CBMF is specialized for plates and shells. All equations of the CBMF, including the boundary compatibility conditions, are derived from the variational formulation of the integrated force method (IFM). These equations are defined only in terms of stresses. Their solution for kinematically stable elastic continua provides stress fields without any reference to displacements. In addition, a stress function formulation for plates and shells is developed by augmenting the classical Airy's formulation with boundary compatibility conditions expressed in terms of the stress function. The versatility of the CBMF and the augmented stress function formulation is demonstrated through analytical solutions of several mixed boundary value problems. The example problems include a composite circular plate and a composite circular cylindrical shell under the simultaneous actions of mechanical and thermal loads.

On the transition towards slow manifold in shallow-water and 3D Euler equations in a rotating frame

NASA Technical Reports Server (NTRS)

Mahalov, A.

1994-01-01

The long-time, asymptotic state of rotating homogeneous shallow-water equations is investigated. Our analysis is based on long-time averaged rotating shallow-water equations describing interactions of large-scale, horizontal, two-dimensional motions with surface inertial-gravity waves field for a shallow, uniformly rotating fluid layer. These equations are obtained in two steps: first by introducing a Poincare/Kelvin linear propagator directly into classical shallow-water equations, then by averaging. The averaged equations describe interaction of wave fields with large-scale motions on time scales long compared to the time scale 1/f(sub o) introduced by rotation (f(sub o)/2-angular velocity of background rotation). The present analysis is similar to the one presented by Waleffe (1991) for 3D Euler equations in a rotating frame. However, since three-wave interactions in rotating shallow-water equations are forbidden, the final equations describing the asymptotic state are simplified considerably. Special emphasis is given to a new conservation law found in the asymptotic state and decoupling of the dynamics of the divergence free part of the velocity field. The possible rising of a decoupled dynamics in the asymptotic state is also investigated for homogeneous turbulence subjected to a background rotation. In our analysis we use long-time expansion, where the velocity field is decomposed into the 'slow manifold' part (the manifold which is unaffected by the linear 'rapid' effects of rotation or the inertial waves) and a formal 3D disturbance. We derive the physical space version of the long-time averaged equations and consider an invariant, basis-free derivation. This formulation can be used to generalize Waleffe's (1991) helical decomposition to viscous inhomogeneous flows (e.g. problems in cylindrical geometry with no-slip boundary conditions on the cylinder surface and homogeneous in the vertical direction).

Quantum optical signatures in strong-field laser physics: Infrared photon counting in high-order-harmonic generation.

PubMed

Gonoskov, I A; Tsatrafyllis, N; Kominis, I K; Tzallas, P

2016-09-07

We analytically describe the strong-field light-electron interaction using a quantized coherent laser state with arbitrary photon number. We obtain a light-electron wave function which is a closed-form solution of the time-dependent Schrödinger equation (TDSE). This wave function provides information about the quantum optical features of the interaction not accessible by semi-classical theories. With this approach we can reveal the quantum optical properties of high harmonic generation (HHG) process in gases by measuring the photon statistics of the transmitted infrared (IR) laser radiation. This work can lead to novel experiments in high-resolution spectroscopy in extreme-ultraviolet (XUV) and attosecond science without the need to measure the XUV light, while it can pave the way for the development of intense non-classical light sources.

Chaos in a 4D dissipative nonlinear fermionic model

NASA Astrophysics Data System (ADS)

Aydogmus, Fatma

2015-12-01

Gursey Model is the only possible 4D conformally invariant pure fermionic model with a nonlinear self-coupled spinor term. It has been assumed to be similar to the Heisenberg's nonlinear generalization of Dirac's equation, as a possible basis for a unitary description of elementary particles. Gursey Model admits particle-like solutions for the derived classical field equations and these solutions are instantonic in character. In this paper, the dynamical nature of damped and forced Gursey Nonlinear Differential Equations System (GNDES) are studied in order to get more information on spinor type instantons. Bifurcation and chaos in the system are observed by constructing the bifurcation diagrams and Poincaré sections. Lyapunov exponent and power spectrum graphs of GNDES are also constructed to characterize the chaotic behavior.

Integral equation methods for vesicle electrohydrodynamics in three dimensions

NASA Astrophysics Data System (ADS)

Veerapaneni, Shravan

2016-12-01

In this paper, we develop a new boundary integral equation formulation that describes the coupled electro- and hydro-dynamics of a vesicle suspended in a viscous fluid and subjected to external flow and electric fields. The dynamics of the vesicle are characterized by a competition between the elastic, electric and viscous forces on its membrane. The classical Taylor-Melcher leaky-dielectric model is employed for the electric response of the vesicle and the Helfrich energy model combined with local inextensibility is employed for its elastic response. The coupled governing equations for the vesicle position and its transmembrane electric potential are solved using a numerical method that is spectrally accurate in space and first-order in time. The method uses a semi-implicit time-stepping scheme to overcome the numerical stiffness associated with the governing equations.

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

DOE PAGES

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

2017-10-26

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin

The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an examplemore » of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.« less

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

On Faraday Instability in Magnetic Liquids: Ince-Erdelyi Approach Applied to the Hill Equation Describing Oscillations of a Ferrofluid Free Surface

NASA Astrophysics Data System (ADS)

Hennenberg, M.; Slavtchev, S.; Valchev, G.

2013-12-01

When an isothermal ferrofluid is submitted to an oscillating magnetic field, the initially motionless liquid free surface can start to oscillate. This physical phenomenon is similar to the Faraday instability for usual Newtonian liquids subjected to a mechanical oscillation. In the present paper, we consider the magnetic field as a sum of a constant part and a time periodic part. Two different cases for the constant part of the field, being vertical in the first one or horizontal in the second one are studied. Assuming both ferrofluid magnetization and magnetic field to be collinear, we develop the linear stability analysis of the motionless reference state taking into account the Kelvin magnetic forces. The Laplace law describing the free surface deformation reduces to Hill's equation, which is studied using the classical method of Ince and Erdelyi. Inside this framework, we obtain the transition conditions leading to the free surface oscillations.

The Mochi project: a field theory approach to plasma dynamics and self-organization

NASA Astrophysics Data System (ADS)

You, Setthivoine; von der Linden, Jens; Lavine, Eric Sander; Card, Alexander; Carroll, Evan

2016-10-01

The Mochi project is designed to study the interaction between plasma flows and magnetic fields from the point-of-view of canonical flux tubes. The Mochi Labjet experiment is being commissioned after achieving first plasma. Analytical and numerical tools are being developed to visualize canonical flux tubes. One analytical tool described here is a field theory approach to plasma dynamics and self-organization. A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. This work is supported by by US DOE Grant DE-SC0010340.

Scattering of massless scalar waves by magnetically charged black holes in Einstein-Yang-Mills-Higgs theory

NASA Astrophysics Data System (ADS)

Gußmann, Alexander

2017-03-01

The existence of the classical black hole solutions of the Einstein-Yang-Mills-Higgs equations with non-Abelian Yang-Mills-Higgs hair implies that not all classical stationary magnetically charged black holes can be uniquely described by their asymptotic characteristics. In fact, in a certain domain of parameters, there exist different spherically-symmetric, non-rotating and asymptotically-flat classical black hole solutions of the Einstein-Yang-Mills-Higgs equations which have the same ADM mass and the same magnetic charge but significantly different geometries in the near-horizon regions. (These are black hole solutions which are described by a Reissner-Nordström metric on the one hand and the black hole solutions with non-Abelian Yang-Mills-Higgs hair which are described by a metric which is not of Reissner-Nordström form on the other hand). One can experimentally distinguish such black holes with the same asymptotic characteristics but different near-horizon geometries classically by probing the near-horizon regions of the black holes. We argue that one way to probe the near-horizon region of a black hole which allows one to distinguish magnetically charged black holes with the same asymptotic characteristics but different near-horizon geometries is by classical scattering of waves. Using the example of a minimally-coupled massless probe scalar field scattered by magnetically charged black holes which can be obtained as solutions of the Einstein-Yang-Mills-Higgs equations with a Higgs triplet and gauge group SU(2) in the limit of an infinite Higgs self-coupling constant we show how, in this case, the scattering cross sections differ for the magnetically charged black holes with different near-horizon geometries but the same asymptotic characteristics. We find in particular that the characteristic glory peaks in the cross sections are located at different scattering angles.

Towards a Unified Field Theory for Classical Electrodynamics

NASA Astrophysics Data System (ADS)

Benci, Vieri; Fortunato, Donato

2004-09-01

In this paper we introduce a model which describes the relation of matter and the electromagnetic field from a unitarian standpoint in the spirit of ideas of Born and Infeld. In this model, based on a semilinear perturbation of Maxwell equations, the particles are finite-energy solitary waves due to the presence of the nonlinearity. In this respect the matter and the electromagnetic field have the same nature. Finite energy means that particles have finite mass and this makes electrodynamics consistent with the special relativity. We analyze the invariants of the motion of the semilinear Maxwell equations (SME) and their static solutions. In the magnetostatic case (i.e., when the electric field E = 0 and the magnetic field H does not depend on time) SME are reduced to the semilinear equation where ∇× denotes the curloperator, f‧ is the gradient of a strictly convex smooth function f:R3→R and A:R3→R3 is the gauge potential related to the magnetic field H (H = ∇× A). Due to the presence of the curl operator, (1) is a strongly degenerate elliptic equation. Moreover, physical considerations impel f to be flat at zero (f‧‧(0)=0) and this fact leads us to study the problem in a functional setting related to the Orlicz space Lp+Lq. The existence of a nontrivial finite- energy solution of (1) is proved under suitable growth conditions on f. The proof is carried out by using a suitable variational framework related to the Hodge splitting of the vector field A.

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

Trajectory-based understanding of the quantum-classical transition for barrier scattering

NASA Astrophysics Data System (ADS)

Chou, Chia-Chun

2018-06-01

The quantum-classical transition of wave packet barrier scattering is investigated using a hydrodynamic description in the framework of a nonlinear Schrödinger equation. The nonlinear equation provides a continuous description for the quantum-classical transition of physical systems by introducing a degree of quantumness. Based on the transition equation, the transition trajectory formalism is developed to establish the connection between classical and quantum trajectories. The quantum-classical transition is then analyzed for the scattering of a Gaussian wave packet from an Eckart barrier and the decay of a metastable state. Computational results for the evolution of the wave packet and the transmission probabilities indicate that classical results are recovered when the degree of quantumness tends to zero. Classical trajectories are in excellent agreement with the transition trajectories in the classical limit, except in some regions where transition trajectories cannot cross because of the single-valuedness of the transition wave function. As the computational results demonstrate, the process that the Planck constant tends to zero is equivalent to the gradual removal of quantum effects originating from the quantum potential. This study provides an insightful trajectory interpretation for the quantum-classical transition of wave packet barrier scattering.

From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''

NASA Astrophysics Data System (ADS)

Bergeron, H.

2001-09-01

Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence principle). Moreover spins for particles are naturally generated, including an approximation of their interaction with magnetic fields. We also recover by this approach the semi-classical formalism developed by E. Prugovečki [Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)].

Peridynamic thermal diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oterkus, Selda; Madenci, Erdogan, E-mail: madenci@email.arizona.edu; Agwai, Abigail

This study presents the derivation of ordinary state-based peridynamic heat conduction equation based on the Lagrangian formalism. The peridynamic heat conduction parameters are related to those of the classical theory. An explicit time stepping scheme is adopted for numerical solution of various benchmark problems with known solutions. It paves the way for applying the peridynamic theory to other physical fields such as neutronic diffusion and electrical potential distribution.

On Generalized Continuous D Semi-Classical Hermite and Chebychev Orthogonal Polynomials of Class One

NASA Astrophysics Data System (ADS)

Azatassou, E.; Hounkonnou, M. N.

2002-10-01

In this contribution, starting from the system of equations for recurrence coefficients generated by continuous D semi-classical Laguerre-Freud equations of class 1, we deduce the β constant recurrence relation coefficient γn leading to the generalized D semi-classical Hermite and Chebychev orthogonal polynomials of class 1. Various interesting cases are pointed out.

The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation

NASA Astrophysics Data System (ADS)

Filipuk, Galina; Van Assche, Walter; Zhang, Lun

2012-05-01

We show that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semi-classical extension of the Laguerre weight satisfy the fourth Painlevé equation when viewed as functions of one of the parameters in the weight. We compare different approaches to derive this result, namely, the ladder operators approach, the isomonodromy deformations approach and combining the Toda system for the recurrence coefficients with a discrete equation. We also discuss a relation between the recurrence coefficients for the Freud weight and the semi-classical Laguerre weight and show how it arises from the Bäcklund transformation of the fourth Painlevé equation.

Finite element solution of torsion and other 2-D Poisson equations

NASA Technical Reports Server (NTRS)

Everstine, G. C.

1982-01-01

The NASTRAN structural analysis computer program may be used, without modification, to solve two dimensional Poisson equations such as arise in the classical Saint Venant torsion problem. The nonhomogeneous term (the right-hand side) in the Poisson equation can be handled conveniently by specifying a gravitational load in a "structural" analysis. The use of an analogy between the equations of elasticity and those of classical mathematical physics is summarized in detail.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sugama, H.; Nunami, M.; Department of Fusion Science, SOKENDAI

Effects of collisions on conservation laws for toroidal plasmas are investigated based on the gyrokinetic field theory. Associating the collisional system with a corresponding collisionless system at a given time such that the two systems have the same distribution functions and electromagnetic fields instantaneously, it is shown how the collisionless conservation laws derived from Noether's theorem are modified by the collision term. Effects of the external source term added into the gyrokinetic equation can be formulated similarly with the collisional effects. Particle, energy, and toroidal momentum balance equations including collisional and turbulent transport fluxes are systematically derived using a novelmore » gyrokinetic collision operator, by which the collisional change rates of energy and canonical toroidal angular momentum per unit volume in the gyrocenter space can be given in the conservative forms. The ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include classical, neoclassical, and turbulent transport fluxes which agree with those derived from conventional recursive formulations.« less

Lie-algebraic Approach to Dynamics of Closed Quantum Systems and Quantum-to-Classical Correspondence

NASA Astrophysics Data System (ADS)

Galitski, Victor

2012-02-01

I will briefly review our recent work on a Lie-algebraic approach to various non-equilibrium quantum-mechanical problems, which has been motivated by continuous experimental advances in the field of cold atoms. First, I will discuss non-equilibrium driven dynamics of a generic closed quantum system. It will be emphasized that mathematically a non-equilibrium Hamiltonian represents a trajectory in a Lie algebra, while the evolution operator is a trajectory in a Lie group generated by the underlying algebra via exponentiation. This turns out to be a constructive statement that establishes, in particular, the fact that classical and quantum unitary evolutions are two sides of the same coin determined uniquely by the same dynamic generators in the group. An equation for these generators - dubbed dual Schr"odinger-Bloch equation - will be derived and analyzed for a few of specific examples. This non-linear equation allows one to construct new exact non-linear solutions to quantum-dynamical systems. An experimentally-relevant example of a family of exact solutions to the many-body Landau-Zener problem will be presented. One practical application of the latter result includes dynamical means to optimize molecular production rate following a quench across the Feshbach resonance.

Insight into the Li{sub 2}CO{sub 3}–K{sub 2}CO{sub 3} eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corradini, Dario; Vuilleumier, Rodolphe, E-mail: rodolphe.vuilleumier@ens.fr; Sorbonne Universités, UPMC Univ. Paris 06, PASTEUR, 75005 Paris

We use molecular dynamics simulations to study the thermodynamics, structure, and dynamics of the Li{sub 2}CO{sub 3}–K{sub 2}CO{sub 3} (62:38 mol. %) eutectic mixture. We present a new classical non-polarizable force field for this molten salt mixture, optimized using experimental and first principles molecular dynamics simulations data as reference. This simple force field allows efficient molecular simulations of phenomena at long time scales. We use this optimized force field to describe the behavior of the eutectic mixture in the 900–1100 K temperature range, at pressures between 0 and 5 GPa. After studying the equation of state in these thermodynamic conditions, wemore » present molecular insight into the structure and dynamics of the melt. In particular, we present an analysis of the temperature and pressure dependence of the eutectic mixture’s self-diffusion coefficients, viscosity, and ionic conductivity.« less

Theoretical analysis of optical poling and frequency doubling effect based on classical model

NASA Astrophysics Data System (ADS)

Feng, Xi; Li, Fuquan; Lin, Aoxiang; Wang, Fang; Chai, Xiangxu; Wang, Zhengping; Zhu, Qihua; Sun, Xun; Zhang, Sen; Sun, Xibo

2018-03-01

Optical poling and frequency doubling effect is one of the effective manners to induce second order nonlinearity and realize frequency doubling in glass materials. The classical model believes that an internal electric field is built in glass when it's exposed by fundamental and frequency-doubled light at the same time, and second order nonlinearity appears as a result of the electric field and the orientation of poles. The process of frequency doubling in glass is quasi phase matched. In this letter, the physical process of poling and doubling process in optical poling and frequency doubling effect is deeply discussed in detail. The magnitude and direction of internal electric field, second order nonlinear coefficient and its components, strength and direction of frequency doubled output signal, quasi phase matched coupled wave equations are given in analytic expression. Model of optical poling and frequency doubling effect which can be quantitatively analyzed are constructed in theory, which set a foundation for intensive study of optical poling and frequency doubling effect.

Scaling analysis and instantons for thermally assisted tunneling and quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Smelyanskiy, Vadim N.; Isakov, Sergei V.; Boixo, Sergio; Mazzola, Guglielmo; Troyer, Matthias; Neven, Hartmut

2017-01-01

We develop an instantonic calculus to derive an analytical expression for the thermally assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path-integral quantum Monte Carlo (QMC). We show analytically that the exponential scaling with the number of spins of the thermally assisted quantum tunneling rate and the escape rate of the QMC process are identical. We relate this effect to the existence of a dominant instantonic tunneling path. The instanton trajectory is described by nonlinear dynamical mean-field theory equations for a single-site magnetization vector, which we solve exactly. Finally, we derive scaling relations for the "spiky" barrier shape when the spin tunneling and QMC rates scale polynomially with the number of spins N while a purely classical over-the-barrier activation rate scales exponentially with N .

Computational-hydrodynamic studies of the Noh compressible flow problem using non-ideal equations of state

NASA Astrophysics Data System (ADS)

Honnell, Kevin; Burnett, Sarah; Yorke, Chloe'; Howard, April; Ramsey, Scott

2017-06-01

The Noh problem is classic verification problem in the field of compressible flows. Simple to conceptualize, it is nonetheless difficult for numerical codes to predict correctly, making it an ideal code-verification test bed. In its original incarnation, the fluid is a simple ideal gas; once validated, however, these codes are often used to study highly non-ideal fluids and solids. In this work the classic Noh problem is extended beyond the commonly-studied polytropic ideal gas to more realistic equations of state (EOS) including the stiff gas, the Nobel-Abel gas, and the Carnahan-Starling hard-sphere fluid, thus enabling verification studies to be performed on more physically-realistic fluids. Exact solutions are compared with numerical results obtained from the Lagrangian hydrocode FLAG, developed at Los Alamos. For these more realistic EOSs, the simulation errors decreased in magnitude both at the origin and at the shock, but also spread more broadly about these points compared to the ideal EOS. The overall spatial convergence rate remained first order.

Brownian motion of classical spins: Anomalous dissipation and generalized Langevin equation

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Malay; Jayannavar, A. M.

2017-10-01

In this work, we derive the Langevin equation (LE) of a classical spin interacting with a heat bath through momentum variables, starting from the fully dynamical Hamiltonian description. The derived LE with anomalous dissipation is analyzed in detail. The obtained LE is non-Markovian with multiplicative noise terms. The concomitant dissipative terms obey the fluctuation-dissipation theorem. The Markovian limit correctly produces the Kubo and Hashitsume equation. The perturbative treatment of our equations produces the Landau-Lifshitz equation and the Seshadri-Lindenberg equation. Then we derive the Fokker-Planck equation corresponding to LE and the concept of equilibrium probability distribution is analyzed.

Principles of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Landé, Alfred

2013-10-01

Preface; Introduction: 1. Observation and interpretation; 2. Difficulties of the classical theories; 3. The purpose of quantum theory; Part I. Elementary Theory of Observation (Principle of Complementarity): 4. Refraction in inhomogeneous media (force fields); 5. Scattering of charged rays; 6. Refraction and reflection at a plane; 7. Absolute values of momentum and wave length; 8. Double ray of matter diffracting light waves; 9. Double ray of matter diffracting photons; 10. Microscopic observation of ρ (x) and σ (p); 11. Complementarity; 12. Mathematical relation between ρ (x) and σ (p) for free particles; 13. General relation between ρ (q) and σ (p); 14. Crystals; 15. Transition density and transition probability; 16. Resultant values of physical functions; matrix elements; 17. Pulsating density; 18. General relation between ρ (t) and σ (є); 19. Transition density; matrix elements; Part II. The Principle of Uncertainty: 20. Optical observation of density in matter packets; 21. Distribution of momenta in matter packets; 22. Mathematical relation between ρ and σ; 23. Causality; 24. Uncertainty; 25. Uncertainty due to optical observation; 26. Dissipation of matter packets; rays in Wilson Chamber; 27. Density maximum in time; 28. Uncertainty of energy and time; 29. Compton effect; 30. Bothe-Geiger and Compton-Simon experiments; 31. Doppler effect; Raman effect; 32. Elementary bundles of rays; 33. Jeans' number of degrees of freedom; 34. Uncertainty of electromagnetic field components; Part III. The Principle of Interference and Schrödinger's equation: 35. Physical functions; 36. Interference of probabilities for p and q; 37. General interference of probabilities; 38. Differential equations for Ψp (q) and Xq (p); 39. Differential equation for фβ (q); 40. The general probability amplitude Φβ' (Q); 41. Point transformations; 42. General theorem of interference; 43. Conjugate variables; 44. Schrödinger's equation for conservative systems; 45. Schrödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.

The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect

NASA Astrophysics Data System (ADS)

Archer, Andrew J.; Chacko, Blesson; Evans, Robert

2017-07-01

In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.

An application of information theory to stochastic classical gravitational fields

NASA Astrophysics Data System (ADS)

Angulo, J.; Angulo, J. C.; Angulo, J. M.

2018-06-01

The objective of this study lies on the incorporation of the concepts developed in the Information Theory (entropy, complexity, etc.) with the aim of quantifying the variation of the uncertainty associated with a stochastic physical system resident in a spatiotemporal region. As an example of application, a relativistic classical gravitational field has been considered, with a stochastic behavior resulting from the effect induced by one or several external perturbation sources. One of the key concepts of the study is the covariance kernel between two points within the chosen region. Using this concept and the appropriate criteria, a methodology is proposed to evaluate the change of uncertainty at a given spatiotemporal point, based on available information and efficiently applying the diverse methods that Information Theory provides. For illustration, a stochastic version of the Einstein equation with an added Gaussian Langevin term is analyzed.

Transferable Pseudo-Classical Electrons for Aufbau of Atomic Ions

PubMed Central

Ekesan, Solen; Kale, Seyit; Herzfeld, Judith

2014-01-01

Generalizing the LEWIS reactive force field from electron pairs to single electrons, we present LEWIS• in which explicit valence electrons interact with each other and with nuclear cores via pairwise interactions. The valence electrons are independently mobile particles, following classical equations of motion according to potentials modified from Coulombic as required to capture quantum characteristics. As proof of principle, the aufbau of atomic ions is described for diverse main group elements from the first three rows of the periodic table, using a single potential for interactions between electrons of like spin and another for electrons of unlike spin. The electrons of each spin are found to distribute themselves in a fashion akin to the major lobes of the hybrid atomic orbitals, suggesting a pointillist description of the electron density. The broader validity of the LEWIS• force field is illustrated by predicting the vibrational frequencies of diatomic and triatomic hydrogen species. PMID:24752384

Normalization in Lie algebras via mould calculus and applications

NASA Astrophysics Data System (ADS)

Paul, Thierry; Sauzin, David

2017-11-01

We establish Écalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincaré-Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging procedure for vector fields with fast angular variables (Hamiltonian or not), or the construction of Birkhoff normal forms both in classical and quantum situations. As a by-product we obtain, in the case of harmonic oscillators, the convergence of the quantum Birkhoff form to the classical one, without any Diophantine hypothesis on the frequencies of the unperturbed Hamiltonians.

Instantons in Lifshitz field theories

NASA Astrophysics Data System (ADS)

Fujimori, Toshiaki; Nitta, Muneto

2015-10-01

BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.

Turbulence in transient solar phenomena

NASA Technical Reports Server (NTRS)

Cross, M.

1982-01-01

If theta dependence is kept in the Navier-Stokes equations for the solar wind, than a density enhancement will grow. This growth is followed in the nonlinear equations until a streamer is formed. Viscosity stops the streamer's growth when there is a large difference in speeds inside and outside of the streamer. Using classical fluid mechanics and a latitude dependent hydrodynamical model, it is shown that unmagnetized perturbed flow evolves into high and low density regions. The growth mechanisms for density enrichments are discussed along with a nonlinear solution for their large amplitude development. It was found that a higher Reynolds number is needed to start turbulence in the presence of a magnetic field because energy is required to bend the field lines attached to the fluid. If cosmological gas was turbulent shortly after the big bang, then galaxies could have been formed by turbulent eddies.

Classical relativistic model for spin dependence in a magnetized electron gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Melrose, D. B.; Mushtaq, A.; TPPD, PINSTECH, P. O. Nilore Islamabad 44000

2011-05-15

The response of a cold electron gas is generalized to include the spin of the electron described by the relativistically correct quasiclassical Bargmann-Michel-Telegdi (BMT) equation. The magnetization of the electron gas is assumed to be along the background magnetic field B and the spin-dependent contribution to the response tensor is proportional to the magnitude of the magnetization. The dispersion equation is shown to be quadratic in the refractive index squared, and dispersion curves for the two wave modes are plotted for cases where the magnetic field associated with magnetization is comparable with B. Two intrinsically spin-dependent wave modes are identified:more » one bounded by two resonances and the other by two cutoffs. The counterpart of the z mode can escape without encountering a resonance or a cutoff.« less

G-Strands on symmetric spaces

PubMed Central

2017-01-01

We study the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G, and we treat in more detail examples with symmetric space SU(2)/S1 and SO(4)/SO(3). The latter model simplifies to an apparently new integrable nine-dimensional system. We also study the G-strands on the infinite dimensional group of diffeomorphisms, which gives, together with the Sobolev norm, systems of 1+2 Camassa–Holm equations. The solutions of these equations on the complementary space related to the Witt algebra decomposition are the odd function solutions. PMID:28413343

Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

NASA Astrophysics Data System (ADS)

Yu, Han; Chen, Yuqing; Hanafy, Sherif M.; Huang, Jiangping

2018-04-01

A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes the squared sum of the traveltime residuals. Even though, wave-equation traveltime inversion can partly avoid the cycle skipping problem, a good initial velocity model is required for the inversion to converge to a reasonable tomogram with different attenuation profiles. When Q model is far away from the real model, the final tomogram is very sensitive to the starting velocity model. Nevertheless, a minor or moderate perturbation of the Q model from the true one does not strongly affect the inversion if the low wavenumber information of the initial velocity model is mostly correct. These claims are validated with numerical tests on both the synthetic and field data sets.

A CLASSICAL ANALOG FOR RELATIVISTIC CONTRACTION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Epstein, L.

1963-12-01

It is possible to construct a mechanical model that demonstrates the Fitzgerald contraction. An equation is derived to describe the shape of a dimple moving across an elastic membrane, clearly showing the analogy to the field of a point charge in free space, including the relativistic contraction in the direction of motion. This model should suggest some reason to the inquiring mind that persists in wondering---- what really makes it shrink.'' (auth)

Theoretical princi les of constructing the equations of motion for a spin color-charged particle in gauge and fermion fields

NASA Astrophysics Data System (ADS)

Markov, Yu. A.; Shishmarev, A. A.

2010-11-01

Based on the most general principles of materiality, gauge, and re-parameterized invariance, the problem of constructing an action describing the dynamics of a classical color-charged particle moving in external non-Abelian gauge and fermion fields is considered. The case of a linear Lagrangian dependence on the external fermion fields is discussed. Within the framework of the description of the color degree of freedom of the particle with half-integer spin by the Grassmann color charges, a new concept of the Grassmann color source of the particle being a fermion analog of the conventional color current is introduced.

Stochastic effects in hybrid inflation

NASA Astrophysics Data System (ADS)

Martin, Jérôme; Vennin, Vincent

2012-02-01

Hybrid inflation is a two-field model where inflation ends due to an instability. In the neighborhood of the instability point, the potential is very flat and the quantum fluctuations dominate over the classical motion of the inflaton and waterfall fields. In this article, we study this regime in the framework of stochastic inflation. We numerically solve the two coupled Langevin equations controlling the evolution of the fields and compute the probability distributions of the total number of e-folds and of the inflation exit point. Then, we discuss the physical consequences of our results, in particular, the question of how the quantum diffusion can affect the observable predictions of hybrid inflation.

BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

Modern gyrokinetic formulation of collisional and turbulent transport in toroidally rotating plasmas

NASA Astrophysics Data System (ADS)

Sugama, H.

2017-12-01

Collisional and turbulent transport processes in toroidal plasmas with large toroidal flows on the order of the ion thermal velocity are formulated based on the modern gyrokinetic theory. Governing equations for background and turbulent electromagnetic fields and gyrocenter distribution functions are derived from the Lagrangian variational principle with effects of collisions and external sources taken into account. Noether's theorem modified for collisional systems and the collision operator given in terms of Poisson brackets are applied to derivation of the particle, energy, and toroidal momentum balance equations in the conservative forms which are desirable properties for long-time global transport simulation. The resultant balance equations are shown to include the classical, neoclassical, and turbulent transport fluxes which agree with those obtained from the conventional recursive formulations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Remming, Ian S.; Khokhlov, Alexei M.

