Failure of geometric electromagnetism in the adiabatic vector Kepler problem

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

Anglin, J.R.; Schmiedmayer, J.

2004-02-01

The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wire's magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only the particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher-order postadiabatic corrections make the orbits precess, but recent analysis of this 'vector Kepler problem' has shown that the effective Hamiltonian incorporating a postadiabatic scalar potential ('geometric electromagnetism') fails to predict themore » precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the postadiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a 1/r{sup 3} singularity which is an artifact of the adiabatic approximation.« less

Chaotic Electron Motion Caused by Sidebands in Free Electron Lasers

DTIC Science & Technology

1988-10-27

sideband. The total vector potential is then, A (z,t) = (1) •w (e~ )ri(krZ-Wr t) l(ksZ-Wst)] -c’-[(ex-iey)AweZ% _+V-(ex+iey)Are ikrzwr _) (ex+iey)Ase... light c, ignoring the small correction of order w 2/W 2 from the dielectric contribution of the beam. Electrostatic contributions to the fields are...mass to me and the vector potentials according to ai=IeIAi/mec2 the dimensionless Hamiltonian describing the electron motion in the fields of Eq. (1

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

On generalized Volterra systems

NASA Astrophysics Data System (ADS)

Charalambides, S. A.; Damianou, P. A.; Evripidou, C. A.

2015-01-01

We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The algorithm uses the root system of a complex simple Lie algebra. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a system to a quadratic Lotka-Volterra system. We present in detail all such systems in the cases of A3, A4 and we also give some examples from higher dimensions. We classify all possible Lotka-Volterra systems that arise via this algorithm in the An case.

Stochastic Evolution of Augmented Born-Infeld Equations

NASA Astrophysics Data System (ADS)

Holm, Darryl D.

2018-06-01

This paper compares the results of applying a recently developed method of stochastic uncertainty quantification designed for fluid dynamics to the Born-Infeld model of nonlinear electromagnetism. The similarities in the results are striking. Namely, the introduction of Stratonovich cylindrical noise into each of their Hamiltonian formulations introduces stochastic Lie transport into their dynamics in the same form for both theories. Moreover, the resulting stochastic partial differential equations retain their unperturbed form, except for an additional term representing induced Lie transport by the set of divergence-free vector fields associated with the spatial correlations of the cylindrical noise. The explanation for this remarkable similarity lies in the method of construction of the Hamiltonian for the Stratonovich stochastic contribution to the motion in both cases, which is done via pairing spatial correlation eigenvectors for cylindrical noise with the momentum map for the deterministic motion. This momentum map is responsible for the well-known analogy between hydrodynamics and electromagnetism. The momentum map for the Maxwell and Born-Infeld theories of electromagnetism treated here is the 1-form density known as the Poynting vector. Two appendices treat the Hamiltonian structures underlying these results.

Representations of spacetime diffeomorphisms. I. Canonical parametrized field theories

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

Isham, C.J.; Kuchar, K.V.

The super-Hamiltonian and supermomentum in canonical geometrodynamics or in a parametried field theory on a given Riemannian background have Poisson brackets which obey the Dirac relations. By smearing the supermomentum with vector fields VepsilonL Diff..sigma.. on the space manifold ..sigma.., the Lie algebra L Diff ..sigma.. of the spatial diffeomorphism group Diff ..sigma.. can be mapped antihomomorphically into the Poisson bracket algebra on the phase space of the system. The explicit dependence of the Poisson brackets between two super-Hamiltonians on canonical coordinates (spatial metrics in geometrodynamics and embedding variables in parametrized theories) is usually regarded as an indication that themore » Dirac relations cannot be connected with a representation of the complete Lie algebra L Diff M of spacetime diffeomorphisms.« less

Extended canonical field theory of matter and space-time

NASA Astrophysics Data System (ADS)

Struckmeier, J.; Vasak, D.; matter, H. Stoecker Field theory of; space-time

2015-11-01

Any physical theory that follows from an action principle should be invariant in its form under mappings of the reference frame in order to comply with the general principle of relativity. The required form-invariance of the action principle implies that the mapping must constitute a particular extended canonical transformation. In the realm of the covariant Hamiltonian formulation of field theory, the term ``extended'' implies that not only the fields but also the space-time geometry is subject to transformation. A canonical transformation maintains the general form of the action principle by simultaneously defining the appropriate transformation rules for the fields, the conjugate momentum fields, and the transformation rule for the Hamiltonian. Provided that the given system of fields exhibits a particular global symmetry, the associated extended canonical transformation determines an amended Hamiltonian that is form-invariant under the corresponding local symmetry. This will be worked out for a Hamiltonian system of scalar and vector fields that is presupposed to be form-invariant under space-time transformations xμ\\mapsto Xμ with partial Xμ/partial xν=const., hence under global space-time transformations such as the Poincaré transformation. The corresponding amended system that is form-invariant under local space-time transformations partial Xμ/partial xν≠qconst. then describes the coupling of the fields to the space-time geometry and thus yields the dynamics of space-time that is associated with the given physical system. Non-zero spin matter determines thereby the space-time curvature via a well-defined source term in a covariant Poisson-type equation for the Riemann tensor.

Hamiltonian dynamics of vortex and magnetic lines in hydrodynamic type systems

NASA Astrophysics Data System (ADS)

Kuznetsov, E. A.; Ruban, V. P.