We present general equations for non-ideal, reactive flow magnetohydrodynamics (RFMHD) in the form best suited for describing thermonuclear combustion in high-density degenerate matter of SNe Ia. The relative importance of various non-ideal effects is analyzed as a function of characteristic spatial and temporal scales of the problem. From the general RFMHD equations, we derive the one-dimensional ordinary differential equations describing the steady-state propagation of a planar thermonuclear flame front in a magnetic field. The physics of the flame is first studied qualitatively using a simple case of one-step Arrhenius kinetics, a perfect gas equation of state (EOS), and constant thermalmore » conductivity coefficients. After that, the equations are solved, the internal flame front structure is calculated, and the flame velocity, S {sub l} , and flame thickness, δ {sub l} , are found for carbon–oxygen degenerate material of supernovae using a realistic EOS, transport properties, and detailed nuclear kinetics. The magnetic field changes the flame behavior significantly, both qualitatively and quantitatively, as compared to the non-magnetic case of classical combustion. (1) The magnetic field influences the evolutionarity of a flame front and makes it impossible for a flame to propagate steadily in a wide range of magnetic field strengths and orientations relative to the front. (2) When the flame moves steadily, it can propagate in several distinct modes, the most important being the slow C {sub S} and super-Alfvénic C {sub sup} modes. (3) The speed of the flame can be diminished or enhanced by up to several factors relative to the non-magnetic laminar flame speed.« less

Nonequilibrium Precondensation of Classical Waves in Two Dimensions Propagating through Atomic Vapors

NASA Astrophysics Data System (ADS)

Šantić, Neven; Fusaro, Adrien; Salem, Sabeur; Garnier, Josselin; Picozzi, Antonio; Kaiser, Robin

2018-02-01

The nonlinear Schrödinger equation, used to describe the dynamics of quantum fluids, is known to be valid not only for massive particles but also for the propagation of light in a nonlinear medium, predicting condensation of classical waves. Here we report on the initial evolution of random waves with Gaussian statistics using atomic vapors as an efficient two dimensional nonlinear medium. Experimental and theoretical analysis of near field images reveal a phenomenon of nonequilibrium precondensation, characterized by a fast relaxation towards a precondensate fraction of up to 75%. Such precondensation is in contrast to complete thermalization to the Rayleigh-Jeans equilibrium distribution, requiring prohibitive long interaction lengths.

Einstein-Langevin and Einstein-Fokker-Planck equations for Oppenheimer-Snyder gravitational collapse in a spacetime with conformal vacuum fluctuations

NASA Astrophysics Data System (ADS)

Miller, Steven David

1999-10-01

A consistent extension of the Oppenheimer-Snyder gravitational collapse formalism is presented which incorporates stochastic, conformal, vacuum fluctuations of the metric tensor. This results in a tractable approach to studying the possible effects of vacuum fluctuations on collapse and singularity formation. The motivation here, is that it is known that coupling stochastic noise to a classical field theory can lead to workable methodologies that accommodate or reproduce many aspects of quantum theory, turbulence or structure formation. The effect of statistically averaging over the metric fluctuations gives the appearance of a deterministic Riemannian structure, with an induced non-vanishing cosmological constant arising from the nonlinearity. The Oppenheimer-Snyder collapse of a perfect fluid or dust star in the fluctuating or `turbulent' spacetime, is reformulated in terms of nonlinear Einstein-Langevin field equations, with an additional noise source in the energy-momentum tensor. The smooth deterministic worldlines of collapsing matter within the classical Oppenheimer-Snyder model, now become nonlinear Brownian motions due to the backreaction induced by vacuum fluctuations. As the star collapses, the matter worldlines become increasingly randomized since the backreaction coupling to the vacuum fluctuations is nonlinear; the input assumptions of the Hawking-Penrose singularity theorems should then be violated. Solving the nonlinear Einstein-Langevin field equation for collapse - via the Ito interpretation - gives a singularity-free solution, which is equivalent to the original Oppenheimer solution but with higher-order stochastic corrections; the original singular solution is recovered in the limit of zero vacuum fluctuations. The `geometro-hydrodynamics' of noisy gravitational collapse, were also translated into an equivalent mathematical formulation in terms of nonlinear Einstein-Fokker-Planck (EFP) continuity equations with respect to comoving coordinates: these describe the collapse as a conserved flow of probability. A solution was found in the dilute limit of weak fluctuations where the EFP equation is linearized. There is zero probability that the star collapses to a singular state in the presence of background vacuum fluctuations, but the singularity returns with unit probability when the fluctuations are reduced to zero. Finally, an EFP equation was considered with respect to standard exterior coordinates. Using the thermal Brownian motion paradigm, an exact stationary or equilibrium solution was found in the infinite standard time relaxation limit. The solution gives the conditions required for the final collapsed object (a black hole) to be in thermal equilibrium with the background vacuum fluctuations. From this solution, one recovers the Hawking temperature without using field theory. The stationary solution then seems to correspond to a black hole in thermal equilibrium with a fluctuating conformal scalar field; or the Hawking-Hartle state.

Quantum mechanical expansion of variance of a particle in a weakly non-uniform electric and magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chan, Poh Kam; Kosaka, Wataru; Oikawa, Shun-ichi

We have solved the Heisenberg equation of motion for the time evolution of the position and momentum operators for a non-relativistic spinless charged particle in the presence of a weakly non-uniform electric and magnetic field. It is shown that the drift velocity operator obtained in this study agrees with the classical counterpart, and that, using the time dependent operators, the variances in position and momentum grow with time. The expansion rate of variance in position and momentum are dependent on the magnetic gradient scale length, however, independent of the electric gradient scale length. In the presence of a weakly non-uniformmore » electric and magnetic field, the theoretical expansion rates of variance expansion are in good agreement with the numerical analysis. It is analytically shown that the variance in position reaches the square of the interparticle separation, which is the characteristic time much shorter than the proton collision time of plasma fusion. After this time, the wavefunctions of the neighboring particles would overlap, as a result, the conventional classical analysis may lose its validity. The broad distribution of individual particle in space means that their Coulomb interactions with other particles become weaker than that expected in classical mechanics.« less

Spinning particles, axion radiation, and the classical double copy

NASA Astrophysics Data System (ADS)

Goldberger, Walter D.; Li, Jingping; Prabhu, Siddharth G.

2018-05-01

We extend the perturbative double copy between radiating classical sources in gauge theory and gravity to the case of spinning particles. We construct, to linear order in spins, perturbative radiating solutions to the classical Yang-Mills equations sourced by a set of interacting color charges with chromomagnetic dipole spin couplings. Using a color-to-kinematics replacement rule proposed earlier by one of the authors, these solutions map onto radiation in a theory of interacting particles coupled to massless fields that include the graviton, a scalar (dilaton) ϕ and the Kalb-Ramond axion field Bμ ν. Consistency of the double copy imposes constraints on the parameters of the theory on both the gauge and gravity sides of the correspondence. In particular, the color charges carry a chromomagnetic interaction which, in d =4 , corresponds to a gyromagnetic ratio equal to Dirac's value g =2 . The color-to-kinematics map implies that on the gravity side, the bulk theory of the fields (ϕ ,gμ ν,Bμ ν) has interactions which match those of d -dimensional "string gravity," as is the case both in the BCJ double copy of pure gauge theory scattering amplitudes and the KLT relations between the tree-level S -matrix elements of open and closed string theory.

Early universe with modified scalar-tensor theory of gravity

NASA Astrophysics Data System (ADS)

Mandal, Ranajit; Sarkar, Chandramouli; Sanyal, Abhik Kumar

2018-05-01

Scalar-tensor theory of gravity with non-minimal coupling is a fairly good candidate for dark energy, required to explain late-time cosmic evolution. Here we study the very early stage of evolution of the universe with a modified version of the theory, which includes scalar curvature squared term. One of the key aspects of the present study is that, the quantum dynamics of the action under consideration ends up generically with de-Sitter expansion under semiclassical approximation, rather than power-law. This justifies the analysis of inflationary regime with de-Sitter expansion. The other key aspect is that, while studying gravitational perturbation, the perturbed generalized scalar field equation obtained from the perturbed action, when matched with the perturbed form of the background scalar field equation, relates the coupling parameter and the potential exactly in the same manner as the solution of classical field equations does, assuming de-Sitter expansion. The study also reveals that the quantum theory is well behaved, inflationary parameters fall well within the observational limit and quantum perturbation analysis shows that the power-spectrum does not deviate considerably from the standard one obtained from minimally coupled theory.

Stoichiometric network analysis and associated dimensionless kinetic equations. Application to a model of the Bray-Liebhafsky reaction.

PubMed

Schmitz, Guy; Kolar-Anić, Ljiljana Z; Anić, Slobodan R; Cupić, Zeljko D

2008-12-25

The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.

Stress in dilute suspensions

NASA Technical Reports Server (NTRS)

Passman, Stephen L.

1989-01-01

Generally, two types of theory are used to describe the field equations for suspensions. The so-called postulated equations are based on the kinetic theory of mixtures, which logically should give reasonable equations for solutions. The basis for the use of such theory for suspensions is tenuous, though it at least gives a logical path for mathematical arguments. It has the disadvantage that it leads to a system of equations which is underdetermined, in a sense that can be made precise. On the other hand, the so-called averaging theory starts with a determined system, but the very process of averaging renders the resulting system underdetermined. A third type of theory is proposed in which the kinetic theory of gases is used to motivate continuum equations for the suspended particles. This entails an interpretation of the stress in the particles that is different from the usual one. Classical theory is used to describe the motion of the suspending medium. The result is a determined system for a dilute suspension. Extension of the theory to more concentrated systems is discussed.

Solvent-Induced Shift of Spectral Lines in Polar–Polarizable Solvents

DOE PAGES

Matyushov, Dmitry V.; Newton, Marshall D.

2017-03-09

Solvent-induced shift of optical transition lines is traditionally described by the Lippert- McRae equation given in terms of the Onsager theory for dipole solvation. It splits the overall shift into the equilibrium solvation by induced dipoles and the reaction field by the permanent dipoles in equilibrium with the chromophore in the ground state. Here we have reconsidered this classical problem from the perspective of microscopic solvation theories. A microscopic solvation functional is derived and continuum solvation is consistently introduced by taking the limit of zero wavevector in the reciprocal-space solvation susceptibility functions. We show that the phenomenological expression for themore » reaction field of permanent dipoles in the Lippert-McRae equation is not consistent with the microscopic theory. The main deficiency of the Lippert- McRae equation equation is the use of additivity of the response by permanent and induced dipoles of the liquid. An alternative closed-form equation for the spectral shift is derived. Its continuum limit allows a new, non-additive functionality for the solvent-induced shift in terms of the high-frequency and static dielectric constants. Finally, the main qualitative outcome of the theory is a significantly weaker dependence of the spectral shift on the polarizability of the solvent than predicted by the Lippert-McRae formula.« less

Compressible Flow Toolbox

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.

A quasi-classical mechanism for microwave induced resistance oscillations in high mobility GaAs/AlGaAs 2DEG samples

NASA Astrophysics Data System (ADS)

Studenikin, S. A.; Fedorych, O. N.; Maude, D. K.; Potemski, M.; Sachrajda, A. S.; Wasilewski, Z. R.; Gupta, J. A.; Magarill, L. I.

2008-03-01

In this work we investigate microwave induced resistance oscillations (MIROs) in a GaAs/AlGaAs heterostructure containing a high mobility two-dimensional electron gas (2DEG). We show that MIROs can be explained within a purely classical mechanism based on the Boltzmann equation [L.I. Magarill, I.A. Panaev, S.A. Studenikin, Condens. Matter 7 (1995) 1101]. The MIRO-related transitions can be observed in absorption and we demonstrate it experimentally for the first time using EPR-cavity absorption technique. Next we investigate MIROs and Shubnikov-de Haas (SdH) oscillations at milli-Kelvin temperatures. We find that MIROs persist to approximately three times lower magnetic field as compared with the SdH oscillations, which at temperatures below 50 mK are defined purely by the quantum relaxation time. This finding indicates a possible quasi-classical origin of MIROs.

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

Analysis of Electromagnetic Wave Propagation in a Magnetized Re-Entry Plasma Sheath Via the Kinetic Equation

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2009-01-01

Based on a theoretical model of the propagation of electromagnetic waves through a hypersonically induced plasma, it has been demonstrated that the classical radiofrequency communications blackout that is experienced during atmospheric reentry can be mitigated through the appropriate control of an external magnetic field of nominal magnitude. The model is based on the kinetic equation treatment of Vlasov and involves an analytical solution for the electric and magnetic fields within the plasma allowing for a description of the attendant transmission, reflection and absorption coefficients. The ability to transmit through the magnetized plasma is due to the magnetic windows that are created within the plasma via the well-known whistler modes of propagation. The case of 2 GHz transmission through a re-entry plasma is considered. The coefficients are found to be highly sensitive to the prevailing electron density and will thus require a dynamic control mechanism to vary the magnetic field as the plasma evolves through the re-entry phase.

Dynamics of anisotropies close to a cosmological bounce in quantum gravity

NASA Astrophysics Data System (ADS)

de Cesare, Marco; Oriti, Daniele; Pithis, Andreas G. A.; Sakellariadou, Mairi

2018-01-01

We study the dynamics of perturbations representing deviations from perfect isotropy in the context of the emergent cosmology obtained from the group field theory formalism for quantum gravity. Working in the mean field approximation of the group field theory formulation of the Lorentzian EPRL model, we derive the equations of motion for such perturbations to first order. We then study these equations around a specific simple isotropic background, characterised by the fundamental representation of SU(2) , and in the regime of the effective cosmological dynamics corresponding to the bouncing region replacing the classical singularity, well approximated by the free GFT dynamics. In this particular example, we identify a region in the parameter space of the model such that perturbations can be large at the bounce but become negligible away from it, i.e. when the background enters the non-linear regime. We also study the departures from perfect isotropy by introducing specific quantities, such as the surface-area-to-volume ratio and the effective volume per quantum, which make them quantitative.

Fluctuation-enhanced electric conductivity in electrolyte solutions.

PubMed

Péraud, Jean-Philippe; Nonaka, Andrew J; Bell, John B; Donev, Aleksandar; Garcia, Alejandro L

2017-10-10

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.

Fluctuation-enhanced electric conductivity in electrolyte solutions

PubMed Central

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.

2017-01-01

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell–Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration. PMID:28973890

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

Simple vector bundles on a nodal Weierstrass cubic and quasi-trigonometric solutions of the classical Yang-Baxter equation

NASA Astrophysics Data System (ADS)

Burban, Igor; Galinat, Lennart; Stolin, Alexander

2017-11-01

In this paper we study the combinatorics of quasi-trigonometric solutions of the classical Yang-Baxter equation, arising from simple vector bundles on a nodal Weierstraß cubic. Dedicated to the memory of Petr Petrovich Kulish.

Static black holes with back reaction from vacuum energy

NASA Astrophysics Data System (ADS)

Ho, Pei-Ming; Matsuo, Yoshinori

2018-03-01

We study spherically symmetric static solutions to the semi-classical Einstein equation sourced by the vacuum energy of quantum fields in the curved space-time of the same solution. We found solutions that are small deformations of the Schwarzschild metric for distant observers, but without horizon. Instead of being a robust feature of objects with high densities, the horizon is sensitive to the energy–momentum tensor in the near-horizon region.

Advances and future directions of research on spectral methods

NASA Technical Reports Server (NTRS)

Patera, A. T.

1986-01-01

Recent advances in spectral methods are briefly reviewed and characterized with respect to their convergence and computational complexity. Classical finite element and spectral approaches are then compared, and spectral element (or p-type finite element) approximations are introduced. The method is applied to the full Navier-Stokes equations, and examples are given of the application of the technique to several transitional flows. Future directions of research in the field are outlined.

Do semiclassical zero temperature black holes exist?

PubMed

Anderson, P R; Hiscock, W A; Taylor, B E

2000-09-18

The semiclassical Einstein equations are solved to first order in epsilon = Planck's over 2pi/M2 for the case of a Reissner-Nordström black hole perturbed by the vacuum stress energy of quantized free fields. Massless and massive fields of spin 0, 1/2, and 1 are considered. We show that in all physically realistic cases, macroscopic zero temperature black hole solutions do not exist. Any static zero temperature semiclassical black hole solutions must then be microscopic and isolated in the space of solutions; they do not join smoothly onto the classical extreme Reissner-Nordström solution as epsilon-->0.

Higher derivative extensions of 3 d Chern-Simons models: conservation laws and stability

NASA Astrophysics Data System (ADS)

Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.

2015-11-01

We consider the class of higher derivative 3 d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

The role of gauge symmetry in spintronics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sobreiro, R.F., E-mail: sobreiro@if.uff.br; Vasquez Otoya, V.J.

2011-12-15

In this work we employ a field theoretical approach to explain the nature of the non-conserved spin current in spintronics. In particular, we consider the usual U(1) gauge theory for the electromagnetism at classical level in order to obtain the broken continuity equation involving the spin current and spin-transfer torque. Inspired by the recent work of A. Vernes, B. L. Gyorffy and P. Weinberger where they obtain such an equation in terms of relativistic quantum mechanics, we formalize their result in terms of the well known currents of field theory such as the Bargmann-Wigner current and the chiral current. Thus,more » an interpretation of spintronics is provided in terms of Noether currents (conserved or not) and symmetries of the electromagnetism. In fact, the main result of the present work is that the non-conservation of the spin current is associated with the gauge invariance of physical observables where the breaking term is proportional to the chiral current. Moreover, we generalize their result by including the electromagnetic field as a dynamical field instead of an external one.« less

Entanglement in Quantum-Classical Hybrid

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

It is noted that the phenomenon of entanglement is not a prerogative of quantum systems, but also occurs in other, non-classical systems such as quantum-classical hybrids, and covers the concept of entanglement as a special type of global constraint imposed upon a broad class of dynamical systems. Application of hybrid systems for physics of life, as well as for quantum-inspired computing, has been outlined. In representing the Schroedinger equation in the Madelung form, there is feedback from the Liouville equation to the Hamilton-Jacobi equation in the form of the quantum potential. Preserving the same topology, the innovators replaced the quantum potential with other types of feedback, and investigated the property of these hybrid systems. A function of probability density has been introduced. Non-locality associated with a global geometrical constraint that leads to an entanglement effect was demonstrated. Despite such a quantum like characteristic, the hybrid can be of classical scale and all the measurements can be performed classically. This new emergence of entanglement sheds light on the concept of non-locality in physics.

On the motion of classical three-body system with consideration of quantum fluctuations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gevorkyan, A. S., E-mail: g-ashot@sci.am

2017-03-15

We obtained the systemof stochastic differential equations which describes the classicalmotion of the three-body system under influence of quantum fluctuations. Using SDEs, for the joint probability distribution of the total momentum of bodies system were obtained the partial differential equation of the second order. It is shown, that the equation for the probability distribution is solved jointly by classical equations, which in turn are responsible for the topological peculiarities of tubes of quantum currents, transitions between asymptotic channels and, respectively for arising of quantum chaos.

Trouble with the Lorentz law of force: incompatibility with special relativity and momentum conservation.

PubMed

Mansuripur, Masud

2012-05-11

The Lorentz law of force is the fifth pillar of classical electrodynamics, the other four being Maxwell's macroscopic equations. The Lorentz law is the universal expression of the force exerted by electromagnetic fields on a volume containing a distribution of electrical charges and currents. If electric and magnetic dipoles also happen to be present in a material medium, they are traditionally treated by expressing the corresponding polarization and magnetization distributions in terms of bound-charge and bound-current densities, which are subsequently added to free-charge and free-current densities, respectively. In this way, Maxwell's macroscopic equations are reduced to his microscopic equations, and the Lorentz law is expected to provide a precise expression of the electromagnetic force density on material bodies at all points in space and time. This Letter presents incontrovertible theoretical evidence of the incompatibility of the Lorentz law with the fundamental tenets of special relativity. We argue that the Lorentz law must be abandoned in favor of a more general expression of the electromagnetic force density, such as the one discovered by Einstein and Laub in 1908. Not only is the Einstein-Laub formula consistent with special relativity, it also solves the long-standing problem of "hidden momentum" in classical electrodynamics.

Extension of the Schrodinger equation

NASA Astrophysics Data System (ADS)

Somsikov, Vyacheslav

2017-03-01

Extension of the Schrodinger equation is submitted by removing its limitations appearing due to the limitations of the formalism of Hamilton, based on which this equation was obtained. For this purpose the problems of quantum mechanics arising from the limitations of classical mechanics are discussed. These limitations, in particular, preclude the use of the Schrodinger equation to describe the time symmetry violation. The extension of the Schrodinger equation is realized based on the principle of duality symmetry. According to this principle the dynamics of the systems is determined by the symmetry of the system and by the symmetry of the space. The extension of the Schrodinger equation was obtained from the dual expression of energy, represented in operator form. For this purpose the independent micro - and macro-variables that determine respectively the dynamics of quantum particle system relative to its center of mass and the movement of the center of mass in space are used. The solution of the extended Schrodinger equation for the system near equilibrium is submitted. The main advantage of the extended Schrodinger equation is that it is applicable to describe the interaction and evolution of quantum systems in inhomogeneous field of external forces.

APPROACH TO EQUILIBRIUM OF A QUANTUM PLASMA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balescu, R.

1961-01-01

The treatment of irreversible processes in a classical plasma (R. Balescu, Phys. Fluids 3, 62(1960)) was extended to a gas of charged particles obeying quantum statistics. The various contributions to the equation of evolution for the reduced one-particle Wigner function were written in a form analogous to the classical formalism. The summation was then performed in a straightforward manner. The resulting equation describes collisions between particles "dressed" by their polarization clouds, exactly as in the classical situation. (auth)

All-Optical Stern-Gerlach Effect

NASA Astrophysics Data System (ADS)

Karnieli, Aviv; Arie, Ady

2018-01-01

We introduce a novel formalism in which the paraxial coupled wave equations of the nonlinear optical sum-frequency generation process are shown to be equivalent to the Pauli equation describing the dynamics of a spin-1 /2 particle in a spatially varying magnetic field. This interpretation gives rise to a new classical state of paraxial light, described by a mutual beam comprising of two frequencies. As a straightforward application, we propose the existence of an all-optical Stern-Gerlach effect, where an idler beam is deflected by a gradient in the nonlinear coupling, into two mutual beams of the idler and signal waves (equivalent to oppositely oriented spinors), propagating in two discrete directions. The Stern-Gerlach deflection angle and the intensity pattern in the far field are then obtained analytically, in terms of the parameters of the original optical system, laying the grounds for future experimental realizations.

Holographically viable extensions of topologically massive and minimal massive gravity?

NASA Astrophysics Data System (ADS)

Altas, Emel; Tekin, Bayram

2016-01-01

Recently [E. Bergshoeff et al., Classical Quantum Gravity 31, 145008 (2014)], an extension of the topologically massive gravity (TMG) in 2 +1 dimensions, dubbed as minimal massive gravity (MMG), which is free of the bulk-boundary unitarity clash that inflicts the former theory and all the other known three-dimensional theories, was found. Field equations of MMG differ from those of TMG at quadratic terms in the curvature that do not come from the variation of an action depending on the metric alone. Here we show that MMG is a unique theory and there does not exist a deformation of TMG or MMG at the cubic and quartic order (and beyond) in the curvature that is consistent at the level of the field equations. The only extension of TMG with the desired bulk and boundary properties having a single massive degree of freedom is MMG.

Extended hamiltonian formalism and Lorentz-violating lagrangians

NASA Astrophysics Data System (ADS)

Colladay, Don

2017-09-01

A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

Phase-field modeling of isothermal quasi-incompressible multicomponent liquids

NASA Astrophysics Data System (ADS)

Tóth, Gyula I.

2016-09-01

In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.

Hydrodynamics of bacterial colonies: A model

NASA Astrophysics Data System (ADS)

Lega, J.; Passot, T.

2003-03-01

We propose a hydrodynamic model for the evolution of bacterial colonies growing on soft agar plates. This model consists of reaction-diffusion equations for the concentrations of nutrients, water, and bacteria, coupled to a single hydrodynamic equation for the velocity field of the bacteria-water mixture. It captures the dynamics inside the colony as well as on its boundary and allows us to identify a mechanism for collective motion towards fresh nutrients, which, in its modeling aspects, is similar to classical chemotaxis. As shown in numerical simulations, our model reproduces both usual colony shapes and typical hydrodynamic motions, such as the whirls and jets recently observed in wet colonies of Bacillus subtilis. The approach presented here could be extended to different experimental situations and provides a general framework for the use of advection-reaction-diffusion equations in modeling bacterial colonies.

Scaling properties of the two-dimensional randomly stirred Navier-Stokes equation.

PubMed

Mazzino, Andrea; Muratore-Ginanneschi, Paolo; Musacchio, Stefano

2007-10-05

We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree 2 - 2 epsilon. This is at variance with the setting usually assumed to derive Kraichnan's classical theory. We contrast accurate numerical experiments with the different predictions provided for the small epsilon regime by Kraichnan's double cascade theory and by renormalization group analysis. We give clear evidence that for all epsilon, Kraichnan's theory is consistent with the observed phenomenology. Our results call for a revision in the renormalization group analysis of (2D) fully developed turbulence.

1+1 Gaudin Model

NASA Astrophysics Data System (ADS)

Zotov, Andrei V.

2011-07-01

We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For sl(N) case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In sl(2) case we study the equations in detail and find the corresponding Hamiltonian densities. The n-site model describes n interacting Landau-Lifshitz models of magnets. The interaction depends on position of the sites (marked points on the curve). We also analyze the 2-site case in its own right and describe its relation to the principal chiral model. We emphasize that 1+1 version impose a restriction on a choice of flows on the level of the corresponding 0+1 classical mechanics.

Non-Existence of Black Hole Solutionsfor a Spherically Symmetric, Static Einstein-Dirac-Maxwell System

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.

Direct numerical simulation of a combusting droplet with convection

NASA Technical Reports Server (NTRS)

Liang, Pak-Yan

1992-01-01

The evaporation and combustion of a single droplet under forced and natural convection was studied numerically from first principles using a numerical scheme that solves the time-dependent multiphase and multispecies Navier-Stokes equations and tracks the sharp gas-liquid interface cutting across an arbitrary Eulerian grid. The flow fields both inside and outside of the droplet are resolved in a unified fashion. Additional governing equations model the interphase mass, energy, and momentum exchange. Test cases involving iso-octane, n-hexane, and n-propanol droplets show reasonable comparison rate, and flame stand-off distance. The partially validated code is, thus, readied to be applied to more demanding droplet combustion situations where substantial drop deformation render classical models inadequate.

ON THE APPROACH TO NON-EQUILIBRIUM STATIONARY STATES AND THE THEORY OF TRANSPORT COEFFICIENTS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balescu, R.

1961-07-01

A general formula for the time dependent electric current arising from a constant electric field is derived similarly to Kubo's theory. This formula connects the time dependence of the current to the singularities of the resolvent of Liouville's operator of a classical system. Direct contact is made with the general theory of approach to equilibrium developed by Prigogine and his coworkers. It constitutes a framework for a diagram expansion of transport coefficients. A proof of the existence of a stationary state and of its stability (to first order in the field) are given. It is rigorously shown that, whereas themore » approach to the stationary state is in general governed by complicated non-markoffian equations, the stationary state itself (and thus the calculation of transport coefficients) is always determined by an asymptotic cross section. This implies that transport coefficients can always be calculated from a markoffian Boltzmann-like equation even in situations in which that equation does not describe properly the approach to the stationary state. (auth)« less

Tensor calculus in polar coordinates using Jacobi polynomials

NASA Astrophysics Data System (ADS)

Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.

2016-11-01

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

HYM-flation: Yang-Mills cosmology with Horndeski coupling

NASA Astrophysics Data System (ADS)

Davydov, E.; Gal'tsov, D.

2016-02-01

We propose new mechanism for inflation using classical SU (2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.

Coercivity of domain wall motion in thin films of amorphous rare earth-transition metal alloys

NASA Technical Reports Server (NTRS)

Mansuripur, M.; Giles, R. C.; Patterson, G.

1991-01-01

Computer simulations of a two dimensional lattice of magnetic dipoles are performed on the Connection Machine. The lattice is a discrete model for thin films of amorphous rare-earth transition metal alloys, which have application as the storage media in erasable optical data storage systems. In these simulations, the dipoles follow the dynamic Landau-Lifshitz-Gilbert equation under the influence of an effective field arising from local anisotropy, near-neighbor exchange, classical dipole-dipole interactions, and an externally applied field. Various sources of coercivity, such as defects and/or inhomogeneities in the lattice, are introduced and the subsequent motion of domain walls in response to external fields is investigated.

Experimental quantum computing to solve systems of linear equations.

PubMed

Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

2013-06-07

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

On the Kerr-AdS/CFT correspondence

NASA Astrophysics Data System (ADS)

Amado, Julián Barragán; da Cunha, Bruno Carneiro; Pallante, Elisabetta

2017-08-01

We review the relation between four-dimensional global conformal blocks and field propagation in AdS5. Following the standard argument that marginal perturbations should backreact in the geometry, we turn to the study of scalar fields in the generic Kerr-AdS5 geometry. On one hand, the result for scattering coefficients can be obtained exactly using the isomonodromy technique, giving exact expressions in terms of c = 1 chiral conformal blocks. On the other hand, one can use the analogy between the scalar field equations to the Level 2 null field Ward identity in two dimensional Liouville field theory to write approximate expressions for the same coefficients in terms of semi-classical chiral Liouville conformal blocks. Surprisingly, the conformal block thus constructed has a well-behaved interpretation in terms of Liouville vertex operators.

Recent developments in bimetric theory

NASA Astrophysics Data System (ADS)

Schmidt-May, Angnis; von Strauss, Mikael

2016-05-01

This review is dedicated to recent progress in the field of classical, interacting, massive spin-2 theories, with a focus on ghost-free bimetric theory. We will outline its history and its development as a nontrivial extension and generalisation of nonlinear massive gravity. We present a detailed discussion of the consistency proofs of both theories, before we review Einstein solutions to the bimetric equations of motion in vacuum as well as the resulting mass spectrum. We introduce couplings to matter and then discuss the general relativity and massive gravity limits of bimetric theory, which correspond to decoupling the massive or the massless spin-2 field from the matter sector, respectively. More general classical solutions are reviewed and the present status of bimetric cosmology is summarised. An interesting corner in the bimetric parameter space which could potentially give rise to a nonlinear theory for partially massless spin-2 fields is also discussed. Relations to higher-curvature theories of gravity are explained and finally we give an overview of possible extensions of the theory and review its formulation in terms of vielbeins.

Classical and quantum cosmology of the little rip abrupt event

NASA Astrophysics Data System (ADS)

Albarran, Imanol; Bouhmadi-López, Mariam; Kiefer, Claus; Marto, João; Vargas Moniz, Paulo

2016-09-01

We analyze from a classical and quantum point of view the behavior of the Universe close to a little rip, which can be interpreted as a big rip sent towards the infinite future. Like a big rip singularity, a little rip implies the destruction of all bounded structures in the Universe and is thus an event where quantum effects could be important. We present here a new phantom scalar field model for the little rip. The quantum analysis is performed in quantum geometrodynamics, with the Wheeler-DeWitt equation as its central equation. We find that the little rip can be avoided in the sense of the DeWitt criterion, that is, by having a vanishing wave function at the place of the little rip. Therefore our analysis completes the answer to the question: can quantum cosmology smoothen or avoid the divergent behavior genuinely caused by phantom matter? We show that this can indeed happen for the little rip, similar to the avoidance of a big rip and a little sibling of the big rip.

On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations

NASA Astrophysics Data System (ADS)

García, Isaac A.; Llibre, Jaume; Maza, Susanna

2018-06-01

In this work we consider real analytic functions , where , Ω is a bounded open subset of , is an interval containing the origin, are parameters, and ε is a small parameter. We study the branching of the zero-set of at multiple points when the parameter ε varies. We apply the obtained results to improve the classical averaging theory for computing T-periodic solutions of λ-families of analytic T-periodic ordinary differential equations defined on , using the displacement functions defined by these equations. We call the coefficients in the Taylor expansion of in powers of ε the averaged functions. The main contribution consists in analyzing the role that have the multiple zeros of the first non-zero averaged function. The outcome is that these multiple zeros can be of two different classes depending on whether the zeros belong or not to the analytic set defined by the real variety associated to the ideal generated by the averaged functions in the Noetheriang ring of all the real analytic functions at . We bound the maximum number of branches of isolated zeros that can bifurcate from each multiple zero z 0. Sometimes these bounds depend on the cardinalities of minimal bases of the former ideal. Several examples illustrate our results and they are compared with the classical theory, branching theory and also under the light of singularity theory of smooth maps. The examples range from polynomial vector fields to Abel differential equations and perturbed linear centers.

Classical Yang-Baxter equations and quantum integrable systems

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1989-06-01

Quantum integrable models associated with nondegenerate solutions of classical Yang-Baxter equations related to the simple Lie algebras are investigated. These models are diagonalized for rational and trigonometric solutions in the cases of sl(N)/gl(N)/, o(N) and sp(N) algebras. The analogy with the quantum inverse scattering method is demonstrated.

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Trajectory description of the quantum–classical transition for wave packet interference

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2016-08-15

The quantum–classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum–classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum–classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow themore » main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum–classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightful trajectory interpretation for the quantum–classical transition of wave packet interference.« less

A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

PubMed

Wapenaar, Kees

2017-06-01

A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.

Confinement and hadron-hadron interactions by general relativistic methods

NASA Astrophysics Data System (ADS)

Recami, Erasmo

By postulating covariance of physical laws under global dilations, one can describe gravitational and strong interactions in a unified way. Namely, in terms of the new discrete dilational degree of freedom, our cosmos and hadrons can be regarded as finite, similar systems. And a discrete hierarchy of finite ``universes'' may be defined, which are governed by fields with strengths inversally proportional to their radii; in each universe an Equivalence Principle holds, so that the relevant field can be there geometrized. Scaled-down Einstein equations -with cosmological term- are assumed to hold inside hadrons (= strong micro-cosmoses); and they yield in a natural way classical confinement, as well as ``asymptotic freedom'', of the hadron constituents. In other words, the association of strong micro-universes of Friedmann type with hadrons (i.e., applying the methods of General Relativity to subnuclear particle physics) allows avoiding recourse to phenomenological models such as the Bag Model. Inside hadrons we have to deal with a tensorial field (= strong gravity), and hadron constituents are supposed to exchange spin-2 ``gluons''. Our approach allows us also to write down a tensorial, bi-scale field theory of hadron-hadron interactions, based on modified Einstein-type equations here proposed for strong interactions in our space. We obtain in particular: (i) the correct Yukawa behaviour of the strong scalar potential at the static limit and for r>~l fm; (ii) the value of hadron radii. As a byproduct, we derive a whole ``numerology'', connecting our gravitational cosmos with the strong micro-cosmoses (hadrons), such that it does imply no variation of G with the epoch. Finally, since a structute of the ``micro-universe'' type seems to be characteristic even of leptons, a hope for the future is including also weak interactions in our classical unification of the fundamental forces.

On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi-Classical Solutions Teach us

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lusanna, Luca

2004-08-19

The four (electro-magnetic, weak, strong and gravitational) interactions are described by singular Lagrangians and by Dirac-Bergmann theory of Hamiltonian constraints. As a consequence a subset of the original configuration variables are gauge variables, not determined by the equations of motion. Only at the Hamiltonian level it is possible to separate the gauge variables from the deterministic physical degrees of freedom, the Dirac observables, and to formulate a well posed Cauchy problem for them both in special and general relativity. Then the requirement of causality dictates the choice of retarded solutions at the classical level. However both the problems of themore » classical theory of the electron, leading to the choice of (1/2) (retarded + advanced) solutions, and the regularization of quantum field theory, leading to the Feynman propagator, introduce anticipatory aspects. The determination of the relativistic Darwin potential as a semi-classical approximation to the Lienard-Wiechert solution for particles with Grassmann-valued electric charges, regularizing the Coulomb self-energies, shows that these anticipatory effects live beyond the semi-classical approximation (tree level) under the form of radiative corrections, at least for the electro-magnetic interaction.Talk and 'best contribution' at The Sixth International Conference on Computing Anticipatory Systems CASYS'03, Liege August 11-16, 2003.« less

THE COLOUR GLASS CONDENSATE: AN INTRODUCTION

DOE Office of Scientific and Technical Information (OSTI.GOV)

IANCU,E.; LEONIDOV,A.; MCLERRAN,L.

2001-08-06

In these lectures, the authors develop the theory of the Colour Glass Condensate. This is the matter made of gluons in the high density environment characteristic of deep inelastic scattering or hadron-hadron collisions at very high energy. The lectures are self contained and comprehensive. They start with a phenomenological introduction, develop the theory of classical gluon fields appropriate for the Colour Glass, and end with a derivation and discussion of the renormalization group equations which determine this effective theory.

Fate of classical solitons in one-dimensional quantum systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pustilnik, M.; Matveev, K. A.

We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, andmore » argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.« less

An analytical model of a curved beam with a T shaped cross section

NASA Astrophysics Data System (ADS)

Hull, Andrew J.; Perez, Daniel; Cox, Donald L.

2018-03-01

This paper derives a comprehensive analytical dynamic model of a closed circular beam that has a T shaped cross section. The new model includes in-plane and out-of-plane vibrations derived using continuous media expressions which produces results that have a valid frequency range above those available from traditional lumped parameter models. The web is modeled using two-dimensional elasticity equations for in-plane motion and the classical flexural plate equation for out-of-plane motion. The flange is modeled using two sets of Donnell shell equations: one for the left side of the flange and one for the right side of the flange. The governing differential equations are solved with unknown wave propagation coefficients multiplied by spatial domain and time domain functions which are inserted into equilibrium and continuity equations at the intersection of the web and flange and into boundary conditions at the edges of the system resulting in 24 algebraic equations. These equations are solved to yield the wave propagation coefficients and this produces a solution to the displacement field in all three dimensions. An example problem is formulated and compared to results from finite element analysis.

Stochastic inflation lattice simulations - Ultra-large scale structure of the universe

NASA Technical Reports Server (NTRS)

Salopek, D. S.

1991-01-01

Non-Gaussian fluctuations for structure formation may arise in inflation from the nonlinear interaction of long wavelength gravitational and scalar fields. Long wavelength fields have spatial gradients, a (exp -1), small compared to the Hubble radius, and they are described in terms of classical random fields that are fed by short wavelength quantum noise. Lattice Langevin calculations are given for a toy model with a scalar field interacting with an exponential potential where one can obtain exact analytic solutions of the Fokker-Planck equation. For single scalar field models that are consistent with current microwave background fluctuations, the fluctuations are Gaussian. However, for scales much larger than our observable Universe, one expects large metric fluctuations that are non-Gaussian. This example illuminates non-Gaussian models involving multiple scalar fields which are consistent with current microwave background limits.

Unified field theory from the classical wave equation: Preliminary application to atomic and nuclear structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Múnera, Héctor A., E-mail: hmunera@hotmail.com; Retired professor, Department of Physics, Universidad Nacional de Colombia, Bogotá, Colombia, South America

2016-07-07

It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrödinger’s first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding amore » unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of ℓ (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich’s unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.« less

Relations between nonlinear Riccati equations and other equations in fundamental physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-10-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.

Statistical Extremes of Turbulence and a Cascade Generalisation of Euler's Gyroscope Equation

NASA Astrophysics Data System (ADS)

Tchiguirinskaia, Ioulia; Scherzer, Daniel

2016-04-01

Turbulence refers to a rather well defined hydrodynamical phenomenon uncovered by Reynolds. Nowadays, the word turbulence is used to designate the loss of order in many different geophysical fields and the related fundamental extreme variability of environmental data over a wide range of scales. Classical statistical techniques for estimating the extremes, being largely limited to statistical distributions, do not take into account the mechanisms generating such extreme variability. An alternative approaches to nonlinear variability are based on a fundamental property of the non-linear equations: scale invariance, which means that these equations are formally invariant under given scale transforms. Its specific framework is that of multifractals. In this framework extreme variability builds up scale by scale leading to non-classical statistics. Although multifractals are increasingly understood as a basic framework for handling such variability, there is still a gap between their potential and their actual use. In this presentation we discuss how to dealt with highly theoretical problems of mathematical physics together with a wide range of geophysical applications. We use Euler's gyroscope equation as a basic element in constructing a complex deterministic system that preserves not only the scale symmetry of the Navier-Stokes equations, but some more of their symmetries. Euler's equation has been not only the object of many theoretical investigations of the gyroscope device, but also generalised enough to become the basic equation of fluid mechanics. Therefore, there is no surprise that a cascade generalisation of this equation can be used to characterise the intermittency of turbulence, to better understand the links between the multifractal exponents and the structure of a simplified, but not simplistic, version of the Navier-Stokes equations. In a given way, this approach is similar to that of Lorenz, who studied how the flap of a butterfly wing could generate a cyclone with the help of a 3D ordinary differential system. Being well supported by the extensive numerical results, the cascade generalisation of Euler's gyroscope equation opens new horizons for predictability and predictions of processes having long-range dependences.

Spin-diffusions and diffusive molecular dynamics

NASA Astrophysics Data System (ADS)

Farmer, Brittan; Luskin, Mitchell; Plecháč, Petr; Simpson, Gideon

2017-12-01

Metastable configurations in condensed matter typically fluctuate about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics (MD) methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive MD which aims at integrating a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive MD has shown itself to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical MD. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive MD. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive MD type models. The key assumptions and approximations include a well-defined time scale separation, a choice of spin-exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive MD. Differences and similarities amongst the models are explored in a simple test problem.

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE PAGES

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; ...

2017-09-26

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Statistical nature of infrared dynamics on de Sitter background

NASA Astrophysics Data System (ADS)

Tokuda, Junsei; Tanaka, Takahiro

2018-02-01

In this study, we formulate a systematic way of deriving an effective equation of motion(EoM) for long wavelength modes of a massless scalar field with a general potential V(phi) on de Sitter background, and investigate whether or not the effective EoM can be described as a classical stochastic process. Our formulation gives an extension of the usual stochastic formalism to including sub-leading secular growth coming from the nonlinearity of short wavelength modes. Applying our formalism to λ phi4 theory, we explicitly derive an effective EoM which correctly recovers the next-to-leading secularly growing part at a late time, and show that this effective EoM can be seen as a classical stochastic process. Our extended stochastic formalism can describe all secularly growing terms which appear in all correlation functions with a specific operator ordering. The restriction of the operator ordering will not be a big drawback because the commutator of a light scalar field becomes negligible at large scales owing to the squeezing.

Classical aspects of higher spin topologically massive gravity

NASA Astrophysics Data System (ADS)

Chen, Bin; Long, Jiang; Zhang, Jian-Dong

2012-10-01

We study the classical solutions of three-dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first-order formulation. The action of higher spin TMG has been proposed by Chen and Long (2011 J. High Energy Phys. JHEP12(2011)114) to be of a Chern-Simons-like form. The equations of motion are more complicated than the ones in pure higher spin AdS3 gravity, but are still tractable. As all the solutions in higher spin gravity are automatically the solutions of higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave solutions with higher spin hair and find that the non-vanishing higher spin fields may or may not modify the pp-wave geometry. In order to discuss the warped spacetime, we introduce the notion of a special Killing vector, which is defined to be the symmetry on the frame-like fields. We reproduce various warped spacetimes of TMG in our framework, with the help of special Killing vectors.

Nucleation theory - Is replacement free energy needed?. [error analysis of capillary approximation

NASA Technical Reports Server (NTRS)

Doremus, R. H.

1982-01-01

It has been suggested that the classical theory of nucleation of liquid from its vapor as developed by Volmer and Weber (1926) needs modification with a factor referred to as the replacement free energy and that the capillary approximation underlying the classical theory is in error. Here, the classical nucleation equation is derived from fluctuation theory, Gibb's result for the reversible work to form a critical nucleus, and the rate of collision of gas molecules with a surface. The capillary approximation is not used in the derivation. The chemical potential of small drops is then considered, and it is shown that the capillary approximation can be derived from thermodynamic equations. The results show that no corrections to Volmer's equation are needed.

Auxiliary field loop expansion of the effective action for a class of stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Cooper, Fred; Dawson, John F.

2016-02-01

We present an alternative to the perturbative (in coupling constant) diagrammatic approach for studying stochastic dynamics of a class of reaction diffusion systems. Our approach is based on an auxiliary field loop expansion for the path integral representation for the generating functional of the noise induced correlation functions of the fields describing these systems. The systems we consider include Langevin systems describable by the set of self interacting classical fields ϕi(x , t) in the presence of external noise ηi(x , t) , namely (∂t - ν∇2) ϕ - F [ ϕ ] = η, as well as chemical reaction annihilation processes obtained by applying the many-body approach of Doi-Peliti to the Master Equation formulation of these problems. We consider two different effective actions, one based on the Onsager-Machlup (OM) approach, and the other due to Janssen-deGenneris based on the Martin-Siggia-Rose (MSR) response function approach. For the simple models we consider, we determine an analytic expression for the Energy landscape (effective potential) in both formalisms and show how to obtain the more physical effective potential of the Onsager-Machlup approach from the MSR effective potential in leading order in the auxiliary field loop expansion. For the KPZ equation we find that our approximation, which is non-perturbative and obeys broken symmetry Ward identities, does not lead to the appearance of a fluctuation induced symmetry breakdown. This contradicts the results of earlier studies.

Mathematical methods of studying physical phenomena

NASA Astrophysics Data System (ADS)

Man'ko, Margarita A.

2013-03-01

In recent decades, substantial theoretical and experimental progress was achieved in understanding the quantum nature of physical phenomena that serves as the foundation of present and future quantum technologies. Quantum correlations like the entanglement of the states of composite systems, the phenomenon of quantum discord, which captures other aspects of quantum correlations, quantum contextuality and, connected with these phenomena, uncertainty relations for conjugate variables and entropies, like Shannon and Rényi entropies, and the inequalities for spin states, like Bell inequalities, reflect the recently understood quantum properties of micro and macro systems. The mathematical methods needed to describe all quantum phenomena mentioned above were also the subject of intense studies in the end of the last, and beginning of the new, century. In this section of CAMOP 'Mathematical Methods of Studying Physical Phenomena' new results and new trends in the rapidly developing domain of quantum (and classical) physics are presented. Among the particular topics under discussion there are some reviews on the problems of dynamical invariants and their relations with symmetries of the physical systems. In fact, this is a very old problem of both classical and quantum systems, e.g. the systems of parametric oscillators with time-dependent parameters, like Ermakov systems, which have specific constants of motion depending linearly or quadratically on the oscillator positions and momenta. Such dynamical invariants play an important role in studying the dynamical Casimir effect, the essence of the effect being the creation of photons from the vacuum in a cavity with moving boundaries due to the presence of purely quantum fluctuations of the electromagnetic field in the vacuum. It is remarkable that this effect was recently observed experimentally. The other new direction in developing the mathematical approach in physics is quantum tomography that provides a new vision of quantum states. In the tomographic picture of quantum mechanics, the states are identified with fair conditional probability distributions, which contain the same information on the states as the wave function or the density matrix. The mathematical methods of the tomographic approach are based on studying the star-product (associative product) quantization scheme. The tomographic star-product technique provides an additional understanding of the associative product, which is connected with the existence of specific pairs of operators called quantizers and dequantizers. These operators code information on the kernels of all the star-product schemes, including the traditional phase-space Weyl-Wigner-Moyal picture describing the quantum-system evolution. The new equation to find quantizers, if the kernel of the star product of functions is given, is presented in this CAMOP section. For studying classical systems, the mathematical methods developed in quantum mechanics can also be used. The case of paraxial-radiation beams propagating in waveguides is a known example of describing a purely classical phenomenon by means of quantum-like equations. Thus, some quantum phenomenon like the entanglement can be mimicked by the properties of classical beams, for example, Gaussian modes. The mathematical structures and relations to the symplectic symmetry group are analogous for both classical and quantum phenomena. Such analogies of the mathematical classical and quantum methods used in research on quantum-like communication channels provide new tools for constructing a theoretical basis of the new information-transmission technologies. The conventional quantum mechanics and its relation to classical mechanics contain mathematical recipes of the correspondence principle and quantization rules. Attempts to find rules for deriving the quantum-mechanical formalism starting from the classical field theory, taking into account the influence of classical fluctuations of the field, is considered in these papers. The methods to solve quantum equations and formulate the boundary conditions in the problems with singular potentials are connected with the mathematical problems of self-adjointness of the Hamiltonians. The progress and some new results in this direction are reflected in this CAMOP section. The Gaussian states of the photons play an important role in quantum optics. The multimode electromagnetic field and quantum correlations in the Gaussian states are considered in this section. The new results in the statistical properties of the laser radiation discussed here are based on applications of mathematical methods in this traditional domain of physics. It is worth stressing that the universality of the mathematical procedures permitted to consider the physical phenomena in the ocean is on the same footing as the phenomena in the microworld. In this CAMOP section, there are also papers devoted to traditional problems of solving the Schrödinger equation for interesting quantum systems. Recently obtained results related to different domains of theoretical physics are united by applying mathematical methods and tools, that provide new possibilities to better understand the theoretical foundations needed to develop new quantum technologies like quantum computing and quantum communications. The papers are arranged alphabetically by the name of the first author. We are grateful to all authors who accepted our invitation to contribute to this CAMOP section.

Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations

NASA Astrophysics Data System (ADS)

Subramani, D. N.; Haley, P., Jr.; Lermusiaux, P. F. J.

2017-12-01

The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex and intermittent with unstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. For efficient and rigorous quantification and prediction of these uncertainities, the stochastic Dynamically Orthogonal (DO) PDEs for a primitive equation ocean modeling system with a nonlinear free-surface are derived and numerical schemes for their space-time integration are obtained. Detailed numerical studies with idealized-to-realistic regional ocean dynamics are completed. These include consistency checks for the numerical schemes and comparisons with ensemble realizations. As an illustrative example, we simulate the 4-d multiscale uncertainty in the Middle Atlantic/New York Bight region during the months of Jan to Mar 2017. To provide intitial conditions for the uncertainty subspace, uncertainties in the region were objectively analyzed using historical data. The DO primitive equations were subsequently integrated in space and time. The probability distribution function (pdf) of the ocean fields is compared to in-situ, remote sensing, and opportunity data collected during the coincident POSYDON experiment. Results show that our probabilistic predictions had skill and are 3- to 4- orders of magnitude faster than classic ensemble schemes.

Solvent-Induced Shift of Spectral Lines in Polar-Polarizable Solvents.

PubMed

Matyushov, Dmitry V; Newton, Marshall D

2017-03-23

Solvent-induced shift of optical transition lines is traditionally described by the Lippert-McRae equation given in terms of the Onsager theory for dipole solvation. It splits the overall shift into the equilibrium solvation by induced dipoles and the reaction field by the permanent dipoles in equilibrium with the chromophore in the ground state. We have reconsidered this classical problem from the perspective of microscopic solvation theories. A microscopic solvation functional is derived, and continuum solvation is consistently introduced by taking the limit of zero wavevector in the reciprocal-space solvation susceptibility functions. We show that the phenomenological expression for the reaction field of permanent dipoles in the Lippert-McRae equation is not consistent with the microscopic theory. The main deficiency of the Lippert-McRae equation is the use of additivity of the response by permanent and induced dipoles of the liquid. An alternative closed-form equation for the spectral shift is derived. Its continuum limit allows a new, nonadditive functionality for the solvent-induced shift in terms of the high-frequency and static dielectric constants. The main qualitative outcome of the theory is a significantly weaker dependence of the spectral shift on the polarizability of the solvent than predicted by the Lippert-McRae formula.

Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincaré symmetry

NASA Astrophysics Data System (ADS)

Barbosa-Cendejas, Nandinii; Herrera-Aguilar, Alfredo; Kanakoglou, Konstantinos; Nucamendi, Ulises; Quiros, Israel

2014-01-01

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schrödinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with , in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to analytically compute the corrections to Newton's law in the thin brane limit. In the first case we consider a novel solution with a mass gap in the spectrum of KK fluctuations with two bound states—the massless 4D graviton free of tachyonic instabilities and a massive KK excitation—as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the thin Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved with positive branes as in the Lykken-Randall (LR) model and the model is completely free of naked singularities. We also show that the scalar-tensor system is stable under scalar perturbations with no scalar modes localized on the braneworld configuration.

Improved computational treatment of transonic flow about swept wings

NASA Technical Reports Server (NTRS)

Ballhaus, W. F.; Bailey, F. R.; Frick, J.

1976-01-01

Relaxation solutions to classical three-dimensional small-disturbance (CSD) theory for transonic flow about lifting swept wings are reported. For such wings, the CSD theory was found to be a poor approximation to the full potential equation in regions of the flow field that are essentially two-dimensional in a plane normal to the sweep direction. The effect of this deficiency on the capture of embedded shock waves in terms of (1) the conditions under which shock waves can exist and (2) the relations they must satisfy when they do exist is emphasized. A modified small-disturbance (MSD) equation, derived by retaining two previously neglected terms, was proposed and shown to be a consistent approximation to the full potential equation over a wider range of sweep angles. The effect of these extra terms is demonstrated by comparing CSD, MSD, and experimental wing surface pressures.

Analysis of delamination related fracture processes in composites

NASA Technical Reports Server (NTRS)

Armanios, Erian A.

1992-01-01

An anisotropic thin walled closed section beam theory was developed based on an asymptotical analysis of the shell energy functional. The displacement field is not assumed a priori and emerges as a result of the analysis. In addition to the classical out-of-plane torsional warping, two new contributions are identified namely, axial strain and bending warping. A comparison of the derived governing equations confirms the theory developed by Reissner and Tsai. Also, explicit closed form expressions for the beam stiffness coefficients, the stress and displacement fields are provided. The predictions of the present theory were validated by comparison with finite element simulation, other closed form analyses and test data.

Interacting charges and the classical electron radius

NASA Astrophysics Data System (ADS)

De Luca, Roberto; Di Mauro, Marco; Faella, Orazio; Naddeo, Adele

2018-03-01

The equation of the motion of a point charge q repelled by a fixed point-like charge Q is derived and studied. In solving this problem useful concepts in classical and relativistic kinematics, in Newtonian mechanics and in non-linear ordinary differential equations are revised. The validity of the approximations is discussed from the physical point of view. In particular the classical electron radius emerges naturally from the requirement that the initial distance is large enough for the non-relativistic approximation to be valid. The relevance of this topic for undergraduate physics teaching is pointed out.

Full multi grid method for electric field computation in point-to-plane streamer discharge in air at atmospheric pressure

NASA Astrophysics Data System (ADS)

Kacem, S.; Eichwald, O.; Ducasse, O.; Renon, N.; Yousfi, M.; Charrada, K.

2012-01-01

Streamers dynamics are characterized by the fast propagation of ionized shock waves at the nanosecond scale under very sharp space charge variations. The streamer dynamics modelling needs the solution of charged particle transport equations coupled to the elliptic Poisson's equation. The latter has to be solved at each time step of the streamers evolution in order to follow the propagation of the resulting space charge electric field. In the present paper, a full multi grid (FMG) and a multi grid (MG) methods have been adapted to solve Poisson's equation for streamer discharge simulations between asymmetric electrodes. The validity of the FMG method for the computation of the potential field is first shown by performing direct comparisons with analytic solution of the Laplacian potential in the case of a point-to-plane geometry. The efficiency of the method is also compared with the classical successive over relaxation method (SOR) and MUltifrontal massively parallel solver (MUMPS). MG method is then applied in the case of the simulation of positive streamer propagation and its efficiency is evaluated from comparisons to SOR and MUMPS methods in the chosen point-to-plane configuration. Very good agreements are obtained between the three methods for all electro-hydrodynamics characteristics of the streamer during its propagation in the inter-electrode gap. However in the case of MG method, the computational time to solve the Poisson's equation is at least 2 times faster in our simulation conditions.

On the classic and modern theories of matching.

PubMed

McDowell, J J

2005-07-01

Classic matching theory, which is based on Herrnstein's (1961) original matching equation and includes the well-known quantitative law of effect, is almost certainly false. The theory is logically inconsistent with known experimental findings, and experiments have shown that its central constant-k assumption is not tenable. Modern matching theory, which is based on the power function version of the original matching equation, remains tenable, although it has not been discussed or studied extensively. The modern theory is logically consistent with known experimental findings, it predicts the fact and details of the violation of the classic theory's constant-k assumption, and it accurately describes at least some data that are inconsistent with the classic theory.

Electroweak baryogenesis and the standard model effective field theory

NASA Astrophysics Data System (ADS)

de Vries, Jordy; Postma, Marieke; van de Vis, Jorinde; White, Graham

2018-01-01

We investigate electroweak baryogenesis within the framework of the Standard Model Effective Field Theory. The Standard Model Lagrangian is supplemented by dimension-six operators that facilitate a strong first-order electroweak phase transition and provide sufficient CP violation. Two explicit scenarios are studied that are related via the classical equations of motion and are therefore identical at leading order in the effective field theory expansion. We demonstrate that formally higher-order dimension-eight corrections lead to large modifications of the matter-antimatter asymmetry. The effective field theory expansion breaks down in the modified Higgs sector due to the requirement of a first-order phase transition. We investigate the source of the breakdown in detail and show how it is transferred to the CP-violating sector. We briefly discuss possible modifications of the effective field theory framework.

The Spiral of Life

NASA Astrophysics Data System (ADS)

Cajiao Vélez, F.; Kamiński, J. Z.; Krajewska, K.

2018-04-01

High-energy photoionization driven by short and circularly-polarized laser pulses is studied in the framework of the relativistic strong-field approximation. The saddle-point analysis of the integrals defining the probability amplitude is used to determine the general properties of the probability distributions. Additionally, an approximate solution to the saddle-point equation is derived. This leads to the concept of the three-dimensional spiral of life in momentum space, around which the ionization probability distribution is maximum. We demonstrate that such spiral is also obtained from a classical treatment.

Modulation Doped GaAs/Al sub xGA sub (1-x)As Layered Structures with Applications to Field Effect Transistors.