2000-01-01

Vortex line and magnetic line representations are introduced for a description of flows in ideal hydrodynamics and magnetohydrodynamics (MHD), respectively. For incompressible fluids, it is shown with the help of this transformation that the equations of motion for vorticity Ω and magnetic field follow from a variational principle. By means of this representation, it is possible to integrate the hydrodynamic type system with the Hamiltonian H=∫\\|Ω\\|dr and some other systems. It is also demonstrated that these representations allow one to remove from the noncanonical Poisson brackets, defined in the space of divergence-free vector fields, the degeneracy connected with the vorticity frozenness for the Euler equation and with magnetic field frozenness for ideal MHD. For MHD, a new Weber-type transformation is found. It is shown how this transformation can be obtained from the two-fluid model when electrons and ions can be considered as two independent fluids. The Weber-type transformation for ideal MHD gives the whole Lagrangian vector invariant. When this invariant is absent, this transformation coincides with the Clebsch representation analog introduced by V.E. Zakharov and E. A. Kuznetsov [Dokl. Ajad. Nauk 194, 1288 (1970) [Sov. Phys. Dokl. 15, 913 (1971)

Differential Geometry and Lie Groups for Physicists

NASA Astrophysics Data System (ADS)

Fecko, Marián.

2006-10-01

Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

Differential Geometry and Lie Groups for Physicists

NASA Astrophysics Data System (ADS)

Fecko, Marián.

2011-03-01

Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

Canonical transformation path to gauge theories of gravity

NASA Astrophysics Data System (ADS)

Struckmeier, J.; Muench, J.; Vasak, D.; Kirsch, J.; Hanauske, M.; Stoecker, H.

2017-06-01

In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a gauge theory. The starting point of our paper is constituted by the general De Donder-Weyl Hamiltonian of a system of scalar and vector fields, which is supposed to be form-invariant under (global) Lorentz transformations. Following the reasoning of gauge theories, the corresponding locally form-invariant system is worked out by means of canonical transformations. The canonical transformation approach ensures by construction that the form of the action functional is maintained. We thus encounter amended Hamiltonian systems which are form-invariant under arbitrary spacetime transformations. This amended system complies with the general principle of relativity and describes both, the dynamics of the given physical system's fields and their coupling to those quantities which describe the dynamics of the spacetime geometry. In this way, it is unambiguously determined how spin-0 and spin-1 fields couple to the dynamics of spacetime. A term that describes the dynamics of the "free" gauge fields must finally be added to the amended Hamiltonian, as common to all gauge theories, to allow for a dynamic spacetime geometry. The choice of this "dynamics" Hamiltonian is outside of the scope of gauge theory as presented in this paper. It accounts for the remaining indefiniteness of any gauge theory of gravity and must be chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of the gauge theory of gravity is shown to be at least quadratic in the conjugate momenta of the gauge fields—this is beyond the Einstein-Hilbert theory of general relativity.

Conformal killing tensors and covariant Hamiltonian dynamics

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

Cariglia, M., E-mail: marco@iceb.ufop.br; Gibbons, G. W., E-mail: G.W.Gibbons@damtp.cam.ac.uk; LE STUDIUM, Loire Valley Institute for Advanced Studies, Tours and Orleans

2014-12-15

A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector formore » planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.« less

Hawking radiation of a vector field and gravitational anomalies

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

Murata, Keiju; Miyamoto, Umpei

2007-10-15

Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with the Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is available. It is found that the total energy emitted from themore » horizon for the electromagnetic field is just (d-2) times that for a scalar field. The results support the picture that Hawking radiation can be regarded as an anomaly eliminator on horizons. Possible extensions and applications of the analysis are discussed.« less

Signatures of the A2 term in ultrastrongly coupled oscillators

NASA Astrophysics Data System (ADS)

Tufarelli, Tommaso; McEnery, K. R.; Maier, S. A.; Kim, M. S.

2015-06-01

We study a bosonic matter excitation coupled to a single-mode cavity field via electric dipole. Counter-rotating and A2 terms are included in the interaction model, A being the vector potential of the cavity field. In the ultrastrong coupling regime the vacuum of the bare modes is no longer the ground state of the Hamiltonian and contains a nonzero population of polaritons, the true normal modes of the system. If the parameters of the model satisfy the Thomas-Reiche-Kuhn sum rule, we find that the two polaritons are always equally populated. We show how this prediction could be tested in a quenching experiment, by rapidly switching on the coupling and analyzing the radiation emitted by the cavity. A refinement of the model based on a microscopic minimal coupling Hamiltonian is also provided, and its consequences on our results are characterized analytically.

Constraints and stability in vector theories with spontaneous Lorentz violation

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

Bluhm, Robert; Gagne, Nolan L.; Potting, Robertus

2008-06-15

Vector theories with spontaneous Lorentz violation, known as bumblebee models, are examined in flat spacetime using a Hamiltonian constraint analysis. In some of these models, Nambu-Goldstone modes appear with properties similar to photons in electromagnetism. However, depending on the form of the theory, additional modes and constraints can appear that have no counterparts in electromagnetism. An examination of these constraints and additional degrees of freedom, including their nonlinear effects, is made for a variety of models with different kinetic and potential terms, and the results are compared with electromagnetism. The Hamiltonian constraint analysis also permits an investigation of the stabilitymore » of these models. For certain bumblebee theories with a timelike vector, suitable restrictions of the initial-value solutions are identified that yield ghost-free models with a positive Hamiltonian. In each case, the restricted phase space is found to match that of electromagnetism in a nonlinear gauge.« less

A Hamiltonian electromagnetic gyrofluid model

NASA Astrophysics Data System (ADS)

Waelbroeck, F. L.; Hazeltine, R. D.; Morrison, P. J.

2009-11-01

An isothermal truncation of the electromagnetic gyrofluid model of Snyder and Hammett [Phys. Plasmas 8, 3199 (2001)] is shown to be Hamiltonian. The corresponding noncanonical Lie-Poisson bracket and its Casimir invariants are presented. The model describes the evolution of the density, the electrostatic potential, and the component of the vector potential along a strong background field. This makes it suitable for describing such phenomena as the propagation of kinetic-Alfv'en modons, the nonlinear saturation of drift-tearing modes, and the diamagnetic stabilization of the internal kink. The invariants are used to obtain a set of coupled Grad-Shafranov equations describing equilibria and propagating coherent structures. They also lead to a Lagrangian formulation of the equations of motion that is well suited to solution with the PIC method.

Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: A local mean-field analysis

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Lookman, Turab; Shenoy, Subodh R.

2010-09-01

We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local mean-field approximation of their pseudospin Hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their NOP -component order parameters, with Landau free energies that have a single zero-strain “austenite” minimum at high temperatures, and spontaneous-strain “martensite” minima of NV structural variants at low temperatures. The total free energy also has gradient terms, and power-law anisotropic effective interactions, induced by “no-dislocation” St Venant compatibility constraints. In a reduced description, the strains at Landau minima induce temperature dependent, clocklike ZNV+1 Hamiltonians, with NOP -component strain-pseudospin vectors S⃗ pointing to NV+1 discrete values (including zero). We study elastic texturing in five such first-order structural transitions through a local mean-field approximation of their pseudospin Hamiltonians, that include the power-law interactions. As a prototype, we consider the two-variant square/rectangle transition, with a one-component pseudospin taking NV+1=3 values of S=0,±1 , as in a generalized Blume-Capel model. We then consider transitions with two-component (NOP=2) pseudospins: the equilateral to centered rectangle (NV=3) ; the square to oblique polygon (NV=4) ; the triangle to oblique (NV=6) transitions; and finally the three-dimensional (3D) cubic to tetragonal transition (NV=3) . The local mean-field solutions in two-dimensional and 3D yield oriented domain-wall patterns as from continuous-variable strain dynamics, showing the discrete-variable models capture the essential ferroelastic texturings. Other related Hamiltonians illustrate that structural transitions in materials science can be the source of interesting spin models in statistical mechanics.

A two-step, fourth-order method with energy preserving properties

NASA Astrophysics Data System (ADS)

Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato

2012-09-01

We introduce a family of fourth-order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. As is the case with linear mutistep and one-leg methods, a prerogative of the new formulae is that the associated nonlinear systems to be solved at each step of the integration procedure have the very same dimension of the underlying continuous problem. The key tools in the new methods are the line integral associated with a conservative vector field (such as the one defined by a Hamiltonian dynamical system) and its discretization obtained by the aid of a quadrature formula. Energy conservation is equivalent to the requirement that the quadrature is exact, which turns out to be always the case in the event that the Hamiltonian function is a polynomial and the degree of precision of the quadrature formula is high enough. The non-polynomial case is also discussed and a number of test problems are finally presented in order to compare the behavior of the new methods to the theoretical results.

Classical spin glass system in external field with taking into account relaxation effects

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

Gevorkyan, A. S., E-mail: g_ashot@sci.am; Abajyan, H. G.

2013-08-15

We study statistical properties of disordered spin systems under the influence of an external field with taking into account relaxation effects. For description of system the spatial 1D Heisenberg spin-glass Hamiltonian is used. In addition, we suppose that interactions occur between nearest-neighboring spins and they are random. Exact solutions which define angular configuration of the spin in nodes were obtained from the equations of stationary points of Hamiltonian and the corresponding conditions for the energy local minimum. On the basis of these recurrent solutions an effective parallel algorithm is developed for simulation of stabile spin-chains of an arbitrary length. Itmore » is shown that by way of an independent order of N{sup 2} numerical simulations (where N is number of spin in each chain) it is possible to generate ensemble of spin-chains, which is completely ergodic which is equivalent to full self-averaging of spin-chains' vector polarization. Distributions of different parameters (energy, average polarization by coordinates, and spin-spin interaction constant) of unperturbed system are calculated. In particular, analytically is proved and numerically is shown, that for the Heisenberg nearest-neighboring Hamiltonian model, the distribution of spin-spin interaction constants as opposed to widely used Gauss-Edwards-Anderson distribution satisfies Levy alpha-stable distribution law. This distribution is nonanalytic function and does not have variance. In the work we have in detail studied critical properties of an ensemble depending on value of external field parameters (from amplitude and frequency) and have shown that even at weak external fields the spin-glass systemis strongly frustrated. It is shown that frustrations have fractal behavior, they are selfsimilar and do not disappear at scale decreasing of area. By the numerical computation is shown that the average polarization of spin-glass on a different coordinates can have values which can lead to catastrophes in the equation ofClausius-Mossotti for dielectric constant. In other words, for some values of external field parameter, a critical phenomenon occurs in the system which is impossible to describe by the real-valued Heisenberg spin-glass Hamiltonian. For the solution of this problem at first the complex-valued disordered Hamiltonian is used. Physically this type of extension of Hamiltonian allows to consider relaxation effects which occur in the system under the influence of an external field. On the basis of developed approach an effective parallel algorithm is developed for simulation of statistic parameters of spin-glass system under the influence of an external field.« less

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

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

2015-07-29

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N 2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less

Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2013-10-01

The Euclidean action with acceleration has been analyzed in Ref. 1, and referred to henceforth as Paper I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation and destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.