DTIC Science & Technology

1982-02-15

function of the doping density at 300 and 77 K for the classical Boltzmann statistics or depletion approximation (solid line) and for the approximate...Fermi-Dirac statistics (equation (19) dotted line)• This comparison demonstrates that the deviation from Boltzmann statistics is quite noticeable...tunneling Schottky barriers cannot be obtained at these doping levels. The dotted lines are obtained when Boltzmann statistics are used in the Al Ga

Perfect relativistic magnetohydrodynamics around black holes in horizon penetrating coordinates

NASA Astrophysics Data System (ADS)

Cherubini, Christian; Filippi, Simonetta; Loppini, Alessandro; Moradi, Rahim; Ruffini, Remo; Wang, Yu; Xue, She-Sheng

2018-03-01

Plasma accreting processes on black holes represent a central problem for relativistic astrophysics. In this context, here we specifically revisit the classical Ruffini-Wilson work developed for analytically modeling via geodesic equations the accretion of perfect magnetized plasma on a rotating Kerr black hole. Introducing the horizon penetrating coordinates found by Doran 25 years later, we revisit the entire approach studying Maxwell invariants, electric and magnetic fields, volumetric charge density and electromagnetic total energy. We finally discuss the physical implications of this analysis.

Current problems in applied mathematics and mathematical physics

NASA Astrophysics Data System (ADS)

Samarskii, A. A.

Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

Classical integrable defects as quasi Bäcklund transformations

NASA Astrophysics Data System (ADS)

Doikou, Anastasia

2016-10-01

We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the ;equations of motion; on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Bäcklund transformations. And although these equations are similar they are not exactly the same to the Bäcklund transformations. We also consider specific examples of integrable models to demonstrate our construction, i.e. the Toda chain and the sine-Gordon model. The equations of the time (space) evolution of the defect (discontinuity) degrees of freedom for these models are explicitly derived.

Radiation-reaction force on a small charged body to second order

NASA Astrophysics Data System (ADS)

Moxon, Jordan; Flanagan, Éanna

2018-05-01

In classical electrodynamics, an accelerating charged body emits radiation and experiences a corresponding radiation-reaction force, or self-force. We extend to higher order in the total charge a previous rigorous derivation of the electromagnetic self-force in flat spacetime by Gralla, Harte, and Wald. The method introduced by Gralla, Harte, and Wald computes the self-force from the Maxwell field equations and conservation of stress-energy in a limit where the charge, size, and mass of the body go to zero, and it does not require regularization of a singular self-field. For our higher-order computation, an adjustment of the definition of the mass of the body is necessary to avoid including self-energy from the electromagnetic field sourced by the body in the distant past. We derive the evolution equations for the mass, spin, and center-of-mass position of the body through second order. We derive, for the first time, the second-order acceleration dependence of the evolution of the spin (self-torque), as well as a mixing between the extended body effects and the acceleration-dependent effects on the overall body motion.

Third Quantization and Quantum Universes

NASA Astrophysics Data System (ADS)

Kim, Sang Pyo

2014-01-01

We study the third quantization of the Friedmann-Robertson-Walker cosmology with N-minimal massless fields. The third quantized Hamiltonian for the Wheeler-DeWitt equation in the minisuperspace consists of infinite number of intrinsic time-dependent, decoupled oscillators. The Hamiltonian has a pair of invariant operators for each universe with conserved momenta of the fields that play a role of the annihilation and the creation operators and that construct various quantum states for the universe. The closed universe exhibits an interesting feature of transitions from stable states to tachyonic states depending on the conserved momenta of the fields. In the classical forbidden unstable regime, the quantum states have googolplex growing position and conjugate momentum dispersions, which defy any measurements of the position of the universe.

Rotational dynamics of a diatomic molecular ion in a Paul trap

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hashemloo, A.; Dion, C. M., E-mail: claude.dion@umu.se

We present models for a heteronuclear diatomic molecular ion in a linear Paul trap in a rigid-rotor approximation, one purely classical and the other where the center-of-mass motion is treated classically, while rotational motion is quantized. We study the rotational dynamics and their influence on the motion of the center-of-mass, in the presence of the coupling between the permanent dipole moment of the ion and the trapping electric field. We show that the presence of the permanent dipole moment affects the trajectory of the ion and that it departs from the Mathieu equation solution found for atomic ions. For themore » case of quantum rotations, we also evidence the effect of the above-mentioned coupling on the rotational states of the ion.« less

Particle Acceleration and Fractional Transport in Turbulent Reconnection

NASA Astrophysics Data System (ADS)

Isliker, Heinz; Pisokas, Theophilos; Vlahos, Loukas; Anastasiadis, Anastasios

2017-11-01

We consider a large-scale environment of turbulent reconnection that is fragmented into a number of randomly distributed unstable current sheets (UCSs), and we statistically analyze the acceleration of particles within this environment. We address two important cases of acceleration mechanisms when particles interact with the UCS: (a) electric field acceleration and (b) acceleration by reflection at contracting islands. Electrons and ions are accelerated very efficiently, attaining an energy distribution of power-law shape with an index 1-2, depending on the acceleration mechanism. The transport coefficients in energy space are estimated from test-particle simulation data, and we show that the classical Fokker-Planck (FP) equation fails to reproduce the simulation results when the transport coefficients are inserted into it and it is solved numerically. The cause for this failure is that the particles perform Levy flights in energy space, while the distributions of the energy increments exhibit power-law tails. We then use the fractional transport equation (FTE) derived by Isliker et al., whose parameters and the order of the fractional derivatives are inferred from the simulation data, and solving the FTE numerically, we show that the FTE successfully reproduces the kinetic energy distribution of the test particles. We discuss in detail the analysis of the simulation data and the criteria that allow one to judge the appropriateness of either an FTE or a classical FP equation as a transport model.

Particle Acceleration and Fractional Transport in Turbulent Reconnection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Isliker, Heinz; Pisokas, Theophilos; Vlahos, Loukas

We consider a large-scale environment of turbulent reconnection that is fragmented into a number of randomly distributed unstable current sheets (UCSs), and we statistically analyze the acceleration of particles within this environment. We address two important cases of acceleration mechanisms when particles interact with the UCS: (a) electric field acceleration and (b) acceleration by reflection at contracting islands. Electrons and ions are accelerated very efficiently, attaining an energy distribution of power-law shape with an index 1–2, depending on the acceleration mechanism. The transport coefficients in energy space are estimated from test-particle simulation data, and we show that the classical Fokker–Planckmore » (FP) equation fails to reproduce the simulation results when the transport coefficients are inserted into it and it is solved numerically. The cause for this failure is that the particles perform Levy flights in energy space, while the distributions of the energy increments exhibit power-law tails. We then use the fractional transport equation (FTE) derived by Isliker et al., whose parameters and the order of the fractional derivatives are inferred from the simulation data, and solving the FTE numerically, we show that the FTE successfully reproduces the kinetic energy distribution of the test particles. We discuss in detail the analysis of the simulation data and the criteria that allow one to judge the appropriateness of either an FTE or a classical FP equation as a transport model.« less

Modeling of high pressure arc-discharge with a fully-implicit Navier-Stokes stabilized finite element flow solver

NASA Astrophysics Data System (ADS)

Sahai, A.; Mansour, N. N.; Lopez, B.; Panesi, M.

2017-05-01

This work addresses the modeling of high pressure electric discharge in an arc-heated wind tunnel. The combined numerical solution of Poisson’s equation, radiative transfer equations, and the set of Favre-averaged thermochemical nonequilibrium Navier-Stokes equations allows for the determination of the electric, radiation, and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles with the Chapman-Enskog method. A multi-temperature formulation is used to account for thermal non-equilibrium. Finally, the turbulence closure of the flow equations is obtained by means of the Spalart-Allmaras model, which requires the solution of an additional scalar transport equation. A Streamline upwind Petrov-Galerkin stabilized finite element formulation is employed to solve the Navier-Stokes equation. The electric field equation is solved using the standard Galerkin formulation. A stable formulation for the radiative transfer equations is obtained using the least-squares finite element method. The developed simulation framework has been applied to investigate turbulent plasma flows in the 20 MW Aerodynamic Heating Facility at NASA Ames Research Center. The current model is able to predict the process of energy addition and re-distribution due to Joule heating and thermal radiation, resulting in a hot central core surrounded by colder flow. The use of an unsteady three-dimensional treatment also allows the asymmetry due to a dynamic electric arc attachment point in the cathode chamber to be captured accurately. The current work paves the way for detailed estimation of operating characteristics for arc-heated wind tunnels which are critical in testing thermal protection systems.

Influence of homogeneous magnetic fields on the flow of a ferrofluid in the Taylor-Couette system.

PubMed

Altmeyer, S; Hoffmann, Ch; Leschhorn, A; Lücke, M

2010-07-01

We investigate numerically the influence of a homogeneous magnetic field on a ferrofluid in the gap between two concentric, independently rotating cylinders. The full Navier-Stokes equations are solved with a combination of a finite difference method and a Galerkin method. Structure, dynamics, symmetry properties, bifurcation, and stability behavior of different vortex structures are investigated for axial and transversal magnetic fields, as well as combinations of them. We show that a transversal magnetic field modulates the Taylor vortex flow and the spiral vortex flow. Thus, a transversal magnetic field induces wavy structures: wavy Taylor vortex flow (wTVF) and wavy spiral vortex flow. In contrast to the classic wTVF, which is a secondarily bifurcating structure, these magnetically generated wavy Taylor vortices are pinned by the magnetic field, i.e., they are stationary and they appear via a primary forward bifurcation out of the basic state of circular Couette flow.

A superstring field theory for supergravity

NASA Astrophysics Data System (ADS)

Reid-Edwards, R. A.; Riccombeni, D. A.

2017-09-01

A covariant closed superstring field theory, equivalent to classical tendimensional Type II supergravity, is presented. The defining conformal field theory is the ambitwistor string worldsheet theory of Mason and Skinner. This theory is known to reproduce the scattering amplitudes of Cachazo, He and Yuan in which the scattering equations play an important role and the string field theory naturally incorporates these results. We investigate the operator formalism description of the ambitwsitor string and propose an action for the string field theory of the bosonic and supersymmetric theories. The correct linearised gauge symmetries and spacetime actions are explicitly reproduced and evidence is given that the action is correct to all orders. The focus is on the NeveuSchwarz sector and the explicit description of tree level perturbation theory about flat spacetime. Application of the string field theory to general supergravity backgrounds and the inclusion of the Ramond sector are briefly discussed.

Effect of partially ionized impurities and radiation on the effective critical electric field for runaway generation

NASA Astrophysics Data System (ADS)

Hesslow, L.; Embréus, O.; Wilkie, G. J.; Papp, G.; Fülöp, T.

2018-07-01

We derive a formula for the effective critical electric field for runaway generation and decay that accounts for the presence of partially ionized impurities in combination with synchrotron and bremsstrahlung radiation losses. We show that the effective critical field is drastically larger than the classical Connor–Hastie field, and even exceeds the value obtained by replacing the free electron density by the total electron density (including both free and bound electrons). Using a kinetic equation solver with an inductive electric field, we show that the runaway current decay after an impurity injection is expected to be linear in time and proportional to the effective critical electric field in highly inductive tokamak devices. This is relevant for the efficacy of mitigation strategies for runaway electrons since it reduces the required amount of injected impurities to achieve a certain current decay rate.

On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

ERIC Educational Resources Information Center

Savoye, Philippe

2009-01-01

In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

Radiation reaction effect on laser driven auto-resonant particle acceleration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sagar, Vikram; Sengupta, Sudip; Kaw, P. K.

2015-12-15

The effects of radiation reaction force on laser driven auto-resonant particle acceleration scheme are studied using Landau-Lifshitz equation of motion. These studies are carried out for both linear and circularly polarized laser fields in the presence of static axial magnetic field. From the parametric study, a radiation reaction dominated region has been identified in which the particle dynamics is greatly effected by this force. In the radiation reaction dominated region, the two significant effects on particle dynamics are seen, viz., (1) saturation in energy gain by the initially resonant particle and (2) net energy gain by an initially non-resonant particlemore » which is caused due to resonance broadening. It has been further shown that with the relaxation of resonance condition and with optimum choice of parameters, this scheme may become competitive with the other present-day laser driven particle acceleration schemes. The quantum corrections to the Landau-Lifshitz equation of motion have also been taken into account. The difference in the energy gain estimates of the particle by the quantum corrected and classical Landau-Lifshitz equation is found to be insignificant for the present day as well as upcoming laser facilities.« less

Numerical algorithms for cold-relativistic plasma models in the presence of discontinuties

NASA Astrophysics Data System (ADS)

Hakim, Ammar; Cary, John; Bruhwiler, David; Geddes, Cameron; Leemans, Wim; Esarey, Eric

2006-10-01

A numerical algorithm is presented to solve cold-relativistic electron fluid equations in the presence of sharp gradients and discontinuities. The intended application is to laser wake-field accelerator simulations in which the laser induces accelerating fields thousands of times those achievable in conventional RF accelerators. The relativistic cold-fluid equations are formulated as non-classical system of hyperbolic balance laws. It is shown that the flux Jacobian for this system can not be diagonalized which causes numerical difficulties when developing shock-capturing algorithms. Further, the system is shown to admit generalized delta-shock solutions, first discovered in the context of sticky-particle dynamics (Bouchut, Ser. Adv. Math App. Sci., 22 (1994) pp. 171--190). A new approach, based on relaxation schemes proposed by Jin and Xin (Comm. Pure Appl. Math. 48 (1995) pp. 235--276) and LeVeque and Pelanti (J. Comput. Phys. 172 (2001) pp. 572--591) is developed to solve this system of equations. The method consists of finding an exact solution to a Riemann problem at each cell interface and coupling these to advance the solution in time. Applications to an intense laser propagating in an under-dense plasma are presented.

Non-classic multiscale modeling of manipulation based on AFM, in aqueous and humid ambient

NASA Astrophysics Data System (ADS)

Korayem, M. H.; Homayooni, A.; Hefzabad, R. N.

2018-05-01

To achieve a precise manipulation, it is important that an accurate model consisting the size effect and environmental conditions be employed. In this paper, the non-classical multiscale modeling is developed to investigate the manipulation in a vacuum, aqueous and humid ambient. The manipulation structure is considered into two parts as a macro-field (MF) and a nano-field (NF). The governing equations of the AFM components (consist of the cantilever and tip) in the MF are derived based on the modified couple stress theory. The material length scale parameter is used to study the size effect. The fluid flow in the MF is assumed as the Couette and Creeping flows. Moreover, the NF is modeled using the molecular dynamics. The Electro-Based (ELBA) model is considered to model the ambient condition in the NF. The nanoparticle in the different conditions is taken into account to study the manipulation. The results of the manipulation indicate that the predicted deflection of the non-classical model is less than the classical one. Comparison of the nanoparticle travelled distance on substrate shows that the manipulation in the submerged condition is close to the ideal manipulation. The results of humid condition illustrate that by increasing the relative humidity (RH) the manipulation force decreases. Furthermore, Root Mean Square (RMS) as a criterion of damage demonstrates that the submerged nanoparticle has the minimum damage, however, the minimum manipulation force occurs in superlative humid ambient.

Solution of the classical Yang-Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model

NASA Astrophysics Data System (ADS)

Links, Jon

2017-03-01

Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang-Baxter equation, from which commuting transfer matrices may be constructed. This procedure is reviewed, specifically for solutions without skew-symmetry. A particular solution with an exotic symmetry is identified, which is not obtained as a limiting expansion of the usual Yang-Baxter equation. This solution facilitates the construction of commuting transfer matrices which will be used to establish the integrability of a multi-species boson tunnelling model. The model generalises the well-known two-site Bose-Hubbard model, to which it reduces in the one-species limit. Due to the lack of an apparent reference state, application of the algebraic Bethe Ansatz to solve the model is prohibitive. Instead, the Bethe Ansatz solution is obtained by the use of operator identities and tensor product decompositions.

Far-Field Lorenz-Mie Scattering in an Absorbing Host Medium: Theoretical Formalism and FORTRAN Program

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Yang, Ping

2018-01-01

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenzâ€"Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html, and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations.

Computation of three-dimensional nozzle-exhaust flow fields with the GIM code

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Anderson, P. G.

1978-01-01

A methodology is introduced for constructing numerical analogs of the partial differential equations of continuum mechanics. A general formulation is provided which permits classical finite element and many of the finite difference methods to be derived directly. The approach, termed the General Interpolants Method (GIM), can combined the best features of finite element and finite difference methods. A quasi-variational procedure is used to formulate the element equations, to introduce boundary conditions into the method and to provide a natural assembly sequence. A derivation is given in terms of general interpolation functions from this procedure. Example computations for transonic and supersonic flows in two and three dimensions are given to illustrate the utility of GIM. A three-dimensional nozzle-exhaust flow field is solved including interaction with the freestream and a coupled treatment of the shear layer. Potential applications of the GIM code to a variety of computational fluid dynamics problems is then discussed in terms of existing capability or by extension of the methodology.

Spin Hartree-Fock approach to studying quantum Heisenberg antiferromagnets in low dimensions

NASA Astrophysics Data System (ADS)

Werth, A.; Kopietz, P.; Tsyplyatyev, O.

2018-05-01

We construct a new mean-field theory for a quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition, in accord with the Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via a Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order 1 /T expansions.

Far-field Lorenz-Mie scattering in an absorbing host medium: Theoretical formalism and FORTRAN program

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Yang, Ping

2018-01-01

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenz-Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html, and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations.

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

NASA Astrophysics Data System (ADS)

Cao, ChunJun; Carroll, Sean M.

2018-04-01

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

Classical r-matrices for the generalised Chern–Simons formulation of 3d gravity

NASA Astrophysics Data System (ADS)

Osei, Prince K.; Schroers, Bernd J.

2018-04-01

We study the conditions for classical r-matrices to be compatible with the generalised Chern–Simons action for 3d gravity. Compatibility means solving the classical Yang–Baxter equations with a prescribed symmetric part for each of the real Lie algebras and bilinear pairings arising in the generalised Chern–Simons action. We give a new construction of r-matrices via a generalised complexification and derive a non-linear set of matrix equations determining the most general compatible r-matrix. We exhibit new families of solutions and show that they contain some known r-matrices for special parameter values.

High-accuracy phase-field models for brittle fracture based on a new family of degradation functions

NASA Astrophysics Data System (ADS)

Sargado, Juan Michael; Keilegavlen, Eirik; Berre, Inga; Nordbotten, Jan Martin

2018-02-01

Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In the phase-field framework, the surface energy associated with crack formation is calculated by evaluating a functional defined in terms of a scalar order parameter and its gradients. These in turn describe the fractures in a diffuse sense following a prescribed regularization length scale. Imposing stationarity of the total energy leads to a coupled system of partial differential equations that enforce stress equilibrium and govern phase-field evolution. These equations are coupled through an energy degradation function that models the loss of stiffness in the bulk material as it undergoes damage. In the present work, we introduce a new parametric family of degradation functions aimed at increasing the accuracy of phase-field models in predicting critical loads associated with crack nucleation as well as the propagation of existing fractures. An additional goal is the preservation of linear elastic response in the bulk material prior to fracture. Through the analysis of several numerical examples, we demonstrate the superiority of the proposed family of functions to the classical quadratic degradation function that is used most often in the literature.

Relational evolution of effectively interacting group field theory quantum gravity condensates

NASA Astrophysics Data System (ADS)

Pithis, Andreas G. A.; Sakellariadou, Mairi

2017-03-01

We study the impact of effective interactions onto relationally evolving group field theory (GFT) condensates based on real-valued fields. In a first step we show that a free condensate configuration in an isotropic restriction settles dynamically into a low-spin configuration of the quantum geometry. This goes hand in hand with the accelerated and exponential expansion of its volume, as well as the vanishing of its relative uncertainty which suggests the classicalization of the quantum geometry. The dynamics of the emergent space can then be given in terms of the classical Friedmann equations. In contrast to models based on complex-valued fields, solutions avoiding the singularity problem can only be found if the initial conditions are appropriately chosen. We then turn to the analysis of the influence of effective interactions on the dynamics by studying in particular the Thomas-Fermi regime. In this context, at the cost of fine-tuning, an epoch of inflationary expansion of quantum geometric origin can be implemented. Finally, and for the first time, we study anisotropic GFT condensate configurations and show that such systems tend to isotropize quickly as the value of the relational clock grows. This paves the way to a more systematic investigation of anisotropies in the context of GFT condensate cosmology.

Introduction of a Classical Level in Quantum Theory

NASA Astrophysics Data System (ADS)

Prosperi, G. M.

2016-11-01

In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of a system during a certain interval of time in the framework of a somewhat generalized approach to quantum mechanics (QM). The outcome was a distribution of probability on the space of all the possible continuous histories of a set of quantities to be considered as a kind of coarse grained approximation to some ordinary quantum observables commuting or not. In fact the main aim was the introduction of a classical level in the context of QM, treating formally a set of basic quantities, to be considered as beables in the sense of Bell, as continuously taken under observation. However the effect of such assumption was a permanent modification of the Liouville-von Neumann equation for the statistical operator by the introduction of a dissipative term which is in conflict with basic conservation rules in all reasonable models we had considered. Difficulties were even encountered for a relativistic extension of the formalism. In this paper I propose a modified version of the original formalism which seems to overcome both difficulties. First I study the simple models of an harmonic oscillator and a free scalar field in which a coarse grain position and a coarse grained field respectively are treated as beables. Then I consider the more realistic case of spinor electrodynamics in which only certain coarse grained electric and magnetic fields are introduced as classical variables and no matter related quantities.

User Guide for Compressible Flow Toolbox Version 2.1 for Use With MATLAB(Registered Trademark); Version 7

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

This report provides a user guide for the Compressible Flow Toolbox, a collection of algorithms that solve almost 300 linear and nonlinear classical compressible flow relations. The algorithms, implemented in the popular MATLAB programming language, are useful for analysis of one-dimensional steady flow with constant entropy, friction, heat transfer, or shock discontinuities. The solutions do not include any gas dissociative effects. The toolbox also contains functions for comparing and validating the equation-solving algorithms against solutions previously published in the open literature. The classical equations solved by the Compressible Flow Toolbox are: isentropic-flow equations, Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section.), normal-shock equations, oblique-shock equations, and Prandtl-Meyer expansion equations. At the time this report was published, the Compressible Flow Toolbox was available without cost from the NASA Software Repository.

Color instabilities in the quark-gluon plasma

NASA Astrophysics Data System (ADS)

Mrówczyński, Stanisław; Schenke, Björn; Strickland, Michael

2017-04-01

When the quark-gluon plasma (QGP) - a system of deconfined quarks and gluons - is in a nonequilibrium state, it is usually unstable with respect to color collective modes. The instabilities, which are expected to strongly influence dynamics of the QGP produced in relativistic heavy-ion collisions, are extensively discussed under the assumption that the plasma is weakly coupled. We begin by presenting the theoretical approaches to study the QGP, which include: field theory methods based on the Keldysh-Schwinger formalism, classical and quantum kinetic theories, and fluid techniques. The dispersion equations, which give the spectrum of plasma collective excitations, are analyzed in detail. Particular attention is paid to a momentum distribution of plasma constituents which is obtained by deforming an isotropic momentum distribution. Mechanisms of chromoelectric and chromomagnetic instabilities are explained in terms of elementary physics. The Nyquist analysis, which allows one to determine the number of solutions of a dispersion equation without explicitly solving it, and stability criteria are also discussed. We then review various numerical approaches - purely classical or quantum - to simulate the temporal evolution of an unstable quark-gluon plasma. The dynamical role of instabilities in the processes of plasma equilibration is analyzed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mrówczyński, Stanisław; Schenke, Björn; Strickland, Michael

When the quark–gluon plasma (QGP) – a system of deconfined quarks and gluons – is in a nonequilibrium state, it is usually unstable with respect to color collective modes. The instabilities, which are expected to strongly influence dynamics of the QGP produced in relativistic heavy-ion collisions, are extensively discussed under the assumption that the plasma is weakly coupled. Here, we begin by presenting the theoretical approaches to study the QGP, which include: field theory methods based on the Keldysh–Schwinger formalism, classical and quantum kinetic theories, and fluid techniques. The dispersion equations, which give the spectrum of plasma collective excitations, aremore » analyzed in detail. We pay particular attention to a momentum distribution of plasma constituents which is obtained by deforming an isotropic momentum distribution. Mechanisms of chromoelectric and chromomagnetic instabilities are explained in terms of elementary physics. The Nyquist analysis, which allows one to determine the number of solutions of a dispersion equation without explicitly solving it, and stability criteria are also discussed. We then review various numerical approaches – purely classical or quantum – to simulate the temporal evolution of an unstable quark–gluon plasma. The dynamical role of instabilities in the processes of plasma equilibration is analyzed.« less

Piezoelectrically actuated flextensional micromachined ultrasound transducers--I: theory.

PubMed

Perçin, Gökhan; Khuri-Yakub, Butrus T

2002-05-01

This series of two papers considers piezoelectrically actuated flextensional micromachined ultrasound transducers (PAFMUTs) and consists of theory, fabrication, and experimental parts. The theory presented in this paper is developed for an ultrasound transducer application presented in the second part. In the absence of analytical expressions for the equivalent circuit parameters of a flextensional transducer, it is difficult to calculate its optimal parameters and dimensions and difficult to choose suitable materials. The influence of coupling between flexural and extensional deformation and that of coupling between the structure and the acoustic volume on the dynamic response of piezoelectrically actuated flextensional transducer are analyzed using two analytical methods: classical thin (Kirchhoff) plate theory and Mindlin plate theory. Classical thin plate theory and Mindlin plate theory are applied to derive two-dimensional plate equations for the transducer and to calculate the coupled electromechanical field variables such as mechanical displacement and electrical input impedance. In these methods, the variations across the thickness direction vanish by using the bending moments per unit length or stress resultants. Thus, two-dimensional plate equations for a step-wise laminated circular plate are obtained as well as two different solutions to the corresponding systems. An equivalent circuit of the transducer is also obtained from these solutions.

Color instabilities in the quark–gluon plasma

DOE PAGES

Mrówczyński, Stanisław; Schenke, Björn; Strickland, Michael

2017-04-09

When the quark–gluon plasma (QGP) – a system of deconfined quarks and gluons – is in a nonequilibrium state, it is usually unstable with respect to color collective modes. The instabilities, which are expected to strongly influence dynamics of the QGP produced in relativistic heavy-ion collisions, are extensively discussed under the assumption that the plasma is weakly coupled. Here, we begin by presenting the theoretical approaches to study the QGP, which include: field theory methods based on the Keldysh–Schwinger formalism, classical and quantum kinetic theories, and fluid techniques. The dispersion equations, which give the spectrum of plasma collective excitations, aremore » analyzed in detail. We pay particular attention to a momentum distribution of plasma constituents which is obtained by deforming an isotropic momentum distribution. Mechanisms of chromoelectric and chromomagnetic instabilities are explained in terms of elementary physics. The Nyquist analysis, which allows one to determine the number of solutions of a dispersion equation without explicitly solving it, and stability criteria are also discussed. We then review various numerical approaches – purely classical or quantum – to simulate the temporal evolution of an unstable quark–gluon plasma. The dynamical role of instabilities in the processes of plasma equilibration is analyzed.« less

Corrections to the Thomson cross section caused by relativistic effects and by the presence of the drift velocity of a classical charged particle in the field of a monochromatic plane wave

NASA Astrophysics Data System (ADS)

Perestoronin, A. V.

2017-03-01

An approach to the solution of the relativistic problem of the motion of a classical charged particle in the field of a monochromatic plane wave with an arbitrary polarization (linear, circular, or elliptic) is proposed. It is based on the analysis of the 4-vector equation of motion of the charged particle together with the 4-vector and tensor equations for the components of the electromagnetic field tensor of a monochromatic plane wave. This approach provides analytical expressions for the time-averaged square of the 4-acceleration of the charge, as well as for the averaged values of any quantities periodic in the time of the reference frame. Expressions for the integral power of scattered radiation, which is proportional to the time-averaged square of the 4-acceleration of the charge, and for the integral scattering cross section, which is the ratio of the power of scattered radiation to the intensity of incident radiation, are obtained for an arbitrary inertial reference frame. An expression for the scattering cross section, which coincides with the known results at the circular and linear polarizations of the incident waves and describes the case of elliptic polarization of the incident wave, is obtained for the reference frame where the charged particle is on average at rest. An expression for the scattering cross section including relativistic effects and the nonzero drift velocity of a particle in this system is obtained for the laboratory reference frame, where the initial velocity of the charged particle is zero. In the case of the circular polarization of the incident wave, the scattering cross section in the laboratory frame is equal to the Thompson cross section.

Theoretical study of high-order harmonic generation from the hydrogen molecular ion with a dichromatic spatially inhomogeneous field

NASA Astrophysics Data System (ADS)

Xu, Xiao-Hu; Wang, Yan-Jun; Miao, Xiang-Yang

2018-05-01

We theoretically investigate the enhancement of high-order harmonic generation by numerically solving the non-Born-Oppenheimer time-dependent Schrödinger equation from the hydrogen molecular ion in a dichromatic inhomogeneous laser field. An ultrabroad supercontinuum up to 300 orders spectral width is generated. It is found that not only the inhomogeneity, but also the dichromatic field contributes to the significant extension of the harmonic cutoff compared with a monochromatic inhomogeneous laser field. Meanwhile, the long quantum paths can be suppressed and short ones can be enhanced by selecting optimized inhomogeneous parameter β, intensity and carrier envelope phase of the dichromatic inhomogeneous laser field. Furthermore, by superposing a properly selected range of the harmonic spectrum in the continuum region, an isolated 29-as pulse is generated. Both the classical theory and quantum time-frequency analysis are adopted to explain the physical mechanism.

Simulation of wave packet tunneling of interacting identical particles

NASA Astrophysics Data System (ADS)

Lozovik, Yu. E.; Filinov, A. V.; Arkhipov, A. S.