Localization noise in deep subwavelength plasmonic devices

NASA Astrophysics Data System (ADS)

Ghoreyshi, Ali; Victora, R. H.

2018-05-01

The grain shape dependence of absorption has been investigated in metal-insulator thin films. We demonstrate that randomness in the size and shape of plasmonic particles can lead to Anderson localization of polarization modes in the deep subwavelength regime. These localized modes can contribute to significant variation in the local field. In the case of plasmonic nanodevices, the effects of the localized modes have been investigated by mapping an electrostatic Hamiltonian onto the Anderson Hamiltonian in the presence of a random vector potential. We show that local behavior of the optical beam can be understood in terms of the weighted local density of the localized modes of the depolarization field. Optical nanodevices that operate on a length scale with high variation in the density of states of localized modes will experience a previously unidentified localized noise. This localization noise contributes uncertainty to the output of plasmonic nanodevices and limits their scalability. In particular, the resulting impact on heat-assisted magnetic recording is discussed.

Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes

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

Dias, Goncalo A. S.; Lemos, Jose P. S.; Centro Multidisciplinar de Astrofisica-CENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Avenida Rovisco Pais 1, 1049-001 Lisboa

2008-10-15

The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free {omega} parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{+-}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3), all with a Maxwell term. The Hamiltonian formalismmore » is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P{sub M};Q,P{sub Q}), where M is the mass parameter, which for {omega}<-(3/2) and for {omega}={+-}{infinity} needs a careful renormalization, P{sub M} is the conjugate momenta of M, Q is the charge parameter, and P{sub Q} is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field {phi}. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.« less

Hamiltonian analysis of curvature-squared gravity with or without conformal invariance

NASA Astrophysics Data System (ADS)

KlusoÅ, Josef; Oksanen, Markku; Tureanu, Anca

2014-03-01

We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable—a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a three-dimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological, since a constraint required by the Hamiltonian analysis imposes the determinant of the metric of spacetime to be zero. In order to resolve this problem by restoring the conformal invariance, we introduce a new scalar field that couples to the curvature of spacetime, reminiscent of the introduction of vector fields for ensuring the gauge invariance.

Non-perturbative RPA-method implemented in the Coulomb gauge QCD Hamiltonian: From quarks and gluons to baryons and mesons

NASA Astrophysics Data System (ADS)

Yepez-Martinez, Tochtli; Civitarese, Osvaldo; Hess, Peter O.

2018-02-01

Starting from an algebraic model based on the QCD-Hamiltonian and previously applied to study meson states, we have developed an extension of it in order to explore the structure of baryon states. In developing our approach we have adapted concepts taken from group theory and non-perturbative many-body methods to describe states built from effective quarks and anti-quarks degrees of freedom. As a Hamiltonian we have used the QCD Hamiltonian written in the Coulomb Gauge, and expressed it in terms of effective quark-antiquark, di-quarks and di-antiquark excitations. To gain some insights about the relevant interactions of quarks in hadronic states, the Hamiltonian was approximately diagonalized by mapping quark-antiquark pairs and di-quarks (di-antiquarks) onto phonon states. In dealing with the structure of the vacuum of the theory, color-scalar and color-vector states are introduced to account for ground-state correlations. While the use of a purely color-scalar ground state is an obvious choice, so that colorless hadrons contain at least three quarks, the presence of coupled color-vector pairs in the ground state allows for colorless excitations resulting from the action of color objects upon it.

Artificial magnetic-field quenches in synthetic dimensions

NASA Astrophysics Data System (ADS)

Yılmaz, F.; Oktel, M. Ö.

2018-02-01

Recent cold atom experiments have realized models where each hyperfine state at an optical lattice site can be regarded as a separate site in a synthetic dimension. In such synthetic ribbon configurations, manipulation of the transitions between the hyperfine levels provide direct control of the hopping in the synthetic dimension. This effect was used to simulate a magnetic field through the ribbon. Precise control over the hopping matrix elements in the synthetic dimension makes it possible to change this artificial magnetic field much faster than the time scales associated with atomic motion in the lattice. In this paper, we consider such a magnetic-flux quench scenario in synthetic dimensions. Sudden changes have not been considered for real magnetic fields as such changes in a conducting system would result in large induced currents. Hence we first study the difference between a time varying real magnetic field and an artificial magnetic field using a minimal six-site model. This minimal model clearly shows the connection between gauge dependence and the lack of on-site induced scalar potential terms. We then investigate the dynamics of a wave packet in an infinite two- or three-leg ladder following a flux quench and find that the gauge choice has a dramatic effect on the packet dynamics. Specifically, a wave packet splits into a number of smaller packets moving with different velocities. Both the weights and the number of packets depend on the implemented gauge. If an initial packet, prepared under zero flux in an n -leg ladder, is quenched to Hamiltonian with a vector potential parallel to the ladder, it splits into at most n smaller wave packets. The same initial wave packet splits into up to n2 packets if the vector potential is implemented to be along the rungs. Even a trivial difference in the gauge choice such as the addition of a constant to the vector potential produces observable effects. We also calculate the packet weights for arbitrary initial and final fluxes. Finally, we show that edge states in a thick ribbon are robust under the quench only when the same gap supports an edge state for the final Hamiltonian.

A Few Discrete Lattice Systems and Their Hamiltonian Structures, Conservation Laws

NASA Astrophysics Data System (ADS)

Guo, Xiu-Rong; Zhang, Yu-Feng; Zhang, Xiang-Zhi; Yue, Rong

2017-04-01

With the help of three shift operators and r-matrix theory, a few discrete lattice systems are obtained which can be reduced to the well-known Toda lattice equation with a constraint whose Hamiltonian structures are generated by Poisson tensors of some induced Lie-Poisson bracket. The recursion operators of these lattice systems are constructed starting from Lax representations. Finally, reducing the given shift operators to get a simpler one and its expanding shift operators, we produce a lattice system with three vector fields whose recursion operator is given. Furthermore, we reduce the lattice system with three vector fields to get a lattice system whose Lax pair and conservation laws are obtained, respectively. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province Hosted by China University of Mining and Technology (2014), the the Key Discipline Construction by China University of Mining and Technology under Grant No. XZD201602, the Shandong Provincial Natural Science Foundation, China under Grant Nos. ZR2016AM31, ZR2016AQ19, ZR2015EM042, the Development of Science and Technology Plan Projects of TaiAn City under Grant No. 2015NS1048, National Social Science Foundation of China under Grant No. 13BJY026, and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58

Hamiltonian structure of real Monge - Ampère equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-06-01

The variational principle for the real homogeneous Monge - Ampère equation in two dimensions is shown to contain three arbitrary functions of four variables. There exist two different specializations of this variational principle where the Lagrangian is degenerate and furthermore contains an arbitrary function of two variables. The Hamiltonian formulation of these degenerate Lagrangian systems requires the use of Dirac's theory of constraints. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. Thus the real homogeneous Monge - Ampère equation in two dimensions admits two classes of infinitely many Hamiltonian operators, namely a family of local, as well as another family non-local Hamiltonian operators and symplectic 2-forms which depend on arbitrary functions of two variables. The simplest non-local Hamiltonian operator corresponds to the Kac - Moody algebra of vector fields and functions on the unit circle. Hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair. In the case of real Monge - Ampère equations with constant right-hand side this compatible pair is the only pair of Hamiltonian operators that survives. Then the complete integrability of all these real Monge - Ampère equations follows by Magri's theorem. Some of the remarkable properties we have obtained for the Hamiltonian structure of the real homogeneous Monge - Ampère equation in two dimensions turn out to be generic to the real homogeneous Monge - Ampère equation and the geodesic flow for the complex homogeneous Monge - Ampère equation in arbitrary number of dimensions. Hence among all integrable nonlinear evolution equations in one space and one time dimension, the real homogeneous Monge - Ampère equation is distinguished as one that retains its character as an integrable system in multiple dimensions.

Quantum and electromagnetic propagation with the conjugate symmetric Lanczos method.

PubMed

Acevedo, Ramiro; Lombardini, Richard; Turner, Matthew A; Kinsey, James L; Johnson, Bruce R

2008-02-14

The conjugate symmetric Lanczos (CSL) method is introduced for the solution of the time-dependent Schrodinger equation. This remarkably simple and efficient time-domain algorithm is a low-order polynomial expansion of the quantum propagator for time-independent Hamiltonians and derives from the time-reversal symmetry of the Schrodinger equation. The CSL algorithm gives forward solutions by simply complex conjugating backward polynomial expansion coefficients. Interestingly, the expansion coefficients are the same for each uniform time step, a fact that is only spoiled by basis incompleteness and finite precision. This is true for the Krylov basis and, with further investigation, is also found to be true for the Lanczos basis, important for efficient orthogonal projection-based algorithms. The CSL method errors roughly track those of the short iterative Lanczos method while requiring fewer matrix-vector products than the Chebyshev method. With the CSL method, only a few vectors need to be stored at a time, there is no need to estimate the Hamiltonian spectral range, and only matrix-vector and vector-vector products are required. Applications using localized wavelet bases are made to harmonic oscillator and anharmonic Morse oscillator systems as well as electrodynamic pulse propagation using the Hamiltonian form of Maxwell's equations. For gold with a Drude dielectric function, the latter is non-Hermitian, requiring consideration of corrections to the CSL algorithm.

Stability of holographic superconductors

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

Kanno, Sugumi; Soda, Jiro

We study the dynamical stability of holographic superconductors. We first classify perturbations around black hole background solutions into vector and scalar sectors by means of a 2-dimensional rotational symmetry. We prove the stability of the vector sector by explicitly constructing the positive definite Hamiltonian. To reveal a mechanism for the stabilization of a superconducting phase, we construct a quadratic action for the scalar sector. From the action, we see the stability of black holes near a critical point is determined by the equation of motion for a charged scalar field. We show the effective mass of the charged scalar fieldmore » in hairy black holes is always above the Breitenlohner-Freedman bound near the critical point due to the backreaction of a gauge field. It implies the stability of the superconducting phase. We also argue that the stability continues away from the critical point.« less

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.