2003-02-01

We demonstrate a different method of simulation of nonstationary quantum processes, considering the tunneling of two interacting identical particles, represented by wave packets. The used method of quantum molecular dynamics (WMD) is based on the Wigner representation of quantum mechanics. In the context of this method ensembles of classical trajectories are used to solve quantum Wigner-Liouville equation. These classical trajectories obey Hamiltonian-like equations, where the effective potential consists of the usual classical term and the quantum term, which depends on the Wigner function and its derivatives. The quantum term is calculated using local distribution of trajectories in phase space, therefore, classical trajectories are not independent, contrary to classical molecular dynamics. The developed WMD method takes into account the influence of exchange and interaction between particles. The role of direct and exchange interactions in tunneling is analyzed. The tunneling times for interacting particles are calculated.

Dilute and dense axion stars

NASA Astrophysics Data System (ADS)

Visinelli, Luca; Baum, Sebastian; Redondo, Javier; Freese, Katherine; Wilczek, Frank

2018-02-01

Axion stars are hypothetical objects formed of axions, obtained as localized and coherently oscillating solutions to their classical equation of motion. Depending on the value of the field amplitude at the core |θ0 | ≡ | θ (r = 0) |, the equilibrium of the system arises from the balance of the kinetic pressure and either self-gravity or axion self-interactions. Starting from a general relativistic framework, we obtain the set of equations describing the configuration of the axion star, which we solve as a function of |θ0 |. For small |θ0 | ≲ 1, we reproduce results previously obtained in the literature, and we provide arguments for the stability of such configurations in terms of first principles. We compare qualitative analytical results with a numerical calculation. For large amplitudes |θ0 | ≳ 1, the axion field probes the full non-harmonic QCD chiral potential and the axion star enters the dense branch. Our numerical solutions show that in this latter regime the axions are relativistic, and that one should not use a single frequency approximation, as previously applied in the literature. We employ a multi-harmonic expansion to solve the relativistic equation for the axion field in the star, and demonstrate that higher modes cannot be neglected in the dense regime. We interpret the solutions in the dense regime as pseudo-breathers, and show that the life-time of such configurations is much smaller than any cosmological time scale.

Simulation of bipolar charge transport in nanocomposite polymer films

NASA Astrophysics Data System (ADS)

Lean, Meng H.; Chu, Wei-Ping L.

2015-03-01

This paper describes 3D particle-in-cell simulation of bipolar charge injection and transport through nanocomposite film comprised of ferroelectric ceramic nanofillers in an amorphous polymer matrix. The classical electrical double layer (EDL) model for a monopolar core is extended (eEDL) to represent the nanofiller by replacing it with a dipolar core. Charge injection at the electrodes assumes metal-polymer Schottky emission at low to moderate fields and Fowler-Nordheim tunneling at high fields. Injected particles migrate via field-dependent Poole-Frenkel mobility and recombine with Monte Carlo selection. The simulation algorithm uses a boundary integral equation method for solution of the Poisson equation coupled with a second-order predictor-corrector scheme for robust time integration of the equations of motion. The stability criterion of the explicit algorithm conforms to the Courant-Friedrichs-Levy limit assuring robust and rapid convergence. The model is capable of simulating a wide dynamic range spanning leakage current to pre-breakdown. Simulation results for BaTiO3 nanofiller in amorphous polymer matrix indicate that charge transport behavior depend on nanoparticle polarization with anti-parallel orientation showing the highest leakage conduction and therefore lowest level of charge trapping in the interaction zone. Charge recombination is also highest, at the cost of reduced leakage conduction charge. The eEDL model predicts the meandering pathways of charge particle trajectories.

A classical but new kinetic equation for hydride transfer reactions.

PubMed

Zhu, Xiao-Qing; Deng, Fei-Huang; Yang, Jin-Dong; Li, Xiu-Tao; Chen, Qiang; Lei, Nan-Ping; Meng, Fan-Kun; Zhao, Xiao-Peng; Han, Su-Hui; Hao, Er-Jun; Mu, Yuan-Yuan

2013-09-28

A classical but new kinetic equation to estimate activation energies of various hydride transfer reactions was developed according to transition state theory using the Morse-type free energy curves of hydride donors to release a hydride anion and hydride acceptors to capture a hydride anion and by which the activation energies of 187 typical hydride self-exchange reactions and more than thirty thousand hydride cross transfer reactions in acetonitrile were safely estimated in this work. Since the development of the kinetic equation is only on the basis of the related chemical bond changes of the hydride transfer reactants, the kinetic equation should be also suitable for proton transfer reactions, hydrogen atom transfer reactions and all the other chemical reactions involved with breaking and formation of chemical bonds. One of the most important contributions of this work is to have achieved the perfect unity of the kinetic equation and thermodynamic equation for hydride transfer reactions.

Adapting the Euler-Lagrange equation to study one-dimensional motions under the action of a constant force

NASA Astrophysics Data System (ADS)

Dias, Clenilda F.; Araújo, Maria A. S.; Carvalho-Santos, Vagson L.

2018-01-01

The Euler-Lagrange equations (ELE) are very important in the theoretical description of several physical systems. In this work we have used a simplified form of ELE to study one-dimensional motions under the action of a constant force. From the use of the definition of partial derivative, we have proposed two operators, here called mean delta operators, which may be used to solve the ELE in a simplest way. We have applied this simplification to solve three simple mechanical problems in which the particle is under the action of the gravitational field: a free fall body, the Atwood’s machine and the inclined plan. The proposed simplification can be used to introduce the lagrangian formalism in teaching classical mechanics in introductory physics courses.

Fundamentals of Polarized Light

NASA Technical Reports Server (NTRS)

Mishchenko, Michael

2003-01-01

The analytical and numerical basis for describing scattering properties of media composed of small discrete particles is formed by the classical electromagnetic theory. Although there are several excellent textbooks outlining the fundamentals of this theory, it is convenient for our purposes to begin with a summary of those concepts and equations that are central to the subject of this book and will be used extensively in the following chapters. We start by formulating Maxwell's equations and constitutive relations for time- harmonic macroscopic electromagnetic fields and derive the simplest plane-wave solution that underlies the basic optical idea of a monochromatic parallel beam of light. This solution naturally leads to the introduction of such fundamental quantities as the refractive index and the Stokes parameters. Finally, we define the concept of a quasi-monochromatic beam of light and discuss its implications.

Multi-Dimensional Quantum Effect Simulation Using a Density-Gradient Model and Script-Level Programming Techniques

NASA Technical Reports Server (NTRS)

Rafferty, Connor S.; Biegel, Bryan A.; Yu, Zhi-Ping; Ancona, Mario G.; Bude, J.; Dutton, Robert W.; Saini, Subhash (Technical Monitor)

1998-01-01

A density-gradient (DG) model is used to calculate quantum-mechanical corrections to classical carrier transport in MOS (Metal Oxide Semiconductor) inversion/accumulation layers. The model is compared to measured data and to a fully self-consistent coupled Schrodinger and Poisson equation (SCSP) solver. Good agreement is demonstrated for MOS capacitors with gate oxide as thin as 21 A. It is then applied to study carrier distribution in ultra short MOSFETs (Metal Oxide Semiconductor Field Effect Transistor) with surface roughness. This work represents the first implementation of the DG formulation on multidimensional unstructured meshes. It was enabled by a powerful scripting approach which provides an easy-to-use and flexible framework for solving the fourth-order PDEs (Partial Differential Equation) of the DG model.

Hamiltonian formulation of Palatini f(R) theories a la Brans-Dicke theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olmo, Gonzalo J.; Sanchis-Alepuz, Helios; Institut fuer Physik, Karl-Franzens-Universitaet Graz

2011-05-15

We study the Hamiltonian formulation of f(R) theories of gravity both in metric and in Palatini formalism using their classical equivalence with Brans-Dicke theories with a nontrivial potential. The Palatini case, which corresponds to the {omega}=-3/2 Brans-Dicke theory, requires special attention because of new constraints associated with the scalar field, which is nondynamical. We derive, compare, and discuss the constraints and evolution equations for the {omega}=-3/2 and {omega}{ne}-3/2 cases. Based on the properties of the constraint and evolution equations, we find that, contrary to certain claims in the literature, the Cauchy problem for the {omega}=-3/2 case is well formulated andmore » there is no reason to believe that it is not well posed in general.« less

Sonic boom interaction with turbulence

NASA Technical Reports Server (NTRS)

Rusak, Zvi; Giddings, Thomas E.

1994-01-01

A recently developed transonic small-disturbance model is used to analyze the interactions of random disturbances with a weak shock. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. It shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed-type elliptic hyperbolic flows around the shock wave is presented. Numerical calculations of shock wave interactions with various deterministic vorticity and temperature disturbances result in complicate shock wave structures and describe peaked as well as rounded pressure signatures behind the shock front, as were recorded in experiments of sonic booms running through atmospheric turbulence.

A free boundary approach to the Rosensweig instability of ferrofluids

NASA Astrophysics Data System (ADS)

Parini, Enea; Stylianou, Athanasios

2018-04-01

We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid undergoing normal field instability. The starting point is the ferrohydrostatic equations for the magnetic potentials in the ferrofluid and air, and the function describing their interface. These constitute the strong form for the Euler-Lagrange equations of a convex-concave functional, which we extend to include interfaces that are not necessarily graphs of functions. Saddle points are then found by iterating the direct method of the calculus of variations and applying classical results of convex analysis. For the existence part, we assume a general nonlinear magnetization law; for a linear law, we also show, via convex duality, that the saddle point is a constrained minimizer of the relevant energy functional.

New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2010-01-01

In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

Ground state for a massive scalar field in the BTZ spacetime with Robin boundary conditions

NASA Astrophysics Data System (ADS)

Bussola, Francesco; Dappiaggi, Claudio; Ferreira, Hugo R. C.; Khavkine, Igor

2017-11-01

We consider a real, massive scalar field in Bañados-Teitelboim-Zanelli spacetime, a 2 +1 -dimensional black hole solution of Einstein's field equations with a negative cosmological constant. First, we analyze the space of classical solutions in a mode decomposition, and we characterize the collection of all admissible boundary conditions of Robin type which can be imposed at infinity. Second, we investigate whether, for a given boundary condition, there exists a ground state by constructing explicitly its two-point function. We demonstrate that for a subclass of the boundary conditions it is possible to construct a ground state that locally satisfies the Hadamard property. In all other cases, we show that bound state mode solutions exist and, therefore, such construction is not possible.

Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models

NASA Astrophysics Data System (ADS)

Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo

2014-04-01

We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.

Reduced Order Podolsky Model

NASA Astrophysics Data System (ADS)

Thibes, Ronaldo

2017-02-01

We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual electromagnetic field. The equivalence with Podolsky's original model is studied at classical and quantum levels. Concerning the dynamical time evolution, we obtain a theory with two first-class and two second-class constraints in phase space. We calculate explicitly the corresponding Dirac brackets involving both vector fields. We use the Senjanovic procedure to implement the second-class constraints and the Batalin-Fradkin-Vilkovisky path integral quantization scheme to deal with the symmetries generated by the first-class constraints. The physical interpretation of the results turns out to be simpler due to the reduced derivatives order permeating the equations of motion, Dirac brackets and effective action.

Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2011-04-01

We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of Stäckel-Killing and Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out. A condition of the electromagnetic field to maintain the hidden symmetry of the system is stated. A concrete realization of this condition is given by the Killing-Maxwell system and exemplified with the Kerr metric. Quantum symmetry operators for the Klein-Gordon and Dirac equations are constructed from Killing tensors. The transfer of the classical conserved quantities to the quantum mechanical level is analyzed in connection with quantum anomalies.

Bose-Einstein condensation of the classical axion field in cosmology?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davidson, Sacha; Elmer, Martin, E-mail: s.davidson@ipnl.in2p3.fr, E-mail: m.elmer@ipnl.in2p3.fr

The axion is a motivated cold dark matter candidate, which it would be interesting to distinguish from weakly interacting massive particles. Sikivie has suggested that axions could behave differently during non-linear galaxy evolution, if they form a Bose-Einstein condensate, and argues that ''gravitational thermalisation'' drives them to a Bose-Einstein condensate during the radiation dominated era. Using classical equations of motion during linear structure formation, we explore whether the gravitational interactions of axions can generate enough entropy. At linear order in G{sub N}, we interpret that the principle activities of gravity are to expand the Universe and grow density fluctuations. Tomore » quantify the rate of entropy creation we use the anisotropic stress to estimate a short dissipation scale for axions which does not confirm previous estimates of their gravitational thermalisation rate.« less

Spin waves in rings of classical magnetic dipoles

NASA Astrophysics Data System (ADS)

Schmidt, Heinz-Jürgen; Schröder, Christian; Luban, Marshall

2017-03-01

We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting cases that can be analyzed in detail. One case is that of spin waves as infinitesimal excitations from the system’s ground state, where the dispersion relation can be determined analytically. The frequencies of these infinitesimal spin waves are compared with the peaks of the Fourier transform of the thermal expectation value of the autocorrelation function calculated by Monte Carlo simulations. In the special case of vanishing wave number an exact solution of the equations of motion is possible describing synchronized oscillations with finite amplitudes. Finally, the limiting case of a dipole chain with N\\longrightarrow ∞ is investigated and completely solved.

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq (sl (2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra.

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

A General Theory of Unsteady Compressible Potential Aerodynamics

NASA Technical Reports Server (NTRS)

Morino, L.

1974-01-01

The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the potential is obtained for both supersonic and subsonic flow. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface, sigma, of the body. Hence, if the point P approaches the surface of the body, the representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface sigma. For the important practical case of small harmonic oscillation around a rest position, the equation reduces to a two-dimensional Fredholm integral equation of second-type. It is shown that this equation reduces properly to the lifting surface theories as well as other classical mathematical formulas. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings.

Theories of Matter, Space and Time, Volume 2; Quantum theories

NASA Astrophysics Data System (ADS)

Evans, N.; King, S. F.

2018-06-01

This book and its prequel Theories of Matter Space and Time: Classical Theories grew out of courses that we have both taught as part of the undergraduate degree program in Physics at Southampton University, UK. Our goal was to guide the full MPhys undergraduate cohort through some of the trickier areas of theoretical physics that we expect our undergraduates to master. Here we teach the student to understand first quantized relativistic quantum theories. We first quickly review the basics of quantum mechanics which should be familiar to the reader from a prior course. Then we will link the Schrödinger equation to the principle of least action introducing Feynman's path integral methods. Next, we present the relativistic wave equations of Klein, Gordon and Dirac. Finally, we convert Maxwell's equations of electromagnetism to a wave equation for photons and make contact with quantum electrodynamics (QED) at a first quantized level. Between the two volumes we hope to move a student's understanding from their prior courses to a place where they are ready, beyond, to embark on graduate level courses on quantum field theory.

Extension of lattice Boltzmann flux solver for simulation of compressible multi-component flows

NASA Astrophysics Data System (ADS)

Yang, Li-Ming; Shu, Chang; Yang, Wen-Ming; Wang, Yan

2018-05-01

The lattice Boltzmann flux solver (LBFS), which was presented by Shu and his coworkers for solving compressible fluid flow problems, is extended to simulate compressible multi-component flows in this work. To solve the two-phase gas-liquid problems, the model equations with stiffened gas equation of state are adopted. In this model, two additional non-conservative equations are introduced to represent the material interfaces, apart from the classical Euler equations. We first convert the interface equations into the full conservative form by applying the mass equation. After that, we calculate the numerical fluxes of the classical Euler equations by the existing LBFS and the numerical fluxes of the interface equations by the passive scalar approach. Once all the numerical fluxes at the cell interface are obtained, the conservative variables at cell centers can be updated by marching the equations in time and the material interfaces can be identified via the distributions of the additional variables. The numerical accuracy and stability of present scheme are validated by its application to several compressible multi-component fluid flow problems.

Algorithmic framework for group analysis of differential equations and its application to generalized Zakharov-Kuznetsov equations

NASA Astrophysics Data System (ADS)

Huang, Ding-jiang; Ivanova, Nataliya M.

2016-02-01

In this paper, we explain in more details the modern treatment of the problem of group classification of (systems of) partial differential equations (PDEs) from the algorithmic point of view. More precisely, we revise the classical Lie algorithm of construction of symmetries of differential equations, describe the group classification algorithm and discuss the process of reduction of (systems of) PDEs to (systems of) equations with smaller number of independent variables in order to construct invariant solutions. The group classification algorithm and reduction process are illustrated by the example of the generalized Zakharov-Kuznetsov (GZK) equations of form ut +(F (u)) xxx +(G (u)) xyy +(H (u)) x = 0. As a result, a complete group classification of the GZK equations is performed and a number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Lie symmetry reductions and exact solutions for two important invariant models, i.e., the classical and modified Zakharov-Kuznetsov equations, are constructed. The algorithmic framework for group analysis of differential equations presented in this paper can also be applied to other nonlinear PDEs.

The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Tweed, J.; Farassat, F.

1999-01-01

The prediction of ducted fan engine noise using a boundary integral equation method (BIEM) is considered. Governing equations for the BIEM are based on linearized acoustics and describe the scattering of incident sound by a thin, finite-length cylindrical duct in the presence of a uniform axial inflow. A classical boundary value problem (BVP) is derived that includes an axisymmetric, locally reacting liner on the duct interior. Using potential theory, the BVP is recast as a system of hypersingular boundary integral equations with subsidiary conditions. We describe the integral equation derivation and solution procedure in detail. The development of the computationally efficient ducted fan noise prediction program TBIEM3D, which implements the BIEM, and its utility in conducting parametric noise reduction studies are discussed. Unlike prediction methods based on spinning mode eigenfunction expansions, the BIEM does not require the decomposition of the interior acoustic field into its radial and axial components which, for the liner case, avoids the solution of a difficult complex eigenvalue problem. Numerical spectral studies are presented to illustrate the nexus between the eigenfunction expansion representation and BIEM results. We demonstrate BIEM liner capability by examining radiation patterns for several cases of practical interest.

Transonic flow of steam with non-equilibrium and homogenous condensation

NASA Astrophysics Data System (ADS)

Virk, Akashdeep Singh; Rusak, Zvi

2017-11-01

A small-disturbance model for studying the physical behavior of a steady transonic flow of steam with non-equilibrium and homogeneous condensation around a thin airfoil is derived. The steam thermodynamic behavior is described by van der Waals equation of state. The water condensation rate is calculated according to classical nucleation and droplet growth models. The current study is based on an asymptotic analysis of the fluid flow and condensation equations and boundary conditions in terms of the small thickness of the airfoil, small angle of attack, closeness of upstream flow Mach number to unity and small amount of condensate. The asymptotic analysis gives the similarity parameters that govern the problem. The flow field may be described by a non-homogeneous transonic small-disturbance equation coupled with a set of four ordinary differential equations for the calculation of the condensate mass fraction. An iterative numerical scheme which combines Murman & Cole's (1971) method with Simpson's integration rule is applied to solve the coupled system of equations. The model is used to study the effects of energy release from condensation on the aerodynamic performance of airfoils operating at high pressures and temperatures and near the vapor-liquid saturation conditions.

Quantum cluster variational method and message passing algorithms revisited

NASA Astrophysics Data System (ADS)

Domínguez, E.; Mulet, Roberto

2018-02-01

We present a general framework to study quantum disordered systems in the context of the Kikuchi's cluster variational method (CVM). The method relies in the solution of message passing-like equations for single instances or in the iterative solution of complex population dynamic algorithms for an average case scenario. We first show how a standard application of the Kikuchi's CVM can be easily translated to message passing equations for specific instances of the disordered system. We then present an "ad hoc" extension of these equations to a population dynamic algorithm representing an average case scenario. At the Bethe level, these equations are equivalent to the dynamic population equations that can be derived from a proper cavity ansatz. However, at the plaquette approximation, the interpretation is more subtle and we discuss it taking also into account previous results in classical disordered models. Moreover, we develop a formalism to properly deal with the average case scenario using a replica-symmetric ansatz within this CVM for quantum disordered systems. Finally, we present and discuss numerical solutions of the different approximations for the quantum transverse Ising model and the quantum random field Ising model in two-dimensional lattices.

Thermodynamic properties for applications in chemical industry via classical force fields.

PubMed

Guevara-Carrion, Gabriela; Hasse, Hans; Vrabec, Jadran

2012-01-01

Thermodynamic properties of fluids are of key importance for the chemical industry. Presently, the fluid property models used in process design and optimization are mostly equations of state or G (E) models, which are parameterized using experimental data. Molecular modeling and simulation based on classical force fields is a promising alternative route, which in many cases reasonably complements the well established methods. This chapter gives an introduction to the state-of-the-art in this field regarding molecular models, simulation methods, and tools. Attention is given to the way modeling and simulation on the scale of molecular force fields interact with other scales, which is mainly by parameter inheritance. Parameters for molecular force fields are determined both bottom-up from quantum chemistry and top-down from experimental data. Commonly used functional forms for describing the intra- and intermolecular interactions are presented. Several approaches for ab initio to empirical force field parameterization are discussed. Some transferable force field families, which are frequently used in chemical engineering applications, are described. Furthermore, some examples of force fields that were parameterized for specific molecules are given. Molecular dynamics and Monte Carlo methods for the calculation of transport properties and vapor-liquid equilibria are introduced. Two case studies are presented. First, using liquid ammonia as an example, the capabilities of semi-empirical force fields, parameterized on the basis of quantum chemical information and experimental data, are discussed with respect to thermodynamic properties that are relevant for the chemical industry. Second, the ability of molecular simulation methods to describe accurately vapor-liquid equilibrium properties of binary mixtures containing CO(2) is shown.

New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

NASA Astrophysics Data System (ADS)

S Saha, Ray

2016-04-01

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

Photons from the early stages of relativistic heavy-ion collisions

NASA Astrophysics Data System (ADS)

Oliva, L.; Ruggieri, M.; Plumari, S.; Scardina, F.; Peng, G. X.; Greco, V.

2017-07-01

We present results about photon-production in relativistic heavy-ion collisions. The main novelty of our study is the calculation of the contribution of the early-stage photons to the photon spectrum. The initial stage is modeled by an ensemble of classical gluon fields which decay to a quark-gluon plasma via the Schwinger mechanism, and the evolution of the system is studied by coupling classical field equations to relativistic kinetic theory; photon production is then computed by including the pertinent collision processes into the collision integral. We find that the contribution of the early-stage photons to the direct photon spectrum is substantial for pT≈2 GeV and higher, the exact value depending on the collision energy; therefore, we identify this part of the photon spectrum as the sign of the early stage. Moreover, the amount of photons produced during the early stage is not negligible with respect to those produced by a thermalized quark-gluon plasma: We support the idea that there is no dark age in relativistic heavy-ion collisions.

Arbitrarily Curved and Twisted Space Beams. Ph.D. Thesis - Va. Polytech. Inst. and State Univ.; [Elastic Deformation, Stress Analysis

NASA Technical Reports Server (NTRS)

Hunter, W. F.

1974-01-01

A derivation of the equations which govern the deformation of an arbitrarily curved and twisted space beam is presented. These equations differ from those of the classical theory in that (1) extensional effects are included; (2) the strain-displacement relations are derived; and (3) the expressions for the stress resultants are developed from the strain displacement relations. It is shown that the torsional stress resultant obtained by the classical approach is basically incorrect except when the cross-section is circular. The governing equations are given in the form of first-order differential equations. A numerical algorithm is given for obtaining the natural vibration characteristics and example problems are presented.

Construction of Chained True Score Equipercentile Equatings under the Kernel Equating (KE) Framework and Their Relationship to Levine True Score Equating. Research Report. ETS RR-09-24

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2009-01-01

In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…

Fractional dynamics of charged particles in magnetic fields

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Alvarado-Méndez, E.; Guerrero-Ramírez, G. V.; Escobar-Jiménez, R. F.

2016-02-01

In many physical applications the electrons play a relevant role. For example, when a beam of electrons accelerated to relativistic velocities is used as an active medium to generate Free Electron Lasers (FEL), the electrons are bound to atoms, but move freely in a magnetic field. The relaxation time, longitudinal effects and transverse variations of the optical field are parameters that play an important role in the efficiency of this laser. The electron dynamics in a magnetic field is a means of radiation source for coupling to the electric field. The transverse motion of the electrons leads to either gain or loss energy from or to the field, depending on the position of the particle regarding the phase of the external radiation field. Due to the importance to know with great certainty the displacement of charged particles in a magnetic field, in this work we study the fractional dynamics of charged particles in magnetic fields. Newton’s second law is considered and the order of the fractional differential equation is (0;1]. Based on the Grünwald-Letnikov (GL) definition, the discretization of fractional differential equations is reported to get numerical simulations. Comparison between the numerical solutions obtained on Euler’s numerical method for the classical case and the GL definition in the fractional approach proves the good performance of the numerical scheme applied. Three application examples are shown: constant magnetic field, ramp magnetic field and harmonic magnetic field. In the first example the results obtained show bistability. Dissipative effects are observed in the system and the standard dynamic is recovered when the order of the fractional derivative is 1.

An Evaluation of Kernel Equating: Parallel Equating with Classical Methods in the SAT Subject Tests[TM] Program. Research Report. ETS RR-09-06

ERIC Educational Resources Information Center

Grant, Mary C.; Zhang, Lilly; Damiano, Michele

2009-01-01

This study investigated kernel equating methods by comparing these methods to operational equatings for two tests in the SAT Subject Tests[TM] program. GENASYS (ETS, 2007) was used for all equating methods and scaled score kernel equating results were compared to Tucker, Levine observed score, chained linear, and chained equipercentile equating…

A nonlinear equation for ionic diffusion in a strong binary electrolyte

PubMed Central

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

Teaching geographical hydrology in a non-stationary world

NASA Astrophysics Data System (ADS)

Hendriks, Martin R.; Karssenberg, Derek

2010-05-01

Understanding hydrological processes in a non-stationary world requires knowledge of hydrological processes and their interactions. Also, one needs to understand the (non-linear) relations between the hydrological system and other parts of our Earth system, such as the climate system, the socio-economic system, and the ecosystem. To provide this knowledge and understanding we think that three components are essential when teaching geographical hydrology. First of all, a student needs to acquire a thorough understanding of classical hydrology. For this, knowledge of the basic hydrological equations, such as the energy equation (Bernoulli), flow equation (Darcy), continuity (or water balance) equation is needed. This, however, is not sufficient to make a student fully understand the interactions between hydrological compartments, or between hydrological subsystems and other parts of the Earth system. Therefore, secondly, a student also needs to be knowledgeable of methods by which the different subsystems can be coupled; in general, numerical models are used for this. A major disadvantage of numerical models is their complexity. A solution may be to use simpler models, provided that a student really understands how hydrological processes function in our real, non-stationary world. The challenge for a student then lies in understanding the interactions between the subsystems, and to be able to answer questions such as: what is the effect of a change in vegetation or land use on runoff? Thirdly, knowledge of field hydrology is of utmost importance. For this a student needs to be trained in the field. Fieldwork is very important as a student is confronted in the field with spatial and temporal variability, as well as with real life uncertainties, rather than being lured into believing the world as presented in hydrological textbooks and models, e.g. the world under study is homogeneous, isotropic, or lumped (averaged). Also, students in the field learn to plan and cooperate. Besides fieldwork, a student should also learn to make use of the many available data sets, such as google earth, or as provided by remote sensing, or automatic data loggers. In our opinion the following sequence of activities should be applied for a student to attain a desirable working knowledge level. As mentioned earlier, a student first of all needs to have sufficient classical hydrological knowledge. After this a student should be educated in using simple models, in which field knowledge is incorporated. After this, a student should learn how to build models for solving typical hydrological problems. Modelling is especially worthwhile when the model is applied to a known area, as this certifies integration of fieldwork and modelling activities. To learn how to model, tailored courses with software that provides a set of easily learned functions to match the student's conceptual thought processes are needed. It is not easy to bring theoretical, field, and modelling knowledge together, and a pitfall may be the lack of knowledge of one or more of the above. Also, a student must learn to be able to deal with uncertainties in data and models, and must be trained to deal with unpredictability. Therefore, in our opinion a modern student should strive to become an integrating specialist in all of the above mentioned fields if we are to take geographical hydrology to a higher level and if we want to come to grips with it in a non-stationary world. A student must learn to think and act in an integrative way, and for this combining classical hydrology, field hydrology and modelling at a high education level in our hydrology curricula, in our opinion, is the way to proceed.

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

NASA Astrophysics Data System (ADS)

Majima, H.; Suzuki, A.

2011-12-01

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity ( -γẋ) and a time-dependent external force ( K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: ℒ=mẋẏ-U(x+{1}/{2}y)+U(x-{1}/{2}y)+{γ}/{2}(xẏ-yẋ)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x±y/2)={1}/{2}k( specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian ℋ. The Heisenberg equations of motion utilizing the quantized Hamiltonian ℋ̂ surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force.

Introduction to quantized LIE groups and algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tjin, T.

1992-10-10

In this paper, the authors give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups the authors study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then the authors explain in detail the concept of quantization for them. As an example the quantization of sl[sub 2] is explicitly carried out. Next, the authors show how quantum groups are related to the Yang-Baxtermore » equation and how they can be used to solve it. Using the quantum double construction, the authors explicitly construct the universal R matrix for the quantum sl[sub 2] algebra. In the last section, the authors deduce all finite-dimensional irreducible representations for q a root of unity. The authors also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory.« less

On the correspondence between quantum and classical variational principles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-06-10

Here, classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality and without appealing to dynamical equations. As examples, first principle variational formulations of classical point-particle and cold-fluid motion are derived from their quantum counterparts for Schrodinger, Pauli, and Klein-Gordon particles.

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

Electrophoresis in strong electric fields.