Dynamics of Vortex and Magnetic Lines in Ideal Hydrodynamics and MHD

NASA Astrophysics Data System (ADS)

Kuznetsov, E. A.; Ruban, V. P.

Vortex line and magnetic line representations are introduced for description of flows in ideal hydrodynamics and MHD, respectively. For incompressible fluids it is shown that the equations of motion for vorticity φ and magnetic field with the help of this transformation follow from the variational principle. By means of this representation it is possible to integrate the system of hydrodynamic type with the Hamiltonian H=|φ|dr. It is also demonstrated that these representations allow to remove from the noncanonical Poisson brackets, defined on the space of divergence-free vector fields, degeneracy connected with the vorticity frozenness for the Euler equation and with magnetic field frozenness for ideal MHD. For MHD a new Weber type transformation is found. It is shown how this transformation can be obtained from the two-fluid model when electrons and ions can be considered as two independent fluids. The Weber type transformation for ideal MHD gives the whole Lagrangian vector invariant. When this invariant is absent this transformation coincides with the Clebsch representation analog introduced in [1].

Non-linear non-local molecular electrodynamics with nano-optical fields.

PubMed

Chernyak, Vladimir Y; Saurabh, Prasoon; Mukamel, Shaul

2015-10-28

The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields may vary appreciably across the molecular length scale. Rather than incrementally adding higher multipoles, it is advantageous and more physically transparent to describe the optical process using non-local response functions that intrinsically include all multipoles. We present a semi-classical approach for calculating non-local response functions based on the minimal coupling Hamiltonian. The first, second, and third order response functions are expressed in terms of correlation functions of the charge and the current densities. This approach is based on the gauge invariant current rather than the polarization, and on the vector potential rather than the electric and magnetic fields.

Quantum theory of electromagnetic fields in a cosmological quantum spacetime

NASA Astrophysics Data System (ADS)

Lewandowski, Jerzy; Nouri-Zonoz, Mohammad; Parvizi, Ali; Tavakoli, Yaser

2017-11-01

The theory of quantum fields propagating on an isotropic cosmological quantum spacetime is reexamined by generalizing the scalar test field to an electromagnetic (EM) vector field. For any given polarization of the EM field on the classical background, the Hamiltonian can be written in the form of the Hamiltonian of a set of decoupled harmonic oscillators, each corresponding to a single mode of the field. In transition from the classical to quantum spacetime background, following the technical procedure given by Ashtekar et al. [Phys. Rev. D 79, 064030 (2009), 10.1103/PhysRevD.79.064030], a quantum theory of the test EM field on an effective (dressed) spacetime emerges. The nature of this emerging dressed geometry is independent of the chosen polarization, but it may depend on the energy of the corresponding field mode. Specifically, when the backreaction of the field on the quantum geometry is negligible (i.e., a test field approximation is assumed), all field modes probe the same effective background independent of the mode's energy. However, when the backreaction of the field modes on the quantum geometry is significant, by employing a Born-Oppenheimer approximation, it is shown that a rainbow (i.e., a mode-dependent) metric emerges. The emergence of this mode-dependent background in the Planck regime may have a significant effect on the creation of quantum particles. The production amount on the dressed background is computed and is compared with the familiar results on the classical geometry.

Spectral Deformation for Two-Body Dispersive Systems with e.g. the Yukawa Potential

NASA Astrophysics Data System (ADS)

Engelmann, Matthias; Rasmussen, Morten Grud

2016-12-01

We find an explicit closed formula for the k'th iterated commutator {{ad}Ak}(HV(ξ )) of arbitrary order k ⩾ 1 between a Hamiltonian HV(ξ )=M_{ω _{ξ }}+S_{\\check V} and a conjugate operator A={i}/2(v_{ξ}\\cdotnabla+nabla\\cdot v_{ξ}), where M_{ω _{ξ }} is the operator of multiplication with the real analytic function ω ξ which depends real analytically on the parameter ξ, and the operator S_{\\check V} is the operator of convolution with the (sufficiently nice) function \\check V, and v ξ is some vector field determined by ω ξ . Under certain assumptions, which are satisfied for the Yukawa potential, we then prove estimates of the form {{{ad}Ak}(HV(ξ ))(H0(ξ )+{i} )}|≤ C_{ξ }kk! where C ξ is some constant which depends continuously on ξ. The Hamiltonian is the fixed total momentum fiber Hamiltonian of an abstract two-body dispersive system and the work is inspired by a recent result [3] which, under conditions including estimates of the mentioned type, opens up for spectral deformation and analytic perturbation theory of embedded eigenvalues of finite multiplicity.

Gyrokinetic equations and full f solution method based on Dirac's constrained Hamiltonian and inverse Kruskal iteration

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

Heikkinen, J. A.; Nora, M.

2011-02-15

Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J= as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allowsmore » direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.« less

Complete Hamiltonian analysis of cosmological perturbations at all orders II: non-canonical scalar field

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

Nandi, Debottam; Shankaranarayanan, S., E-mail: debottam@iisertvm.ac.in, E-mail: shanki@iisertvm.ac.in

2016-10-01

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [1] to non-canonical scalar field and obtain an unique expression of speed of sound in terms of phase-space variable. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that ourmore » approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.« less

Rényi entropy, stationarity, and entanglement of the conformal scalar

NASA Astrophysics Data System (ADS)

Lee, Jeongseog; Lewkowycz, Aitor; Perlmutter, Eric; Safdi, Benjamin R.