PubMed

Barany, Sandor

2009-01-01

Two kinds of non-linear electrophoresis (ef) that can be detected in strong electric fields (several hundred V/cm) are considered. The first ("classical" non-linear ef) is due to the interaction of the outer field with field-induced ionic charges in the electric double layer (EDL) under conditions, when field-induced variations of electrolyte concentration remain to be small comparatively to its equilibrium value. According to the Shilov theory, the non-linear component of the electrophoretic velocity for dielectric particles is proportional to the cubic power of the applied field strength (cubic electrophoresis) and to the second power of the particles radius; it is independent of the zeta-potential but is determined by the surface conductivity of particles. The second one, the so-called "superfast electrophoresis" is connected with the interaction of a strong outer field with a secondary diffuse layer of counterions (space charge) that is induced outside the primary (classical) diffuse EDL by the external field itself because of concentration polarization. The Dukhin-Mishchuk theory of "superfast electrophoresis" predicts quadratic dependence of the electrophoretic velocity of unipolar (ionically or electronically) conducting particles on the external field gradient and linear dependence on the particle's size in strong electric fields. These are in sharp contrast to the laws of classical electrophoresis (no dependence of V(ef) on the particle's size and linear dependence on the electric field gradient). A new method to measure the ef velocity of particles in strong electric fields is developed that is based on separation of the effects of sedimentation and electrophoresis using videoimaging and a new flowcell and use of short electric pulses. To test the "classical" non-linear electrophoresis, we have measured the ef velocity of non-conducting polystyrene, aluminium-oxide and (semiconductor) graphite particles as well as Saccharomice cerevisiae yeast cells as a function of the electric field strength, particle size, electrolyte concentration and the adsorbed polymer amount. It has been shown that the electrophoretic velocity of the particles/cells increases with field strength linearly up to about 100 and 200 V/cm (for cells) without and with adsorbed polymers both in pure water and in electrolyte solutions. In line with the theoretical predictions, in stronger fields substantial non-linear effects were recorded (V(ef)~E(3)). The ef velocity of unipolar ion-type conducting (ion-exchanger particles and fibres), electron-type conducting (magnesium and Mg/Al alloy) and semiconductor particles (graphite, activated carbon, pyrite, molybdenite) increases significantly with the electric field (V(ef)~E(2)) and the particle's size but is almost independent of the ionic strength. These trends are inconsistent with Smoluchowski's equation for dielectric particles, but are consistent with the Dukhin-Mishchuk theory of superfast electrophoresis.

Loop quantum corrected Einstein Yang-Mills black holes

NASA Astrophysics Data System (ADS)

Protter, Mason; DeBenedictis, Andrew

2018-05-01

In this paper, we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills fields subject to corrections inspired by loop quantum gravity. The systems studied possess both magnetic and induced electric Yang-Mills fields. We consider the system of equations both with and without Wilson loop corrections to the Yang-Mills potential. The structure of the Yang-Mills Hamiltonian, along with the restriction to homogeneity, allows for an anomaly-free effective quantization. In particular, we study the bounce which replaces the classical singularity and the behavior of the Yang-Mills fields in the quantum corrected interior, which possesses topology R ×S2 . Beyond the bounce, the magnitude of the Yang-Mills electric field asymptotically grows monotonically. This results in an ever-expanding R sector even though the two-sphere volume is asymptotically constant. The results are similar with and without Wilson loop corrections on the Yang-Mills potential.

Derivation of the Lorentz force law, the magnetic field concept and the Faraday Lenz and magnetic Gauss laws using an invariant formulation of the Lorentz transformation

NASA Astrophysics Data System (ADS)

Field, J. H.

2006-06-01

It is demonstrated how the right-hand sides of the Lorentz transformation equations may be written, in a Lorentz-invariant manner, as 4-vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. An important distinction between the physical meanings of the space time and energy momentum 4-vectors is pointed out. The formalism is shown to provide a short derivation of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field, in terms of spatial derivatives of the 4-vector potential, as well as the Faraday Lenz law and the Gauss law for magnetic fields. The connection between the Gauss law for the electric field and the electrodynamic Ampère law, due to the 4-vector character of the electromagnetic potential, is also pointed out.

Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tao E.; Nitzan, Abraham; Sukharev, Maxim

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one- and three-dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. Here, we consider three flavors of mixed quantum-classical dynamics: (i) the classical path approximation (CPA), (ii) Ehrenfest dynamics, and (iii) symmetrical quasiclassical (SQC) dynamics. Our findings are as follows: (i) The CPA fails to recover a consistent description of spontaneous emission, (ii) a consistent “spontaneous” emission can be obtained from Ehrenfest dynamics, provided that one starts in an electronic superposition state, and (iii) spontaneous emission is always obtained using SQC dynamics. Using themore » SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by Miller [J. Chem. Phys. 69, 2188 (1978)] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.« less

Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy

NASA Astrophysics Data System (ADS)

Li, Tao E.; Nitzan, Abraham; Sukharev, Maxim; Martinez, Todd; Chen, Hsing-Ta; Subotnik, Joseph E.

2018-03-01

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one- and three-dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. We consider three flavors of mixed quantum-classical dynamics: (i) the classical path approximation (CPA), (ii) Ehrenfest dynamics, and (iii) symmetrical quasiclassical (SQC) dynamics. Our findings are as follows: (i) The CPA fails to recover a consistent description of spontaneous emission, (ii) a consistent "spontaneous" emission can be obtained from Ehrenfest dynamics, provided that one starts in an electronic superposition state, and (iii) spontaneous emission is always obtained using SQC dynamics. Using the SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by Miller [J. Chem. Phys. 69, 2188 (1978), 10.1063/1.436793] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.

Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy

DOE PAGES

Li, Tao E.; Nitzan, Abraham; Sukharev, Maxim; ...

2018-03-12

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one- and three-dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. Here, we consider three flavors of mixed quantum-classical dynamics: (i) the classical path approximation (CPA), (ii) Ehrenfest dynamics, and (iii) symmetrical quasiclassical (SQC) dynamics. Our findings are as follows: (i) The CPA fails to recover a consistent description of spontaneous emission, (ii) a consistent “spontaneous” emission can be obtained from Ehrenfest dynamics, provided that one starts in an electronic superposition state, and (iii) spontaneous emission is always obtained using SQC dynamics. Using themore » SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by Miller [J. Chem. Phys. 69, 2188 (1978)] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.« less

Hybrid quantum-classical modeling of quantum dot devices

NASA Astrophysics Data System (ADS)

Kantner, Markus; Mittnenzweig, Markus; Koprucki, Thomas

2017-11-01

The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we introduce a new hybrid quantum-classical modeling approach, which provides a comprehensive description of quantum dot devices on multiple scales: it enables the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.

A position-dependent mass harmonic oscillator and deformed space

NASA Astrophysics Data System (ADS)

da Costa, Bruno G.; Borges, Ernesto P.

2018-04-01

We consider canonically conjugated generalized space and linear momentum operators x^ q and p^ q in quantum mechanics, associated with a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter q. A canonical transformation (x ^ ,p ^ ) →(x^ q,p^ q ) leads the Hamiltonian of a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space. The equation of motion for the classical phase space (x, p) may be expressed in terms of the deformed (dual) q-derivative. We revisit the problem of a q-deformed oscillator in both classical and quantum formalisms. Particularly, this canonical transformation leads a particle with position-dependent mass in a harmonic potential to a particle with constant mass in a Morse potential. The trajectories in phase spaces (x, p) and (xq, pq) are analyzed for different values of the deformation parameter. Finally, we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.

Symbolic Solution of Linear Differential Equations

NASA Technical Reports Server (NTRS)

Feinberg, R. B.; Grooms, R. G.

1981-01-01

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

An analytical theory of radio-wave scattering from meteoric ionization - I. Basic equation

NASA Astrophysics Data System (ADS)

Pecina, P.

2016-01-01

We have developed an analytical theory of radio-wave scattering from ionization of meteoric origin. It is based on an integro-differential equation for the polarization vector, P, inside the meteor trail, representing an analytical solution of the set of Maxwell equations, in combination with a generalized radar equation involving an integral of the trail volume electron density, Ne, and P represented by an auxiliary vector, Q, taken over the whole trail volume. During the derivation of the final formulae, the following assumptions were applied: transversal as well as longitudinal dimensions of the meteor trail are small compared with the distances of the relevant trail point to both the transmitter and receiver and the ratio of these distances to the wavelength of the wave emitted by the radar is very large, so that the stationary-phase method can be employed for evaluation of the relevant integrals. Further, it is shown that in the case of sufficiently low electron density, Ne, corresponding to the case of underdense trails, the classical McKinley's radar equation results as a special case of the general theory. The same also applies regarding the Fresnel characteristics. Our approach is also capable of yielding solutions to the problems of the formation of Fresnel characteristics on trails having any electron density, forward scattering and scattering on trails immersed in the magnetic field. However, we have also shown that the geomagnetic field can be removed from consideration, due to its low strength. The full solution of the above integro-differential equation, valid for any electron volume densities, has been left to subsequent works dealing with this particular problem, due to its complexity.

An Exploration of Kernel Equating Using SAT® Data: Equating to a Similar Population and to a Distant Population. Research Report. ETS RR-07-17

ERIC Educational Resources Information Center

Liu, Jinghua; Low, Albert C.

2007-01-01

This study applied kernel equating (KE) in two scenarios: equating to a very similar population and equating to a very different population, referred to as a distant population, using SAT® data. The KE results were compared to the results obtained from analogous classical equating methods in both scenarios. The results indicate that KE results are…

Does ℏ play a role in multidimensional spectroscopy? Reduced hierarchy equations of motion approach to molecular vibrations.

PubMed

Sakurai, Atsunori; Tanimura, Yoshitaka

2011-04-28

To investigate the role of quantum effects in vibrational spectroscopies, we have carried out numerically exact calculations of linear and nonlinear response functions for an anharmonic potential system nonlinearly coupled to a harmonic oscillator bath. Although one cannot carry out the quantum calculations of the response functions with full molecular dynamics (MD) simulations for a realistic system which consists of many molecules, it is possible to grasp the essence of the quantum effects on the vibrational spectra by employing a model Hamiltonian that describes an intra- or intermolecular vibrational motion in a condensed phase. The present model fully includes vibrational relaxation, while the stochastic model often used to simulate infrared spectra does not. We have employed the reduced quantum hierarchy equations of motion approach in the Wigner space representation to deal with nonperturbative, non-Markovian, and nonsecular system-bath interactions. Taking the classical limit of the hierarchy equations of motion, we have obtained the classical equations of motion that describe the classical dynamics under the same physical conditions as in the quantum case. By comparing the classical and quantum mechanically calculated linear and multidimensional spectra, we found that the profiles of spectra for a fast modulation case were similar, but different for a slow modulation case. In both the classical and quantum cases, we identified the resonant oscillation peak in the spectra, but the quantum peak shifted to the red compared with the classical one if the potential is anharmonic. The prominent quantum effect is the 1-2 transition peak, which appears only in the quantum mechanically calculated spectra as a result of anharmonicity in the potential or nonlinearity of the system-bath coupling. While the contribution of the 1-2 transition is negligible in the fast modulation case, it becomes important in the slow modulation case as long as the amplitude of the frequency fluctuation is small. Thus, we observed a distinct difference between the classical and quantum mechanically calculated multidimensional spectra in the slow modulation case where spectral diffusion plays a role. This fact indicates that one may not reproduce the experimentally obtained multidimensional spectrum for high-frequency vibrational modes based on classical molecular dynamics simulations if the modulation that arises from surrounding molecules is weak and slow. A practical way to overcome the difference between the classical and quantum simulations was discussed.

An introduction to generalized functions with some applications in aerodynamics and aeroacoustics

NASA Technical Reports Server (NTRS)

Farassat, F.

1994-01-01

In this paper, we start with the definition of generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support. The concept of generalization differentiation is introduced next. This is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some of the results of classical analysis, such as Leibniz rule of differentiation under the integral sign and the divergence theorem, are derived using the generalized function theory. It is shown that the divergence theorem remains valid for discontinuous vector fields provided that the derivatives are all viewed as generalized derivatives. This implies that all conservation laws of fluid mechanics are valid as they stand for discontinuous fields with all derivatives treated as generalized deriatives. Once these derivatives are written as ordinary derivatives and jumps in the field parameters across discontinuities, the jump conditions can be easily found. For example, the unsteady shock jump conditions can be derived from mass and momentum conservation laws. By using a generalized function theory, this derivative becomes trivial. Other applications of the generalized function theory in aerodynamics discussed in this paper are derivation of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of finite part of divergent integrals, derivation of Oswatiitsch integral equation of transonic flow, and analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics presented here include the derivation of the Kirchoff formula for moving surfaces,the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

A novel approach to gravitation from fluid theory: Titius-Bode structures, flat rotation rate of galaxies, and other predictions

NASA Astrophysics Data System (ADS)

Munera, Hector A.

Following the discovery of quantum phenomena at laboratory scale (Couder & Fort 2006), de Broglie pilot wave theory (De Broglie 1962) has been revived under a hydrodynamic guise (Bush 2015). Theoretically, it boils down to solving the transport equations for the energy and linear momentum densities of a postulated fundamental fluid in terms of classical wave equations, which inherently are Lorentz-invariant and scale-invariant. Instead of the conventional harmonic solutions, for astronomical and gravitational problems the novel solutions for the homogeneous wave equation in spherical coordinates are more suitable (Munera et al. 1995, Munera & Guzman 1997, and Munera 2000). Two groups of solutions are particularly relevant: (a) The inherently-quantized helicoidal solutions that may be applicable to describe spiral galaxies, and (b) The non-harmonic solutions with time (t) and distance (r) entangled in the single variable q = Ct/r (C is the two-way local electromagnetic speed). When these functions are plotted against 1/q they manifestly depict quantum effects in the near field, and Newtonian-like gravity in the far-field. The near-field predicts quantized effects similar to ring structures and to Titius-Bode structures, both in our own solar system and in exoplanets, the correlation between predicted and observed structures being typically larger than 99 per cent. In the far-field, some non-harmonic functions have a rate of decrement with distance slower than inverse-square thus explaining the flat rotation rate of galaxies. Additional implications for Trojan orbits, and quantized effects in photon deflection were also noted.

Some exact solutions for maximally symmetric topological defects in Anti de Sitter space

NASA Astrophysics Data System (ADS)

Alvarez, Orlando; Haddad, Matthew

2018-03-01

We obtain exact analytical solutions for a class of SO( l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = ( p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects ( p = 0 , 1 , 2 , . . . ; l = 1), vortex-like defects ( p = 1 , 2 , 3; l = 2), and the 't Hooft-Polyakov monopole ( p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

Bose–Einstein graviton condensate in a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Alfaro, Jorge; Espriu, Domènec; Gabbanelli, Luciano

2018-01-01

We analyze in detail a previous proposal by Dvali and Gómez that black holes could be treated as consisting of a Bose–Einstein condensate of gravitons. In order to do so we extend the Einstein–Hilbert action with a chemical potential-like term, thus placing ourselves in a grand-canonical ensemble. The form and characteristics of this chemical potential-like piece are discussed in some detail. We argue that the resulting equations of motion derived from the action could be interpreted as the Gross–Pitaevskii equation describing a graviton Bose–Einstein condensate trapped by the black hole gravitational field. After this, we proceed to expand the ensuring equations of motion up to second order around the classical Schwarzschild metric so that some non-linear terms in the metric fluctuation are kept. Next we search for solutions and, modulo some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. Inspired by a linearized approximation around the horizon we are able to find an exact solution for the mean-field wave function describing the graviton Bose–Einstein condensate in the black hole interior. After this, we can rederive some of the relations involving the number of gravitons N and the black hole characteristics along the lines suggested by Dvali and Gómez.

Causal dissipation for the relativistic dynamics of ideal gases

NASA Astrophysics Data System (ADS)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Zubarev's Nonequilibrium Statistical Operator Method in the Generalized Statistics of Multiparticle Systems

NASA Astrophysics Data System (ADS)

Glushak, P. A.; Markiv, B. B.; Tokarchuk, M. V.

2018-01-01

We present a generalization of Zubarev's nonequilibrium statistical operator method based on the principle of maximum Renyi entropy. In the framework of this approach, we obtain transport equations for the basic set of parameters of the reduced description of nonequilibrium processes in a classical system of interacting particles using Liouville equations with fractional derivatives. For a classical systems of particles in a medium with a fractal structure, we obtain a non-Markovian diffusion equation with fractional spatial derivatives. For a concrete model of the frequency dependence of a memory function, we obtain generalized Kettano-type diffusion equation with the spatial and temporal fractality taken into account. We present a generalization of nonequilibrium thermofield dynamics in Zubarev's nonequilibrium statistical operator method in the framework of Renyi statistics.

Causal dissipation for the relativistic dynamics of ideal gases

PubMed Central

2017-01-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations. PMID:28588397

Causal dissipation for the relativistic dynamics of ideal gases.

PubMed

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Below-threshold harmonic generation from strong non-uniform fields

NASA Astrophysics Data System (ADS)

Yavuz, I.

2017-10-01

Strong-field photoemission below the ionization threshold is a rich/complex region where atomic emission and harmonic generation may coexist. We studied the mechanism of below-threshold harmonics (BTH) from spatially non-uniform local fields near the metallic nanostructures. Discrete harmonics are generated due to the broken inversion symmetry, suggesting enriched coherent emission in the vuv frequency range. Through the numerical solution of the time-dependent Schrödinger equation, we investigate wavelength and intensity dependence of BTH. Wavelength dependence identifies counter-regular resonances; individual contributions from the multi-photon emission and channel-closing effects due to quantum path interferences. In order to understand the underlying mechanism of BTH, we devised a generalized semi-classical model, including the influence of Coulomb and non-uniform field interactions. As in uniform fields, Coulomb potential in non-uniform fields is the determinant of BTH; we observed that the generation of BTH are due to returning trajectories with negative energies. Due to large distance effectiveness of the non-uniformity, only long trajectories are noticeably affected.

Early Time Dynamics of Gluon Fields in High Energy Nuclear Collisions

NASA Astrophysics Data System (ADS)

Kapusta, Joseph I.; Chen, Guangyao; Fries, Rainer J.; Li, Yang

2016-12-01

Nuclei colliding at very high energy create a strong, quasi-classical gluon field during the initial phase of their interaction. We present an analytic calculation of the initial space-time evolution of this field in the limit of very high energies using a formal recursive solution of the Yang-Mills equations. We provide analytic expressions for the initial chromo-electric and chromo-magnetic fields and for their energy-momentum tensor. In particular, we discuss event-averaged results for energy density and energy flow as well as for longitudinal and transverse pressure of this system. Our results are generally applicable if τ < 1 /Qs. The transverse energy flow of the gluon field exhibits hydrodynamic-like contributions that follow transverse gradients of the energy density. In addition, a rapidity-odd energy flow also emerges from the non-abelian analog of Gauss' Law and generates non-vanishing angular momentum of the field. We will discuss the space-time picture that emerges from our analysis and its implications for observables in heavy ion collisions.

Cumulants, free cumulants and half-shuffles

PubMed Central

Ebrahimi-Fard, Kurusch; Patras, Frédéric

2015-01-01

Free cumulants were introduced as the proper analogue of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants. Whereas the combinatorics of classical cumulants is well expressed in terms of set partitions, that of free cumulants is described and often introduced in terms of non-crossing set partitions. The formal series approach to classical and free cumulants also largely differs. The purpose of this study is to put forward a different approach to these phenomena. Namely, we show that cumulants, whether classical or free, can be understood in terms of the algebra and combinatorics underlying commutative as well as non-commutative (half-)shuffles and (half-) unshuffles. As a corollary, cumulants and free cumulants can be characterized through linear fixed point equations. We study the exponential solutions of these linear fixed point equations, which display well the commutative, respectively non-commutative, character of classical and free cumulants. PMID:27547078

Computational method for exact frequency-dependent rays on the basis of the solution of the Helmholtz equation

NASA Astrophysics Data System (ADS)

Protasov, M.; Gadylshin, K.

2017-07-01

A numerical method is proposed for the calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known. The properties of frequency-dependent rays are analysed and compared with classical ray theory and with the method of finite-difference modelling for the first time. In this paper, we study the dependence of these rays on the frequency of signals and show the convergence of the exact rays to the classical rays with increasing frequency. A number of numerical experiments demonstrate the distinctive features of exact frequency-dependent rays, in particular, their ability to penetrate into shadow zones that are impenetrable for classical rays.

A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation

NASA Astrophysics Data System (ADS)

Terrana, S.; Vilotte, J. P.; Guillot, L.

2018-04-01

We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin (DG) spectral element method (HDG-SEM) for wave equations in coupled elastic-acoustic media. The method is based on a first-order hyperbolic velocity-strain formulation of the wave equations written in conservative form. This method follows the HDG approach by introducing a hybrid unknown, which is the approximation of the velocity on the elements boundaries, as the only globally (i.e. interelement) coupled degrees of freedom. In this paper, we first present a hybridized formulation of the exact Riemann solver at the element boundaries, taking into account elastic-elastic, acoustic-acoustic and elastic-acoustic interfaces. We then use this Riemann solver to derive an explicit construction of the HDG stabilization function τ for all the above-mentioned interfaces. We thus obtain an HDG scheme for coupled elastic-acoustic problems. This scheme is then discretized in space on quadrangular/hexahedral meshes using arbitrary high-order polynomial basis for both volumetric and hybrid fields, using an approach similar to the spectral element methods. This leads to a semi-discrete system of algebraic differential equations (ADEs), which thanks to the structure of the global conservativity condition can be reformulated easily as a classical system of first-order ordinary differential equations in time, allowing the use of classical explicit or implicit time integration schemes. When an explicit time scheme is used, the HDG method can be seen as a reformulation of a DG with upwind fluxes. The introduction of the velocity hybrid unknown leads to relatively simple computations at the element boundaries which, in turn, makes the HDG approach competitive with the DG-upwind methods. Extensive numerical results are provided to illustrate and assess the accuracy and convergence properties of this HDG-SEM. The approximate velocity is shown to converge with the optimal order of k + 1 in the L2-norm, when element polynomials of order k are used, and to exhibit the classical spectral convergence of SEM. Additional inexpensive local post-processing in both the elastic and the acoustic case allow to achieve higher convergence orders. The HDG scheme provides a natural framework for coupling classical, continuous Galerkin SEM with HDG-SEM in the same simulation, and it is shown numerically in this paper. As such, the proposed HDG-SEM can combine the efficiency of the continuous SEM with the flexibility of the HDG approaches. Finally, more complex numerical results, inspired from real geophysical applications, are presented to illustrate the capabilities of the method for wave propagation in heterogeneous elastic-acoustic media with complex geometries.

Unitary evolution of the quantum Universe with a Brown-Kuchař dust

NASA Astrophysics Data System (ADS)

Maeda, Hideki

2015-12-01

We study the time evolution of a wave function for the spatially flat Friedmann-Lemaître-Robertson-Walker Universe governed by the Wheeler-DeWitt equation in both analytical and numerical methods. We consider a Brown-Kuchař dust as a matter field in order to introduce a ‘clock’ in quantum cosmology and adopt the Laplace-Beltrami operator-ordering. The Hamiltonian operator admits an infinite number of self-adjoint extensions corresponding to a one-parameter family of boundary conditions at the origin in the minisuperspace. For any value of the extension parameter in the boundary condition, the evolution of a wave function is unitary and the classical initial singularity is avoided and replaced by the big bounce in the quantum system. Exact wave functions show that the expectation value of the spatial volume of the Universe obeys the classical-time evolution in the late time but its variance diverges.

Light-cone quantization of two dimensional field theory in the path integral approach

NASA Astrophysics Data System (ADS)

Cortés, J. L.; Gamboa, J.

1999-05-01

A quantization condition due to the boundary conditions and the compatification of the light cone space-time coordinate x- is identified at the level of the classical equations for the right-handed fermionic field in two dimensions. A detailed analysis of the implications of the implementation of this quantization condition at the quantum level is presented. In the case of the Thirring model one has selection rules on the excitations as a function of the coupling and in the case of the Schwinger model a double integer structure of the vacuum is derived in the light-cone frame. Two different quantized chiral Schwinger models are found, one of them without a θ-vacuum structure. A generalization of the quantization condition to theories with several fermionic fields and to higher dimensions is presented.

Plasma and field observations of a compressional Pc 5 wave event

NASA Astrophysics Data System (ADS)

Baumjohann, W.; Sckopke, N.; LaBelle, J.; Klecker, B.; Lühr, H.; Glassmeier, K. H.

1987-11-01

The full complement of data obtained by all the instruments on board the AMPTE/IRM satellite during a Pc 5 wave event on October 24, 1984 is analyzed. Both energetic proton and electron fluxes were anticorrelated with the compressional magnetic field oscillations, indicating that the event belongs to the class of 'in-phase events'. The energetic proton data also exhibited a new feature: flux minima and maxima at low energies were observed somewhat later than those at higher energies. The magnetic and plasma pressure oscillations satisfy the pressure balance equation for the drift mirror mode much better than that for drift compressional Alfven waves. However, the classical criterion for the onset of the mirror instability is not satisfied.

Hamilton's Principle and Approximate Solutions to Problems in Classical Mechanics

ERIC Educational Resources Information Center

Schlitt, D. W.

1977-01-01

Shows how to use the Ritz method for obtaining approximate solutions to problems expressed in variational form directly from the variational equation. Application of this method to classical mechanics is given. (MLH)

Cosmological signature change in Cartan gravity with dynamical symmetry breaking

NASA Astrophysics Data System (ADS)

Magueijo, João; Rodríguez-Vázquez, Matías; Westman, Hans; Złośnik, Tom

2014-03-01

We investigate the possibility for classical metric signature change in a straightforward generalization of the first-order formulation of gravity, dubbed "Cartan gravity." The mathematical structure of this theory mimics the electroweak theory in that the basic ingredients are an SO(1,4) Yang-Mills gauge field Aabμ and a symmetry breaking Higgs field Va, with no metric or affine structure of spacetime presupposed. However, these structures can be recovered, with the predictions of general relativity exactly reproduced, whenever the Higgs field breaking the symmetry to SO(1,3) is forced to have a constant (positive) norm VaVa. This restriction is usually imposed "by hand," but in analogy with the electroweak theory we promote the gravitational Higgs field Va to a genuine dynamical field, subject to nontrivial equations of motion. Even though we limit ourselves to actions polynomial in these variables, we discover a rich phenomenology. Most notably we derive classical cosmological solutions exhibiting a smooth transition between Euclidean and Lorentzian signature in the four-metric. These solutions are nonsingular and arise whenever the SO(1,4) norm of the Higgs field changes sign; i.e. the signature of the metric of spacetime is determined dynamically by the gravitational Higgs field. It is possible to find a plethora of such solutions and in some of them this dramatic behavior is confined to the early Universe, with the theory asymptotically tending to Einstein gravity at late times. Curiously the theory can also naturally embody a well-known dark energy model: Peebles-Ratra quintessence.

Quantum gravity and renormalization

NASA Astrophysics Data System (ADS)

Anselmi, Damiano

2015-02-01

The properties of quantum gravity are reviewed from the point of view of renormalization. Various attempts to overcome the problem of non-renormalizability are presented, and the reasons why most of them fail for quantum gravity are discussed. Interesting possibilities come from relaxing the locality assumption, which also can inspire the investigation of a largely unexplored sector of quantum field theory. Another possibility is to work with infinitely many independent couplings, and search for physical quantities that only depend on a finite subset of them. In this spirit, it is useful to organize the classical action of quantum gravity, determined by renormalization, in a convenient way. Taking advantage of perturbative local field redefinitions, we write the action as the sum of the Hilbert term, the cosmological term, a peculiar scalar that is important only in higher dimensions, plus invariants constructed with at least three Weyl tensors. We show that the FRLW configurations, and many other locally conformally flat metrics, are exact solutions of the field equations in arbitrary dimensions d>3. If the metric is expanded around such configurations the quadratic part of the action is free of higher-time derivatives. Other well-known metrics, such as those of black holes, are instead affected in nontrivial ways by the classical corrections of quantum origin.

Nonlinear waveform distortion and shock formation in the near field of a continuous wave piston source

NASA Astrophysics Data System (ADS)

Sapozhnikov, Oleg A.; Khokhlova, Vera A.; Cathignol, Dominique

2004-05-01

A classical effect of nonlinear acoustics is that a plane sinusoidal acoustic wave propagating in a nonlinear medium transforms to a sawtooth wave with one shock per cycle. However, the waveform evolution can be quite different in the near field of a plane source due to diffraction. Previous numerical simulations of nonlinear acoustic waves in the near field of a circular piston source predict the development of two shocks per wave cycle [Khokhlova et al., J. Acoust. Soc. Am. 110, 95-108 (2001)]. Moreover, at some locations the peak pressure may be up to 4 times the source amplitude. The motivation of this work was to experimentally verify and further explain the phenomena of the nonlinear waveform distortion. Measurements were conducted in water with a 47-mm-diameter unfocused transducer, working at 1-MHz frequency. For pressure amplitudes higher than 0.5 MPa, two shocks per cycle were observed in the waveform beyond the last minimum of the fundamental harmonic amplitude. With the increase of the observation distance, these two shocks collided and formed one shock (per cycle), i.e., the waveform developed into the classical sawtooth wave. The experimental results were in a very good agreement with the modeling based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation.

Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. I. The role of molecular anchoring

NASA Astrophysics Data System (ADS)

Cattes, Stefanie M.; Gubbins, Keith E.; Schoen, Martin

2016-05-01

In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.

On Gravitational Effects in the Schrödinger Equation

NASA Astrophysics Data System (ADS)

Pollock, M. D.

2014-04-01

The Schrödinger equation for a particle of rest mass and electrical charge interacting with a four-vector potential can be derived as the non-relativistic limit of the Klein-Gordon equation for the wave function , where and , or equivalently from the one-dimensional action for the corresponding point particle in the semi-classical approximation , both methods yielding the equation in Minkowski space-time , where and . We show that these two methods generally yield equations that differ in a curved background space-time , although they coincide when if is replaced by the effective mass in both the Klein-Gordon action and , allowing for non-minimal coupling to the gravitational field, where is the Ricci scalar and is a constant. In this case , where and , the correctness of the gravitational contribution to the potential having been verified to linear order in the thermal-neutron beam interferometry experiment due to Colella et al. Setting and regarding as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space-time. Conservation of probability and electrical current requires both electromagnetic gauge and space-time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div, where and . The quantum-cosmological Schrödinger (Wheeler-DeWitt) equation is also discussed in the -dimensional mini-superspace idealization, with particular regard to the vacuum potential and the characteristics of the ground state, assuming a gravitational Lagrangian which contains higher-derivative terms up to order . For the heterotic superstring theory , consists of an infinite series in , where is the Regge slope parameter, and in the perturbative approximation , is positive semi-definite for . The maximally symmetric ground state satisfying the field equations is Minkowski space for and anti-de Sitter space for.

Evaluating Students' Conceptual Understanding of Balanced Equations and Stoichiometric Ratios Using a Particulate Drawing

ERIC Educational Resources Information Center

Sanger, Michael J.

2005-01-01

A total of 156 students were asked to provide free-response balanced chemical equations for a classic multiple-choice particulate-drawing question first used by Nurrenbern and Pickering. The balanced equations and the number of students providing each equation are reported in this study. The most common student errors included a confusion between…

Classical metaphyseal lesions thought to be pathognomonic of child abuse are often artifacts or indicative of metabolic bone disease.

PubMed

Miller, Marvin; Mirkin, L David

2018-06-01

The objective of the present study was to review the histopathology in the original articles by authors Kleinman and Marks that described the specificity of the classical metaphyseal lesion for child abuse and to determine if there were any oversights in the authors' analysis. We reviewed the histopathology of the original studies that equated the classical metaphyseal lesion with child abuse. We compared this with the histopathology of metaphyseal fractures caused by known accidental, severe trauma in children and reviewed the histopathology of artifacts that can sometimes be produced in bone histology preparations. Acute classical metaphyseal lesions showed no hemorrhage, and the chronic classical metaphyseal showed islands of cartilage proliferation at the metaphyses and growth plate, findings consistent with rickets and other metabolic bone disorders. Some of the acute metaphyseal lesions were consistent with artifacts. We believe the original studies that equate the classical metaphyseal lesion with child abuse are flawed. The most compelling observation that challenges the histopathology of the classical metaphyseal lesion as being a fracture is the absence of hemorrhage in the acute classical metaphyseal lesion. We hypothesize that some of the classical metaphyseal lesions were artifacts or represent metabolic bone disorders that were not considered and that these two non-traumatic explanations may have been the basis of the abnormal bone findings. Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserved.

Essential core of the Hawking–Ellis types

NASA Astrophysics Data System (ADS)

Martín-Moruno, Prado; Visser, Matt

2018-06-01

The Hawking–Ellis (Segre–Plebański) classification of possible stress–energy tensors is an essential tool in analyzing the implications of the Einstein field equations in a more-or-less model-independent manner. In the current article the basic idea is to simplify the Hawking–Ellis type I, II, III, and IV classification by isolating the ‘essential core’ of the type II, type III, and type IV stress–energy tensors; this being done by subtracting (special cases of) type I to simplify the (Lorentz invariant) eigenvalue structure as much as possible without disturbing the eigenvector structure. We will denote these ‘simplified cores’ type II0, type III0, and type IV0. These ‘simplified cores’ have very nice and simple algebraic properties. Furthermore, types I and II0 have very simple classical interpretations, while type IV0 is known to arise semi-classically (in renormalized expectation values of standard stress–energy tensors). In contrast type III0 stands out in that it has neither a simple classical interpretation, nor even a simple semi-classical interpretation. We will also consider the robustness of this classification considering the stability of the different Hawking–Ellis types under perturbations. We argue that types II and III are definitively unstable, whereas types I and IV are stable.

On the solution of the generalized wave and generalized sine-Gordon equations

NASA Technical Reports Server (NTRS)

Ablowitz, M. J.; Beals, R.; Tenenblat, K.

1986-01-01

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.

Time Reparametrization Group and the Long Time Behavior in Quantum Glassy Systems

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio

2001-02-01

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( RpG) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.

The classical equation of state of fully ionized plasmas

NASA Astrophysics Data System (ADS)

Eisa, Dalia Ahmed

2011-03-01

The aim of this paper is to calculate the analytical form of the equation of state until the third virial coefficient of a classical system interacting via an effective potential of fully Ionized Plasmas. The excess osmotic pressure is represented in the forms of a convergent series expansions in terms of the plasma Parameter μ _{ab} = {{{e_a e_b χ } over {DKT}}}, where χ2 is the square of the inverse Debye radius. We consider only the thermal equilibrium plasma.

Transfer function modeling of damping mechanisms in viscoelastic plates

NASA Technical Reports Server (NTRS)

Slater, J. C.; Inman, D. J.

1991-01-01

This work formulates a method for the modeling of material damping characteristics in plates. The Sophie German equation of classical plate theory is modified to incorporate hysteresis effects represented by complex stiffness using the transfer function approach proposed by Golla and Hughes, (1985). However, this procedure is not limited to this representation. The governing characteristic equation is decoupled through separation of variables, yielding a solution similar to that of undamped classical plate theory, allowing solution of the steady state as well as the transient response problem.

A compressible two-layer model for transient gas-liquid flows in pipes

NASA Astrophysics Data System (ADS)

Demay, Charles; Hérard, Jean-Marc

2017-03-01

This work is dedicated to the modeling of gas-liquid flows in pipes. As a first step, a new two-layer model is proposed to deal with the stratified regime. The starting point is the isentropic Euler set of equations for each phase where the classical hydrostatic assumption is made for the liquid. The main difference with the models issued from the classical literature is that the liquid as well as the gas is assumed compressible. In that framework, an averaging process results in a five-equation system where the hydrostatic constraint has been used to define the interfacial pressure. Closure laws for the interfacial velocity and source terms such as mass and momentum transfer are provided following an entropy inequality. The resulting model is hyperbolic with non-conservative terms. Therefore, regarding the homogeneous part of the system, the definition and uniqueness of jump conditions is studied carefully and acquired. The nature of characteristic fields and the corresponding Riemann invariants are also detailed. Thus, one may build analytical solutions for the Riemann problem. In addition, positivity is obtained for heights and densities. The overall derivation deals with gas-liquid flows through rectangular channels, circular pipes with variable cross section and includes vapor-liquid flows.

Dynamic Gas Flow Effects on the ESD of Aerospace Vehicle Surfaces

NASA Technical Reports Server (NTRS)

Hogue, Michael D.; Kapat, Jayanta; Ahmed, Kareem; Cox, Rachel E.; Wilson, Jennifer G.; Calle, Luz M.; Mulligan, Jaysen

2016-01-01

The purpose of this work is to develop a dynamic version of Paschen's Law that takes into account the flow of ambient gas past aerospace vehicle surfaces. However, the classic Paschen's Law does not take into account the flow of gas of an aerospace vehicle, whose surfaces may be triboelectrically charged by dust or ice crystal impingement, traversing the atmosphere. The basic hypothesis of this work is that the number of electron-ion pairs created per unit distance by the electric field between the electrodes is mitigated by the electron-ion pairs removed per unit distance by the flow of gas. The revised Paschen equation must be a function of the mean velocity, v(sub xm), of the ambient gas and reduces to the classical version of Paschen's law when the gas mean velocity, v(sub xm) = 0. New formulations of Paschen's Law, taking into account Mach number and dynamic pressure, derived by the authors, will be discussed. These equations will be evaluated by wind tunnel experimentation later this year. Based on the results of this work, it is hoped that the safety of aerospace vehicles will be enhanced with a redefinition of electrostatic launch commit criteria. It is also possible that new products, such as new anti-static coatings, may be formulated from this data.

On the Construction and Dynamics of Knotted Fields

NASA Astrophysics Data System (ADS)

Kedia, Hridesh

Representing a physical field in terms of its field lines has often enabled a deeper understanding of complex physical phenomena, from Faraday's law of magnetic induction, to the Helmholtz laws of vortex motion, to the free energy density of liquid crystals in terms of the distortions of the lines of the director field. At the same time, the application of ideas from topology--the study of properties that are invariant under continuous deformations--has led to robust insights into the nature of complex physical systems from defects in crystal structures, to the earth's magnetic field, to topological conservation laws. The study of knotted fields, physical fields in which the field lines encode knots, emerges naturally from the application of topological ideas to the investigation of the physical phenomena best understood in terms of the lines of a field. A knot--a closed loop tangled with itself which can not be untangled without cutting the loop--is the simplest topologically non-trivial object constructed from a line. Remarkably, knots in the vortex (magnetic field) lines of a dissipationless fluid (plasma), persist forever as they are transported by the flow, stretching and rotating as they evolve. Moreover, deeply entwined with the topology-preserving dynamics of dissipationless fluids and plasmas, is an additional conserved quantity--helicity, a measure of the average linking of the vortex (magnetic field) lines in a fluid (plasma)--which has had far-reaching consequences for fluids and plasmas. Inspired by the persistence of knots in dissipationless flows, and their far-reaching physical consequences, we seek to understand the interplay between the dynamics of a field and the topology of its field lines in a variety of systems. While it is easy to tie a knot in a shoelace, tying a knot in the the lines of a space-filling field requires contorting the lines everywhere to match the knotted region. The challenge of analytically constructing knotted field configurations has impeded a deeper understanding of the interplay between topology and dynamics in fluids and plasmas. We begin by analytically constructing knotted field configurations which encode a desired knot in the lines of the field, and show that their helicity can be tuned independently of the encoded knot. The nonlinear nature of the physical systems in which these knotted field configurations arise, makes their analytical study challenging. We ask if a linear theory such as electromagnetism can allow knotted field configurations to persist with time. We find analytical expressions for an infinite family of knotted solutions to Maxwell's equations in vacuum and elucidate their connections to dissipationless flows. We present a design rule for constructing such persistently knotted electromagnetic fields, which could possibly be used to transfer knottedness to matter such as quantum fluids and plasmas. An important consequence of the persistence of knots in classical dissipationless flows is the existence of an additional conserved quantity, helicity, which has had far-reaching implications. To understand the existence of analogous conserved quantities, we ask if superfluids, which flow without dissipation just like classical dissipationless flows, have an additional conserved quantity akin to helicity. We address this question using an analytical approach based on defining the particle relabeling symmetry--the symmetry underlying helicity conservation--in superfluids, and find that an analogous conserved quantity exists but vanishes identically owing to the intrinsic geometry of complex scalar fields. Furthermore, to address the question of a ``classical limit'' of superfluid vortices which recovers classical helicity conservation, we perform numerical simulations of \\emph{bundles} of superfluid vortices, and find behavior akin to classical viscous flows.

Chiral anomaly, Berry phase, and chiral kinetic theory from worldlines in quantum field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mueller, Niklas; Venugopalan, Raju

Here, we outline a novel chiral kinetic theory framework for systematic computations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ion collisions. The real part of the fermion determinant in the QCD effective action is expressed as a supersymmetric world-line action of spinning, colored, Grassmanian point particles in background gauge fields, with equations of motion that are covariant generalizations of the Bargmann-Michel-Telegdi and Wong equations. Berry’s phase is obtained in a consistent non-relativistic adiabatic limit. The chiral anomaly, in contrast, arises from the phase of the fermion determinant; its topological properties are therefore distinct from those of the Berry phase.more » We show that the imaginary contribution to the fermion determinant too can be expressed as a point particle world-line path integral and derive the corresponding anomalous axial vector current. Our results can be used to derive a covariant relativistic chiral kinetic theory including the effects of topological fluctuations that has overlap with classical-statistical simulations of the CME at early times and anomalous hydrodynamics at late times.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fromm, Andrea; Bonitz, Michael; Dufty, James

The idea of treating quantum systems by semiclassical representations using effective quantum potentials (forces) has been successfully applied in equilibrium by many authors, see e.g. [D. Bohm, Phys. Rev. 85 (1986) 166 and 180; D.K. Ferry, J.R. Zhou, Phys. Rev. B 48 (1993) 7944; A.V. Filinov, M. Bonitz, W. Ebeling, J. Phys. A 36 (2003) 5957 and references cited therein]. Here, this idea is extended to nonequilibrium quantum systems in an external field. A gauge-invariant quantum kinetic theory for weakly inhomogeneous charged particle systems in a strong electromagnetic field is developed within the framework of nonequilibrium Green's functions. The equationmore » for the spectral density is simplified by introducing a classical (local) form for the kinetics. Nonlocal quantum effects are accounted for in this way by replacing the bare external confinement potential with an effective quantum potential. The equation for this effective potential is identified and solved for weak inhomogeneity in the collisionless limit. The resulting nonequilibrium spectral function is used to determine the density of states and the modification of the Born collision operator in the kinetic equation for the Wigner function due to quantum confinement effects.« less

Three-dimensional, ten-moment multifluid simulation of the solar wind interaction with Mercury

NASA Astrophysics Data System (ADS)

Dong, Chuanfei; Hakim, Ammar; Wang, Liang; Bhattacharjee, Amitava; Germaschewski, Kai; Dibraccio, Gina

2017-10-01

We investigate Mercury's magnetosphere by using Gkeyll ten-moment multifluid code that solves the continuity, momentum and pressure tensor equations of both protons and electrons, as well as the full Maxwell equations. Non-ideal effects like the Hall effect, inertia, and tensorial pressures are self-consistently embedded without the need to explicitly solve a generalized Ohm's law. Previously, we have benchmarked this approach in classical test problems like the Orszag-Tang vortex and GEM reconnection challenge problem. We first validate the model by using MESSENGER magnetic field data through data-model comparisons. Both day- and night-side magnetic reconnection are studied in detail. In addition, we include a mantle layer (with a resistivity profile) and a perfect conducting core inside the planet body to accurately represent Mercury's interior. The intrinsic dipole magnetic fields may be modified inside the planetary body due to the weak magnetic moment of Mercury. By including the planetary interior, we can capture the correct plasma boundary locations (e.g., bow shock and magnetopause), especially during a space weather event.

Dynamics of f(R) gravity models and asymmetry of time

NASA Astrophysics Data System (ADS)

Verma, Murli Manohar; Yadav, Bal Krishna

We solve the field equations of modified gravity for f(R) model in metric formalism. Further, we obtain the fixed points of the dynamical system in phase-space analysis of f(R) models, both with and without the effects of radiation. The stability of these points is studied against the perturbations in a smooth spatial background by applying the conditions on the eigenvalues of the matrix obtained in the linearized first-order differential equations. Following this, these fixed points are used for analyzing the dynamics of the system during the radiation, matter and acceleration-dominated phases of the universe. Certain linear and quadratic forms of f(R) are determined from the geometrical and physical considerations and the behavior of the scale factor is found for those forms. Further, we also determine the Hubble parameter H(t), the Ricci scalar R and the scale factor a(t) for these cosmic phases. We show the emergence of an asymmetry of time from the dynamics of the scalar field exclusively owing to the f(R) gravity in the Einstein frame that may lead to an arrow of time at a classical level.

Quantum gravity in three dimensions, Witten spinors and the quantisation of length

NASA Astrophysics Data System (ADS)

Wieland, Wolfgang

2018-05-01

In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is introduced that couples the gravitational field in the interior to a two-dimensional conformal field theory for an SU (2) boundary spinor, whose norm determines the conformal factor between the fiducial boundary metric and the physical metric in the bulk. The equations of motion for this boundary spinor are derived from the boundary action and turn out to be the two-dimensional analogue of the Witten equations appearing in Witten's proof of the positive mass theorem. The paper concludes with some comments on the resulting quantum theory. It is shown, in particular, that the length of a one-dimensional cross section of the boundary turns into a number operator on the Fock space of the theory. The spectrum of this operator is discrete and matches the results from loop quantum gravity in the spin network representation.

Chiral anomaly, Berry phase, and chiral kinetic theory from worldlines in quantum field theory

DOE PAGES

Mueller, Niklas; Venugopalan, Raju

2018-03-21

Here, we outline a novel chiral kinetic theory framework for systematic computations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ion collisions. The real part of the fermion determinant in the QCD effective action is expressed as a supersymmetric world-line action of spinning, colored, Grassmanian point particles in background gauge fields, with equations of motion that are covariant generalizations of the Bargmann-Michel-Telegdi and Wong equations. Berry’s phase is obtained in a consistent non-relativistic adiabatic limit. The chiral anomaly, in contrast, arises from the phase of the fermion determinant; its topological properties are therefore distinct from those of the Berry phase.more » We show that the imaginary contribution to the fermion determinant too can be expressed as a point particle world-line path integral and derive the corresponding anomalous axial vector current. Our results can be used to derive a covariant relativistic chiral kinetic theory including the effects of topological fluctuations that has overlap with classical-statistical simulations of the CME at early times and anomalous hydrodynamics at late times.« less

Cosmological evolution of generalized non-local gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Xue; Wu, Ya-Bo; Liu, Yu-Chen

2016-07-01

We construct a class of generalized non-local gravity (GNLG) model which is the modified theory of general relativity (GR) obtained by adding a term m {sup 2} {sup n} {sup -2} R □{sup -} {sup n} R to the Einstein-Hilbert action. Concretely, we not only study the gravitational equation for the GNLG model by introducing auxiliary scalar fields, but also analyse the classical stability and examine the cosmological consequences of the model for different exponent n . We find that the half of the scalar fields are always ghost-like and the exponent n must be taken even number for amore » stable GNLG model. Meanwhile, the model spontaneously generates three dominant phases of the evolution of the universe, and the equation of state parameters turn out to be phantom-like. Furthermore, we clarify in another way that exponent n should be even numbers by the spherically symmetric static solutions in Newtonian gauge. It is worth stressing that the results given by us can include ones in refs. [28, 34] as the special case of n =2.« less

Design Equations and Criteria of Orthotropic Composite Panels

DTIC Science & Technology

2013-05-01

33  Appendix A Classical Laminate Theory ( CLT ): ....................................................................... A–1  Appendix...Science London , 1990. NSWCCD-65-TR–2004/16A A–1 Appendix A Classical Laminate Theory ( CLT ): In Section 6 of this report, preliminary design...determined using:  Classical Laminate Theory, CLT , to Predict Equivalent Stiffness Characteristics, First- Ply Strength Note: CLT is valid for

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

Extended theory of harmonic maps connects general relativity to chaos and quantum mechanism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Gang; Duan, Yi-Shi

General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the line between classical and quantum physics by connecting chaos and entanglement equation. Here in this paper, we showed the Duan's extended HM theory, which has the solution of the general relativity, can also have the solutions of the classic chaos equations and even the solution of Schrödinger equation in quantum physics, suggesting the extended theory of harmonic maps may act as a universal theory ofmore » physics.« less

Extended theory of harmonic maps connects general relativity to chaos and quantum mechanism

DOE PAGES

Ren, Gang; Duan, Yi-Shi

2017-07-20

General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the line between classical and quantum physics by connecting chaos and entanglement equation. Here in this paper, we showed the Duan's extended HM theory, which has the solution of the general relativity, can also have the solutions of the classic chaos equations and even the solution of Schrödinger equation in quantum physics, suggesting the extended theory of harmonic maps may act as a universal theory ofmore » physics.« less

IRT Equating of the MCAT. MCAT Monograph.

ERIC Educational Resources Information Center

Hendrickson, Amy B.; Kolen, Michael J.

This study compared various equating models and procedures for a sample of data from the Medical College Admission Test(MCAT), considering how item response theory (IRT) equating results compare with classical equipercentile results and how the results based on use of various IRT models, observed score versus true score, direct versus linked…

On the Mo-Papas equation

NASA Astrophysics Data System (ADS)

Aguirregabiria, J. M.; Chamorro, A.; Valle, M. A.

1982-05-01

A new heuristic derivation of the Mo-Papas equation for charged particles is given. It is shown that this equation cannot be derived for a point particle by closely following Dirac's classical treatment of the problem. The Mo-Papas theory and the Bonnor-Rowe-Marx variable mass dynamics are not compatible.

Mapping quantum-classical Liouville equation: projectors and trajectories.

PubMed

Kelly, Aaron; van Zon, Ramses; Schofield, Jeremy; Kapral, Raymond

2012-02-28

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility, and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.

Effective equations for the quantum pendulum from momentous quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez, Hector H.; Chacon-Acosta, Guillermo; Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

Comparing Alternative Kernels for the Kernel Method of Test Equating: Gaussian, Logistic, and Uniform Kernels. Research Report. ETS RR-08-12

ERIC Educational Resources Information Center

Lee, Yi-Hsuan; von Davier, Alina A.

2008-01-01

The kernel equating method (von Davier, Holland, & Thayer, 2004) is based on a flexible family of equipercentile-like equating functions that use a Gaussian kernel to continuize the discrete score distributions. While the classical equipercentile, or percentile-rank, equating method carries out the continuization step by linear interpolation,…

Recent developments on the Kardar-Parisi-Zhang surface-growth equation.

PubMed

Wio, Horacio S; Escudero, Carlos; Revelli, Jorge A; Deza, Roberto R; de la Lama, Marta S

2011-01-28

The stochastic nonlinear partial differential equation known as the Kardar-Parisi-Zhang (KPZ) equation is a highly successful phenomenological mesoscopic model of surface and interface growth processes. Its suitability for analytical work, its explicit symmetries and its prediction of an exact dynamic scaling relation for a one-dimensional substratum led people to adopt it as a 'standard' model in the field during the last quarter of a century. At the same time, several conjectures deserving closer scrutiny were established as dogmas throughout the community. Among these, we find the beliefs that 'genuine' non-equilibrium processes are non-variational in essence, and that the exactness of the dynamic scaling relation owes its existence to a Galilean symmetry. Additionally, the equivalence among planar and radial interface profiles has been generally assumed in the literature throughout the years. Here--among other topics--we introduce a variational formulation of the KPZ equation, remark on the importance of consistency in discretization and challenge the mainstream view on the necessity for scaling of both Galilean symmetry and the one-dimensional fluctuation-dissipation theorem. We also derive the KPZ equation on a growing domain as a first approximation to radial growth, and outline the differences with respect to the classical case that arises in this new situation.

Phase-field model for isothermal phase transitions in binary alloys

NASA Technical Reports Server (NTRS)

Wheeler, A. A.; Boettinger, W. J.; Mcfadden, G. B.

1992-01-01

A new phase field model is described which models isothermal phase transitions between ideal binary alloy solution phases. Equations are developed for the temporal and spatial variation of the phase field, which describes the identity of the phase, and of the composition. An asymptotic analysis, as the gradient energy coefficient of the phase field becomes small, was conducted. From the analysis, it is shown that the model recovers classical sharp interface models of this situation when the interfacial layers are thin, and they show how to relate the parameters appearing in the phase field model to material and growth parameters in real systems. Further, three stages of temporal evolution are identified: the first corresponding to interfacial genesis which occurs very rapidly; the second to interfacial motion controlled by the local energy difference across the interface and diffusion; the last taking place on a long time scale in which curvature effects are important and which correspond to Ostwald ripening. The results of the numerical calculations are presented.

Remote sensing of the solar photosphere: a tale of two methods

NASA Astrophysics Data System (ADS)

Viavattene, G.; Berrilli, F.; Collados Vera, M.; Del Moro, D.; Giovannelli, L.; Ruiz Cobo, B.; Zuccarello, F.

2018-01-01

Solar spectro-polarimetry is a powerful tool to investigate the physical processes occurring in the solar atmosphere. The different states of polarization and wavelengths have in fact encoded the information about the thermodynamic state of the solar plasma and the interacting magnetic field. In particular, the radiative transfer theory allows us to invert the spectro-polarimetric data to obtain the physical parameters of the different atmospheric layers and, in particular, of the photosphere. In this work, we present a comparison between two methods used to analyze spectro-polarimetric data: the classical Center of Gravity method in the weak field approximation and an inversion code that solves numerically the radiative transfer equation. The Center of Gravity method returns reliable values for the magnetic field and for the line-of-sight velocity in those regions where the weak field approximation is valid (field strength below 400 G), while the inversion code is able to return the stratification of many physical parameters in the layers where the spectral line used for the inversion is formed.

Variational symmetries, conserved quantities and identities for several equations of mathematical physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donchev, Veliko, E-mail: velikod@ie.bas.bg

2014-03-15

We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.

Generation of Squeezed Light Using Photorefractive Degenerate Two-Wave Mixing

NASA Technical Reports Server (NTRS)

Lu, Yajun; Wu, Meijuan; Wu, Ling-An; Tang, Zheng; Li, Shiqun

1996-01-01

We present a quantum nonlinear model of two-wave mixing in a lossless photorefractive medium. A set of equations describing the quantum nonlinear coupling for the field operators is obtained. It is found that, to the second power term, the commutation relationship is maintained. The expectation values for the photon number concur with those of the classical electromagnetic theory when the initial intensities of the two beams are strong. We also calculate the quantum fluctuations of the two beams initially in the coherent state. With an appropriate choice of phase, quadrature squeezing or number state squeezing can be produced.

Study of the time evolution of correlation functions of the transverse Ising chain with ring frustration by perturbative theory

NASA Astrophysics Data System (ADS)

Zheng, Zhen-Yu; Li, Peng

2018-04-01

We consider the time evolution of two-point correlation function in the transverse-field Ising chain (TFIC) with ring frustration. The time-evolution procedure we investigated is equivalent to a quench process in which the system is initially prepared in a classical kink state and evolves according to the time-dependent Schrödinger equation. Within a framework of perturbative theory (PT) in the strong kink phase, the evolution of the correlation function is disclosed to demonstrate a qualitatively new behavior in contrast to the traditional case without ring frustration.

Radiative double copy for Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Chester, David

2018-04-01

Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that the Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in the Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric h¯μ ν is a natural double copy of the gauge boson Aμ a . This work provides additional evidence that solutions in gauge and gravity theories are related, even though their respective Lagrangians and nonlinear equations of motion appear to be different.

Symbolic computer vector analysis

NASA Technical Reports Server (NTRS)

Stoutemyer, D. R.

1977-01-01

A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.

Dielectric response in Bloch’s hydrodynamic model of an electron-ion plasma

NASA Astrophysics Data System (ADS)

Ishikawa, K.; Felderhof, B. U.

The linear response of an electron-ion plasma to an applied oscillating electric field is studied within the framework of Bloch’s classical hydrodynamic model. The ions are assumed to be fixed in space and distributed according to a known probability distribution. The linearized equations of motion for electron density and flow velocity are studied with the aid of a multiple scattering analysis and cluster expansion. This allows systematic reduction of the many-ion problem to a composition of few-ion problems, and shows how the longitudinal dielectric response function can in principle be calculated.

Fermi problem in disordered systems

NASA Astrophysics Data System (ADS)

Menezes, G.; Svaiter, N. F.; de Mello, H. R.; Zarro, C. A. D.

2017-10-01

We revisit the Fermi two-atom problem in the framework of disordered systems. In our model, we consider a two-qubit system linearly coupled with a quantum massless scalar field. We analyze the energy transfer between the qubits under different experimental perspectives. In addition, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that the classical notion of causality emerges only in the wave zone in the presence of random fluctuations of the light cone. Possible repercussions are discussed.

High-order harmonic generation driven by inhomogeneous plasmonics fields spatially bounded: influence on the cut-off law

NASA Astrophysics Data System (ADS)

Neyra, E.; Videla, F.; Ciappina, M. F.; Pérez-Hernández, J. A.; Roso, L.; Lewenstein, M.; Torchia, G. A.

2018-03-01

We study high-order harmonic generation (HHG) in model atoms driven by plasmonic-enhanced fields. These fields result from the illumination of plasmonic nanostructures by few-cycle laser pulses. We demonstrate that the spatial inhomogeneous character of the laser electric field, in a form of Gaussian-shaped functions, leads to an unexpected relationship between the HHG cutoff and the laser wavelength. Precise description of the spatial form of the plasmonic-enhanced field allows us to predict this relationship. We combine the numerical solutions of the time-dependent Schrödinger equation (TDSE) with the plasmonic-enhanced electric fields obtained from 3D finite element simulations. We additionally employ classical simulations to supplement the TDSE outcomes and characterize the extended HHG spectra by means of their associated electron trajectories. A proper definition of the spatially inhomogeneous laser electric field is instrumental to accurately describe the underlying physics of HHG driven by plasmonic-enhanced fields. This characterization opens up new perspectives for HHG control with various experimental nano-setups.

On the Electrostatic Born-Infeld Equation with Extended Charges

NASA Astrophysics Data System (ADS)

Bonheure, Denis; d'Avenia, Pietro; Pomponio, Alessio

2016-09-01

In this paper, we deal with the electrostatic Born-Infeld equation -operatorname{div} (nablaφ/√{1-|nabla φ|^2} )= ρ quad{in} {R}^N, lim_{|x|to ∞} φ(x)= 0,. quad quad quad quad ({{BI}}) where {ρ} is an assigned extended charge density. We are interested in the existence and uniqueness of the potential {φ} and finiteness of the energy of the electrostatic field {-nabla φ}. We first relax the problem and treat it with the direct method of the Calculus of Variations for a broad class of charge densities. Assuming {ρ} is radially distributed, we recover the weak formulation of {({{BI}})} and the regularity of the solution of the Poisson equation (under the same smoothness assumptions). In the case of a locally bounded charge, we also recover the weak formulation without assuming any symmetry. The solution is even classical if {ρ} is smooth. Then we analyze the case where the density {ρ} is a superposition of point charges and discuss the results in (Kiessling, Commun Math Phys 314:509-523, 2012). Other models are discussed, as for instance a system arising from the coupling of the nonlinear Klein-Gordon equation with the Born-Infeld theory.

Axion as a Cold Dark Matter Candidate: Proof to Fully Nonlinear Order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noh, Hyerim; Hwang, Jai-chan; Park, Chan-Gyung

2017-09-01

We present proof of the axion as a cold dark matter (CDM) candidate to the fully nonlinear order perturbations based on Einstein’s gravity. We consider the axion as a coherently oscillating massive classical scalar field without interaction. We present the fully nonlinear and exact, except for ignoring the transverse-tracefree tensor-type perturbation, hydrodynamic equations for an axion fluid in Einstein’s gravity. We show that the axion has the characteristic pressure and anisotropic stress; the latter starts to appear from the second-order perturbation. But these terms do not directly affect the hydrodynamic equations in our axion treatment. Instead, what behaves as themore » effective pressure term in relativistic hydrodynamic equations is the perturbed lapse function and the relativistic result coincides exactly with the one known in the previous non-relativistic studies. The effective pressure term leads to a Jeans scale that is of the solar-system scale for conventional axion mass. As the fully nonlinear and relativistic hydrodynamic equations for an axion fluid coincide exactly with the ones of a zero-pressure fluid in the super-Jeans scale, we have proved the CDM nature of such an axion in that scale.« less

Stochastic description of quantum Brownian dynamics

NASA Astrophysics Data System (ADS)

Yan, Yun-An; Shao, Jiushu

2016-08-01

Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems such as the dynamical description of quantum phase transition (local- ization) and the numerical stability of the trace-conserving, nonlinear stochastic Liouville equation are outlined.

A quantum model of option pricing: When Black-Scholes meets Schrödinger and its semi-classical limit

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo; Ruiz, Aaron

2010-12-01

The Black-Scholes equation can be interpreted from the point of view of quantum mechanics, as the imaginary time Schrödinger equation of a free particle. When deviations of this state of equilibrium are considered, as a product of some market imperfection, such as: Transaction cost, asymmetric information issues, short-term volatility, extreme discontinuities, or serial correlations; the classical non-arbitrage assumption of the Black-Scholes model is violated, implying a non-risk-free portfolio. From Haven (2002) [1] we know that an arbitrage environment is a necessary condition to embedding the Black-Scholes option pricing model in a more general quantum physics setting. The aim of this paper is to propose a new Black-Scholes-Schrödinger model based on the endogenous arbitrage option pricing formulation introduced by Contreras et al. (2010) [2]. Hence, we derive a more general quantum model of option pricing, that incorporates arbitrage as an external time dependent force, which has an associated potential related to the random dynamic of the underlying asset price. This new resultant model can be interpreted as a Schrödinger equation in imaginary time for a particle of mass 1/σ2 with a wave function in an external field force generated by the arbitrage potential. As pointed out above, this new model can be seen as a more general formulation, where the perfect market equilibrium state postulated by the Black-Scholes model represent a particular case. Finally, since the Schrödinger equation is in place, we can apply semiclassical methods, of common use in theoretical physics, to find an approximate analytical solution of the Black-Scholes equation in the presence of market imperfections, as it is the case of an arbitrage bubble. Here, as a numerical illustration of the potential of this Schrödinger equation analogy, the semiclassical approximation is performed for different arbitrage bubble forms (step, linear and parabolic) and compare with the exact solution of our general quantum model of option pricing.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

Diagrammar in classical scalar field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cattaruzza, E., E-mail: Enrico.Cattaruzza@gmail.com; Gozzi, E., E-mail: gozzi@ts.infn.it; INFN, Sezione di Trieste

2011-09-15

In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplifymore » the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.« less

General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

Dirac field and gravity in NC SO(2,3)_\\star model

NASA Astrophysics Data System (ADS)

Gočanin, Dragoljub; Radovanović, Voja

2018-03-01

Action for the Dirac spinor field coupled to gravity on noncommutative (NC) Moyal-Weyl spacetime is obtained without prior knowledge of the metric tensor. We emphasize gauge origins of gravity and its interaction with fermions by demonstrating that a classical action invariant under SO(2, 3) gauge transformations can be exactly reduced to the Dirac action in curved spacetime after breaking the original symmetry down to the local Lorentz SO(1, 3) symmetry. The commutative SO(2, 3) invariant action can be straightforwardly deformed via Moyal-Weyl \\star -product to its NC SO(2,3)_\\star invariant version which can be expanded perturbatively in powers of the deformation parameter using the Seiberg-Witten map. The NC gravity-matter couplings in the expansion arise as an effect of the gauge symmetry breaking. We calculate in detail the first order NC correction to the classical Dirac action in curved spacetime and show that it does not vanish. Moreover, linear NC effects are apparent even in flat spacetime. We analyse NC deformation of the Dirac equation, Feynman propagator and dispersion relation for electrons in Minkowski spacetime and conclude that constant NC background acts as a birefringent medium for electrons propagating in it.

Statistical mechanics in the context of special relativity. II.

PubMed

Kaniadakis, G

2005-09-01

The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various physical observables (e.g., momentum, energy, etc.), as well as the mathematical apparatus of the theory. Here, following the general lines of [Phys. Rev. E 66, 056125 (2002)], we show that the Lorentz transformations impose also a proper one-parameter generalization of the classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits us to construct a coherent and self-consistent relativistic statistical theory, preserving the main features of the ordinary statistical theory, which is recovered in the classical limit. The predicted distribution function is a one-parameter continuous deformation of the classical Maxwell-Boltzmann distribution and has a simple analytic form, showing power law tails in accordance with the experimental evidence. Furthermore, this statistical mechanics can be obtained as the stationary case of a generalized kinetic theory governed by an evolution equation obeying the H theorem and reproducing the Boltzmann equation of the ordinary kinetics in the classical limit.

Airfoil Design and Optimization by the One-Shot Method

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Taasan, Shlomo; Salas, M. D.

1995-01-01

An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Lagrange multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.

A novel model for the chaotic dynamics of superdiffusion

NASA Astrophysics Data System (ADS)

Cushman, J. H.; Park, M.; O'Malley, D.

2009-04-01

Previously we've shown that by modeling the convective velocity in a turbulent flow field as Brownian, one obtains Richardson super diffusion where the expected distance between pairs of particles scales with time cubed. By proving generalized central limit type theorems it's possible to show that modeling the velocity or the acceleration as α-stable Levy gives rise to more general scaling laws that can easily explain other super diffusive regimes. The problem with this latter approach is that the mean square displacement of a particle is infinite. Here we provide an alternate approach that gives a power law mean square displacement of any desired order. We do so by constructing compressed and stretched extensions to Brownian motion. The finite size Lyapunov exponent, the underlying stochastic differential equation and its corresponding Fokker-Planck equations are derived. The fractal dimension of these processes turns out to be the same as that of classical Brownian motion.

Laminated beams: deflection and stress as a function of epoxy shear modulus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bialek, J.

1976-01-01

The large toroidal field coil deflections observed during the PLT power test are due to the poor shear behavior of the insulation material used between layers of copper. Standard techniques for analyzing such laminated structures do not account for this effect. This paper presents an analysis of laminated beams that corrects this deficiency. The analysis explicitly models the mechanical behavior of each layer in a laminated beam and hence avoids the pitfalls involved in any averaging technique. In particular, the shear modulus of the epoxy in a laminated beam (consisting of alternate layers of metal and epoxy) may span themore » entire range of values from zero to classical. Solution of the governing differential equations defines the stress, strain, and deflection for any point within a laminated beam. The paper summarizes these governing equations and also includes a parametric study of a simple laminated beam.« less

New exact solutions of the Dirac and Klein-Gordon equations of a charged particle propagating in a strong laser field in an underdense plasma

NASA Astrophysics Data System (ADS)

Varró, Sándor

2014-03-01

Exact solutions are presented of the Dirac and Klein-Gordon equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave in a medium of index of refraction nm<1. In the Dirac case the solutions are expressed in terms of new complex polynomials, and in the Klein-Gordon case the found solutions are expressed in terms of Ince polynomials. In each case they form a doubly infinite set, labeled by two integer quantum numbers. These integer numbers represent quantized momentum components of the charged particle along the polarization vector and along the propagation direction of the electromagnetic radiation. Since this radiation may represent a plasmon wave of arbitrary high amplitude, propagating in an underdense plasma, the solutions obtained may have relevance in describing possible quantum features of novel acceleration mechanisms.

Nonlinear responses of chiral fluids from kinetic theory

NASA Astrophysics Data System (ADS)

Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

2018-01-01

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

Airfoil optimization by the one-shot method

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Taasan, Shlomo; Salas, M. D.

1994-01-01

An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (Governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Language multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.

Tales from the prehistory of Quantum Gravity. Léon Rosenfeld's earliest contributions

NASA Astrophysics Data System (ADS)

Peruzzi, Giulio; Rocci, Alessio

2018-05-01

The main purpose of this paper is to analyse the earliest work of Léon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld tried to face this problem in 1927, analysing the role of his mentors: Oskar Klein, Louis de Broglie and Théophile De Donder. Rosenfeld asked himself how quantum mechanics should concretely modify general relativity. In the context of a five-dimensional theory, Rosenfeld tried to construct a unifying framework for the gravitational and electromagnetic interaction and wave mechanics. Using a sort of "general relativistic quantum mechanics" Rosenfeld introduced a wave equation on a curved background. He investigated the metric created by what he called `quantum phenomena', represented by wave functions. Rosenfeld integrated Einstein equations in the weak field limit, with wave functions as source of the gravitational field. The author performed a sort of semi-classical approximation obtaining at the first order the Reissner-Nordström metric. We analyse how Rosenfeld's work is part of the history of Quantum Mechanics, because in his investigation Rosenfeld was guided by Bohr's correspondence principle. Finally we briefly discuss how his contribution is connected with the task of finding out which metric can be generated by a quantum field, a problem that quantum field theory on curved backgrounds will start to address 35 years later.

Tales from the prehistory of Quantum Gravity - Léon Rosenfeld's earliest contributions

NASA Astrophysics Data System (ADS)

Peruzzi, Giulio; Rocci, Alessio

2018-04-01

The main purpose of this paper is to analyse the earliest work of Léon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld tried to face this problem in 1927, analysing the role of his mentors: Oskar Klein, Louis de Broglie and Théophile De Donder. Rosenfeld asked himself how quantum mechanics should concretely modify general relativity. In the context of a five-dimensional theory, Rosenfeld tried to construct a unifying framework for the gravitational and electromagnetic interaction and wave mechanics. Using a sort of "general relativistic quantum mechanics" Rosenfeld introduced a wave equation on a curved background. He investigated the metric created by what he called `quantum phenomena', represented by wave functions. Rosenfeld integrated Einstein equations in the weak field limit, with wave functions as source of the gravitational field. The author performed a sort of semi-classical approximation obtaining at the first order the Reissner-Nordström metric. We analyse how Rosenfeld's work is part of the history of Quantum Mechanics, because in his investigation Rosenfeld was guided by Bohr's correspondence principle. Finally we briefly discuss how his contribution is connected with the task of finding out which metric can be generated by a quantum field, a problem that quantum field theory on curved backgrounds will start to address 35 years later.

Electric and magnetic dipoles in the Lorentz and Einstein-Laub formulations of classical electrodynamics

NASA Astrophysics Data System (ADS)

Mansuripur, Masud

2015-01-01

The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just as it postulates the existence and properties of electric charges and currents. Maxwell's macroscopic equations are mathematically exact and self-consistent differential equations that relate the electromagnetic (EM) field to its sources, namely, electric charge-density 𝜌𝜌free, electric current-density 𝑱𝑱free, polarization 𝑷𝑷, and magnetization 𝑴𝑴. At the level of Maxwell's macroscopic equations, there is no need for models of electric and magnetic dipoles. For example, whether a magnetic dipole is an Amperian current-loop or a Gilbertian pair of north and south magnetic monopoles has no effect on the solution of Maxwell's equations. Electromagnetic fields carry energy as well as linear and angular momenta, which they can exchange with material media—the seat of the sources of the EM field—thereby exerting force and torque on these media. In the Lorentz formulation of classical electrodynamics, the electric and magnetic fields, 𝑬𝑬 and 𝑩𝑩, exert forces and torques on electric charge and current distributions. An electric dipole is then modeled as a pair of electric charges on a stick (or spring), and a magnetic dipole is modeled as an Amperian current loop, so that the Lorentz force law can be applied to the corresponding (bound) charges and (bound) currents of these dipoles. In contrast, the Einstein-Laub formulation circumvents the need for specific models of the dipoles by simply providing a recipe for calculating the force- and torque-densities exerted by the 𝑬𝑬 and 𝑯𝑯 fields on charge, current, polarization and magnetization. The two formulations, while similar in many respects, have significant differences. For example, in the Lorentz approach, the Poynting vector is 𝑺𝑺𝐿𝐿 = 𝜇𝜇0 -1𝑬𝑬 × 𝑩𝑩, and the linear and angular momentum densities of the EM field are 𝓹𝓹𝐿𝐿 = 𝜀𝜀0𝑬𝑬 × 𝑩𝑩 and 𝓛𝓛𝐿𝐿 = 𝒓𝒓 × 𝓹𝓹𝐿𝐿, whereas in the Einstein-Laub formulation the corresponding entities are 𝑺𝑺𝐸𝐸𝐸𝐸= 𝑬𝑬 × 𝑯𝑯, 𝓹𝓹𝐸𝐸𝐸𝐸= 𝑬𝑬 × 𝑯𝑯⁄𝑐𝑐2, and 𝓛𝓛𝐸𝐸𝐸𝐸= 𝒓𝒓 × 𝓹𝓹𝐸𝐸𝐸𝐸. (Here 𝜇𝜇0 and 𝜀𝜀0 are the permeability and permittivity of free space, 𝑐𝑐 is the speed of light in vacuum, 𝑩𝑩 = 𝜇𝜇0𝑯𝑯 + 𝑴𝑴, and 𝒓𝒓 is the position vector.) Such differences can be reconciled by recognizing the need for the so-called hidden energy and hidden momentum associated with Amperian current loops of the Lorentz formalism. (Hidden entities of the sort do not arise in the Einstein-Laub treatment of magnetic dipoles.) Other differences arise from over-simplistic assumptions concerning the equivalence between free charges and currents on the one hand, and their bound counterparts on the other. A more nuanced treatment of EM force and torque densities exerted on polarization and magnetization in the Lorentz approach would help bridge the gap that superficially separates the two formulations. Atoms and molecules may collide with each other and, in general, material constituents can exchange energy, momentum, and angular momentum via direct mechanical interactions. In the case of continuous media, elastic and hydrodynamic stresses, phenomenological forces such as those related to exchange coupling in ferromagnets, etc., subject small volumes of materials to external forces and torques. Such matter-matter interactions, although fundamentally EM in nature, are distinct from field-matter interactions in classical physics. Beyond the classical regime, however, the dichotomy that distinguishes the EM field from EM sources gets blurred. An electron's wavefunction may overlap that of an atomic nucleus, thereby initiating a contact interaction between the magnetic dipole moments of the two particles. Or a neutron passing through a ferromagnetic material may give rise to scattering events involving overlaps between the wave-functions of the neutron and magnetic electrons. Such matter-matter interactions exert equal and opposite forces and/or torques on the colliding particles, and their observable effects often shed light on the nature of the particles involved. It is through such observations that the Amperian model of a magnetic dipole has come to gain prominence over the Gilbertian model. In situations involving overlapping particle wave-functions, it is imperative to take account of the particle-particle interaction energy when computing the scattering amplitudes. As far as total force and total torque on a given volume of material are concerned, such particle-particle interactions do not affect the outcome of calculations, since the mutual actions of the two (overlapping) particles cancel each other out. Both Lorentz and Einstein-Laub formalisms thus yield the same total force and total torque on a given volume—provided that hidden entities are properly removed. The Lorentz formalism, with its roots in the Amperian current-loop model, correctly predicts the interaction energy between two overlapping magnetic dipoles 𝒎𝒎1 and 𝒎𝒎2 as being proportional to -𝒎𝒎1 • 𝒎𝒎2. In contrast, the Einstein-Laub formalism, which is ignorant of such particle-particle interactions, needs to account for them separately.

Photon mirror acceleration in the quantum regime

NASA Astrophysics Data System (ADS)

Mendonça, J. T.; Fedele, R.

2014-12-01

Reflection of an electron beam by an intense laser pulse is considered. This is the so-called photon mirror configuration for laser acceleration in vacuum, where the energy of the incident electron beam is nearly double-Doppler shifted due to reflection on the laser pulse front. A wave-electron optical description for electron reflection and resonant backscattering, due to both linear electric field force and quadratic ponderomotive force, is provided beyond the paraxial approximation. This is done by assuming that the single electron of the beam is spin-less and therefore its motion can be described by a quantum scalar field whose spatiotemporal evolution is governed by the Klein-Gordon equation (Klein-Gordon field). Our present model, not only confirms the classical results but also shows the occurrence of purely quantum effects, such as partial reflection of the incident electron beam and enhanced backscattering due to Bragg resonance.

Momentum conserving defects in affine Toda field theories

NASA Astrophysics Data System (ADS)

Bristow, Rebecca; Bowcock, Peter

2017-05-01

Type II integrable defects with more than one degree of freedom at the defect are investigated. A condition on the form of the Lagrangian for such defects is found which ensures the existence of a conserved momentum in the presence of the defect. In addition it is shown that for any Lagrangian satisfying this condition, the defect equations of motion, when taken to hold everywhere, can be extended to give a Bäcklund transformation between the bulk theories on either side of the defect. This strongly suggests that such systems are integrable. Momentum conserving defects and Bäcklund transformations for affine Toda field theories based on the A n , B n , C n and D n series of Lie algebras are found. The defect associated with the D 4 affine Toda field theory is examined in more detail. In particular classical time delays for solitons passing through the defect are calculated.

Thermodynamics Fundamental Equation of a "Non-Ideal" Rubber Band from Experiments

ERIC Educational Resources Information Center

Ritacco, Herna´n A.; Fortunatti, Juan C.; Devoto, Walter; Ferna´ndez-Miconi, Eugenio; Dominguez, Claudia; Sanchez, Miguel D.

2014-01-01

In this paper, we describe laboratory and classroom exercises designed to obtain the "fundamental" equation of a rubber band by combining experiments and theory. The procedure shows students how classical thermodynamics formalism can help to obtain empirical equations of state by constraining and guiding in the construction of the…

The Bernoulli Equation in a Moving Reference Frame

ERIC Educational Resources Information Center

Mungan, Carl E.

2011-01-01

Unlike other standard equations in introductory classical mechanics, the Bernoulli equation is not Galilean invariant. The explanation is that, in a reference frame moving with respect to constrictions or obstacles, those surfaces do work on the fluid, constituting an extra term that needs to be included in the work-energy calculation. A…

A van der Waals Equation of State for a Dilute Boson Gas

ERIC Educational Resources Information Center

Deeney, F. A.; O'Leary, J. P.

2012-01-01

An equation of state of a system is a relationship that connects the thermodynamic variables of the system such as pressure and temperature. Such equations are well known for classical gases but less so for quantum systems. In this paper we develop a van der Waals equation of state for a dilute boson gas that may be used to explain the occurrence…

Solving the Vlasov equation in two spatial dimensions with the Schrödinger method

NASA Astrophysics Data System (ADS)

Kopp, Michael; Vattis, Kyriakos; Skordis, Constantinos

2017-12-01

We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schrödinger method (ScM). With the ScM, one solves the Schrödinger-Poisson system of equations for a complex wave function in d dimensions, rather than the Vlasov equation for a 2 d -dimensional phase space density. The ScM also allows calculating the d -dimensional cumulants directly through quasilocal manipulations of the wave function, avoiding the complexity of 2 d -dimensional phase space. We perform for the first time a quantitative comparison of the ScM and a conventional Vlasov solver in d =2 dimensions. Our numerical tests were carried out using two types of cold cosmological initial conditions: the classic collapse of a sine wave and those of a Gaussian random field as commonly used in cosmological cold dark matter N-body simulations. We compare the first three cumulants, that is, the density, velocity and velocity dispersion, to those obtained by solving the Vlasov equation using the publicly available code ColDICE. We find excellent qualitative and quantitative agreement between these codes, demonstrating the feasibility and advantages of the ScM as an alternative to N-body simulations. We discuss, the emergence of effective vorticity in the ScM through the winding number around the points where the wave function vanishes. As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure.

Application of Direct Parallel Methods to Reconstruction and Forecasting Problems

NASA Astrophysics Data System (ADS)

Song, Changgeun

Many important physical processes in nature are represented by partial differential equations. Numerical weather prediction in particular, requires vast computational resources. We investigate the significance of parallel processing technology to the real world problem of atmospheric prediction. In this paper we consider the classic problem of decomposing the observed wind field into the irrotational and nondivergent components. Recognizing the fact that on a limited domain this problem has a non-unique solution, Lynch (1989) described eight different ways to accomplish the decomposition. One set of elliptic equations is associated with the decomposition--this determines the initial nondivergent state for the forecast model. It is shown that the entire decomposition problem can be solved in a fraction of a second using multi-vector processor such as ALLIANT FX/8. Secondly, the barotropic model is used to track hurricanes. Also, one set of elliptic equations is solved to recover the streamfunction from the forecasted vorticity. A 72 h prediction of Elena is made while it is in the Gulf of Mexico. During this time the hurricane executes a dramatic re-curvature that is captured by the model. Furthermore, an improvement in the track prediction results when a simple assimilation strategy is used. This technique makes use of the wind fields in the 24 h period immediately preceding the initial time for the prediction. In this particular application, solutions to systems of elliptic equations are the center of the computational mechanics. We demonstrate that direct, parallel methods based on accelerated block cyclic reduction (BCR) significantly reduce the computational time required to solve the elliptic equations germane to the decomposition, the forecast and adjoint assimilation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gevorkyan, A. S., E-mail: g-ashot@sci.am; Sahakyan, V. V.

We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.

The Equivalence of the Radial Return and Mendelson Methods for Integrating the Classical Plasticity Equations

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Aboudi, Jacob; Arnold, Steven M.

2006-01-01

The radial return and Mendelson methods for integrating the equations of classical plasticity, which appear independently in the literature, are shown to be identical. Both methods are presented in detail as are the specifics of their algorithmic implementation. Results illustrate the methods' equivalence across a range of conditions and address the question of when the methods require iteration in order for the plastic state to remain on the yield surface. FORTRAN code implementations of the radial return and Mendelson methods are provided in the appendix.

Coherent Structures in Magnetic Confinement Systems

NASA Astrophysics Data System (ADS)

Horton, W.

2006-04-01

Coherent structures are long-lived, nonlinear localized solutions of the selfconsistient plasma-electromagnetic field equations. They contain appreciable energy density and control various transport and magnetic reconnection processes in plasmas. These structures are self-binding from the nonlinearity balancing, or overcoming, the wave dispersion of energy in smaller amplitude structures. The structures evolve out of the nonlinear interactions in various instabilities or external driving fields. The theoretical basis for these structures are reviewed giving examples from various plasma instabilities and their reduced descriptions from the appropriate partial differential equations. A classic example from drift waves is the formation of monopole, dipole and tripolar vortex structures which have been created in both laboratory and simulation experiments. For vortices, the long life-time and nonlinear interactions of the structures can be understood with conservation laws of angular momentum given by the vorticity field associated with dynamics. Other morphologies include mushrooms, Kelvin-Helmholtz vorticity roll-up, streamers and blobs. We show simulation movies of various examples drawn from ETG modes in NSTX, H-mode like shear flow layers in LAPD and the vortices measured with soft x-ray tomography in the GAMMA 10 tandem mirror. Coherent current-sheet structures form in driven magnetic reconnection layers and control the rate of transformation of magnetic energy to flow and thermal energy.

Three-Dimensional Multi-fluid Moment Simulation of Ganymede

NASA Astrophysics Data System (ADS)

Wang, L.; Germaschewski, K.; Hakim, A.; Bhattacharjee, A.; Dong, C.

2016-12-01

Plasmas in space environments, such as solar wind and Earth's magnetosphere, are often constituted of multiple species. Conventional MHD-based, single-fluid systems, have additional complications when multiple fluid species are introduced. We suggest space application of an alternative multi-fluid moment approach, treating each species on equal footing using exact evolution equations for moments of their distribution function, and electromagnetic fields through full Maxwell equations. Non-ideal effects like Hall effect, inertia, and even tensorial pressures, are self-consistently embedded without the need to explicitly solve a complicated Ohm's law. Previously, we have benchmarked this approach in classical test problems like the Orszag-Tang vortex and GEM reconnection challenge problem. Recently, we performed three-dimensional two-fluid simulation of the magnetosphere of Ganymede, using both five-moment (scalar pressures) and ten-moment (tensorial pressures) models. In both models, the formation of Alfven wing structure due to subsonic inflow is correctly captured, and the magnetic field data agree well with in-situ measurements from the Galileo flyby G8. The ten-moment simulation also showed the contribution of pressure tensor divergence to the reconnecting electric field. Initial results of coupling to state-of-art global simulation codes like OpenGGCM will also be shown, which will in the future provide a rigorous way for integration of ionospheric physics.

Generalized Onsager's reciprocal relations for the master and Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Peng, Liangrong; Zhu, Yi; Hong, Liu

2018-06-01

The Onsager's reciprocal relation plays a fundamental role in the nonequilibrium thermodynamics. However, unfortunately, its classical version is valid only within a narrow region near equilibrium due to the linear regression hypothesis, which largely restricts its usage. In this paper, based on the conservation-dissipation formalism, a generalized version of Onsager's relations for the master equations and Fokker-Planck equations was derived. Nonlinear constitutive relations with nonsymmetric and positively stable operators, which become symmetric under the detailed balance condition, constitute key features of this new generalization. Similar conclusions also hold for many other classical models in physics and chemistry, which in turn make the current study as a benchmark for the application of generalized Onsager's relations in nonequilibrium thermodynamics.

Quantum no-singularity theorem from geometric flows

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

High-order above-threshold ionization beyond the electric dipole approximation

NASA Astrophysics Data System (ADS)

Brennecke, Simon; Lein, Manfred

2018-05-01

Photoelectron momentum distributions from strong-field ionization are calculated by numerical solution of the one-electron time-dependent Schrödinger equation for a model atom including effects beyond the electric dipole approximation. We focus on the high-energy electrons from rescattering and analyze their momentum component along the field propagation direction. We show that the boundary of the calculated momentum distribution is deformed in accordance with the classical three-step model including the beyond-dipole Lorentz force. In addition, the momentum distribution exhibits an asymmetry in the signal strengths of electrons emitted in the forward/backward directions. Taken together, the two non-dipole effects give rise to a considerable average forward momentum component of the order of 0.1 a.u. for realistic laser parameters.

Interaction with a field: a simple integrable model with backreaction

NASA Astrophysics Data System (ADS)

Mouchet, Amaury

2008-09-01

The classical model of an oscillator linearly coupled to a string captures, for a low price in technique, many general features of more realistic models for describing a particle interacting with a field or an atom in an electromagnetic cavity. The scattering matrix and the asymptotic in and out-waves on the string can be computed exactly and the phenomenon of resonant scattering can be introduced in the simplest way. The dissipation induced by the coupling of the oscillator to the string can be studied completely. In the case of a d'Alembert string, the backreaction leads to an Abraham-Lorentz-Dirac-like equation. In the case of a Klein-Gordon string, one can see explicitly how radiation governs the (meta)stability of the (quasi)bounded mode.

Geometric Approaches to Quadratic Equations from Other Times and Places.

ERIC Educational Resources Information Center

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

A quantum-classical theory with nonlinear and stochastic dynamics

NASA Astrophysics Data System (ADS)

Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

2014-12-01

The method of constrained dynamical systems on the quantum-classical phase space is utilized to develop a theory of quantum-classical hybrid systems. Effects of the classical degrees of freedom on the quantum part are modeled using an appropriate constraint, and the interaction also includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement.

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Da; Zheng, Bin; Lin, Guang

2014-08-29

We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is themore » number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.« less

Multiphysics modeling of non-linear laser-matter interactions for optically active semiconductors

NASA Astrophysics Data System (ADS)

Kraczek, Brent; Kanp, Jaroslaw

Development of photonic devices for sensors and communications devices has been significantly enhanced by computational modeling. We present a new computational method for modelling laser propagation in optically-active semiconductors within the paraxial wave approximation (PWA). Light propagation is modeled using the Streamline-upwind/Petrov-Galerkin finite element method (FEM). Material response enters through the non-linear polarization, which serves as the right-hand side of the FEM calculation. Maxwell's equations for classical light propagation within the PWA can be written solely in terms of the electric field, producing a wave equation that is a form of the advection-diffusion-reaction equations (ADREs). This allows adaptation of the computational machinery developed for solving ADREs in fluid dynamics to light-propagation modeling. The non-linear polarization is incorporated using a flexible framework to enable the use of multiple methods for carrier-carrier interactions (e.g. relaxation-time-based or Monte Carlo) to enter through the non-linear polarization, as appropriate to the material type. We demonstrate using a simple carrier-carrier model approximating the response of GaN. Supported by ARL Materials Enterprise.