2015-03-01

We extend previous work on the perturbative expansion of the Rényi entropy, S q , around q = 1 for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Rényi entropies. On the other hand, the perturbative results agree with known Rényi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. We propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total-derivative terms in the definition of the modular Hamiltonian. As a corollary, we are able to resolve an outstanding puzzle in the literature regarding the Rényi entropy of super-Yang-Mills near q = 1. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. We point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity. Moreover, IR divergences appear in perturbation theory about the massless fixed point that inhibit our ability to reliably calculate the REE at small non-zero mass.

Analysis of recurrent patterns in toroidal magnetic fields.

PubMed

Sanderson, Allen R; Chen, Guoning; Tricoche, Xavier; Pugmire, David; Kruger, Scott; Breslau, Joshua

2010-01-01

In the development of magnetic confinement fusion which will potentially be a future source for low cost power, physicists must be able to analyze the magnetic field that confines the burning plasma. While the magnetic field can be described as a vector field, traditional techniques for analyzing the field's topology cannot be used because of its Hamiltonian nature. In this paper we describe a technique developed as a collaboration between physicists and computer scientists that determines the topology of a toroidal magnetic field using fieldlines with near minimal lengths. More specifically, we analyze the Poincaré map of the sampled fieldlines in a Poincaré section including identifying critical points and other topological features of interest to physicists. The technique has been deployed into an interactive parallel visualization tool which physicists are using to gain new insight into simulations of magnetically confined burning plasmas.

Beyond generalized Proca theories

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

2016-09-01

We consider higher-order derivative interactions beyond second-order generalized Proca theories that propagate only the three desired polarizations of a massive vector field besides the two tensor polarizations from gravity. These new interactions follow the similar construction criteria to those arising in the extension of scalar-tensor Horndeski theories to Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories. On the isotropic cosmological background, we show the existence of a constraint with a vanishing Hamiltonian that removes the would-be Ostrogradski ghost. We study the behavior of linear perturbations on top of the isotropic cosmological background in the presence of a matter perfect fluid and find the same number of propagating degrees of freedom as in generalized Proca theories (two tensor polarizations, two transverse vector modes, and two scalar modes). Moreover, we obtain the conditions for the avoidance of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations. We observe key differences in the scalar sound speed, which is mixed with the matter sound speed outside the domain of generalized Proca theories.

A Hamiltonian approach to the planar optimization of mid-course corrections

NASA Astrophysics Data System (ADS)

Iorfida, E.; Palmer, P. L.; Roberts, M.

2016-04-01

Lawden's primer vector theory gives a set of necessary conditions that characterize the optimality of a transfer orbit, defined accordingly to the possibility of adding mid-course corrections. In this paper a novel approach is proposed where, through a polar coordinates transformation, the primer vector components decouple. Furthermore, the case when transfer, departure and arrival orbits are coplanar is analyzed using a Hamiltonian approach. This procedure leads to approximate analytic solutions for the in-plane components of the primer vector. Moreover, the solution for the circular transfer case is proven to be the Hill's solution. The novel procedure reduces the mathematical and computational complexity of the original case study. It is shown that the primer vector is independent of the semi-major axis of the transfer orbit. The case with a fixed transfer trajectory and variable initial and final thrust impulses is studied. The acquired related optimality maps are presented and analyzed and they express the likelihood of a set of trajectories to be optimal. Furthermore, it is presented which kind of requirements have to be fulfilled by a set of departure and arrival orbits to have the same profile of primer vector.

Eigenfunction Expansions and Lippmann-Schwinger Formulas

NASA Astrophysics Data System (ADS)

Gadella, M.; Kielanowski, P.

2011-12-01

In this paper we discuss in the mathematically precise way the definition of a resonance, that requires two Hamiltonians (free and perturbed), the notion of Gamow vectors, Lippmann-Schwinger equations and the analytic properties of their solutions in the context of the Gamow vectors. Next we discuss the eigenfunction expansions in the presence of resonances. In the case of the Friedrichs model, the precise form of these generalized eigenfunctions has been given in the literature. Although there are two families of eigenfunction expansions which are related through the time reversal operator, free and perturbed Hamiltonians are time invariant. On the other hand, PT symmetries play no role in this discussion. Our discussion clarifies the results of the paper [1], which contains imprecise or even wrong statements.

Adsorption of asymmetric rigid rods or heteronuclear diatomic moleculeson homogeneous surfaces

NASA Astrophysics Data System (ADS)

Engl, W.; Courbin, L.; Panizza, P.

2004-10-01

We treat the adsorption on homogeneous surfaces of asymmetric rigid rods (like for instance heteronuclear diatomic molecules). We show that the n→0 vector spin formalism is well suited to describe such a problem. We establish an isomorphism between the coupling constants of the magnetic Hamiltonian and the adsorption parameters of the rigid rods. By solving this Hamiltonian within a mean-field approximation, we obtain analytical expressions for the densities of the different rod’s configurations, both isotherm and isobar adsorptions curves. The most probable configurations of the molecules (normal or parallel to the surface) which depends on temperature and energy parameters are summarized in a diagram. We derive that the variation of Qv , the heat of adsorption at constant volume, with the temperature is a direct signature of the adsorbed molecules configuration change. We show that this formalism can be generalized to more complicated problems such as for instance the adsorption of symmetric and asymmetric rigid rods mixtures in the presence or not of interactions.

Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański

NASA Astrophysics Data System (ADS)

Sheftel, Mikhail; Yazıcı, Devrim

2016-09-01

We present first heavenly equation of Plebański in a two-component evolutionary form and obtain Lagrangian and Hamiltonian representations of this system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We derive two linearly independent recursion operators for symmetries of this system related by a discrete symmetry of both the two-component system and its symmetry condition. Acting by these operators on the first Hamiltonian operator J_0 we obtain second and third Hamiltonian operators. However, we were not able to find Hamiltonian densities corresponding to the latter two operators. Therefore, we construct two recursion operators, which are either even or odd, respectively, under the above-mentioned discrete symmetry. Acting with them on J_0, we generate another two Hamiltonian operators J_+ and J_- and find the corresponding Hamiltonian densities, thus obtaining second and third Hamiltonian representations for the first heavenly equation in a two-component form. Using P. Olver's theory of the functional multi-vectors, we check that the linear combination of J_0, J_+ and J_- with arbitrary constant coefficients satisfies Jacobi identities. Since their skew symmetry is obvious, these three operators are compatible Hamiltonian operators and hence we obtain a tri-Hamiltonian representation of the first heavenly equation. Our well-founded conjecture applied here is that P. Olver's method works fine for nonlocal operators and our proof of the Jacobi identities and bi-Hamiltonian structures crucially depends on the validity of this conjecture.

Quantized Vector Potential and the Photon Wave-function

NASA Astrophysics Data System (ADS)

Meis, C.; Dahoo, P. R.

2017-12-01

The vector potential function {\\overrightarrow{α }}kλ (\\overrightarrow{r},t) for a k-mode and λ-polarization photon, with the quantized amplitude α 0k (ω k ) = ξω k , satisfies the classical wave propagation equation as well as the Schrodinger’s equation with the relativistic massless Hamiltonian \\mathop{H}\\limits∼ =-i\\hslash c\\overrightarrow{\

Bi-Hamiltonian Structure in 2-d Field Theory

NASA Astrophysics Data System (ADS)

Ferapontov, E. V.; Galvão, C. A. P.; Mokhov, O. I.; Nutku, Y.

We exhibit the bi-Hamiltonian structure of the equations of associativity (Witten-Dijkgraaf-Verlinde-Verlinde-Dubrovin equations) in 2-d topological field theory, which reduce to a single equation of Monge-Ampère type $ fttt}=f{xxt;;;;;2 - fxxx}f{xtt ,$ in the case of three primary fields. The first Hamiltonian structure of this equation is based on its representation as a 3-component system of hydrodynamic type and the second Hamiltonian structure follows from its formulation in terms of a variational principle with a degenerate Lagrangian.

Measurement of the β-asymmetry parameter of Cu67 in search for tensor-type currents in the weak interaction

NASA Astrophysics Data System (ADS)

Soti, G.; Wauters, F.; Breitenfeldt, M.; Finlay, P.; Herzog, P.; Knecht, A.; Köster, U.; Kraev, I. S.; Porobic, T.; Prashanth, P. N.; Towner, I. S.; Tramm, C.; Zákoucký, D.; Severijns, N.

2014-09-01

Background: Precision measurements at low energy search for physics beyond the standard model in a way complementary to searches for new particles at colliders. In the weak sector the most general β-decay Hamiltonian contains, besides vector and axial-vector terms, also scalar, tensor, and pseudoscalar terms. Current limits on the scalar and tensor coupling constants from neutron and nuclear β decay are on the level of several percent. Purpose: Extracting new information on tensor coupling constants by measuring the β-asymmetry parameter in the pure Gamow-Teller decay of Cu67, thereby testing the V-A structure of the weak interaction. Method: An iron sample foil into which the radioactive nuclei were implanted was cooled down to mK temperatures in a 3He-4He dilution refrigerator. An external magnetic field of 0.1 T, in combination with the internal hyperfine magnetic field, oriented the nuclei. The anisotropic β radiation was observed with planar high-purity germanium detectors operating at a temperature of about 10 K. An on-line measurement of the β asymmetry of Cu68 was performed as well for normalization purposes. Systematic effects were investigated using geant4 simulations. Results: The experimental value, Ã=0.587(14), is in agreement with the standard model value of 0.5991(2) and is interpreted in terms of physics beyond the standard model. The limits obtained on possible tensor-type charged currents in the weak interaction Hamiltonian are -0.045<(CT+CT')/CA<0.159 (90% C.L.). Conclusions: The obtained limits are comparable to limits from other correlation measurements in nuclear β decay and contribute to further constraining tensor coupling constants.

Waves on the Free Surface Described by Linearized Equations of Hydrodynamics with Localized Right-Hand Sides

NASA Astrophysics Data System (ADS)

Dobrokhotov, S. Yu.; Nazaikinskii, V. E.

2018-01-01

A linearized system of equations of hydrodynamics with time-dependent spatially localized right-hand side placed both on the free surface (and on the bottom of the basin) and also in the layer of the liquid is considered in a layer of variable depth with a given basic plane-parallel flow. A method of constructing asymptotic solutions of this problem is suggested; it consists of two stages: (1) a reduction of the three-dimensional problem to a two-dimensional inhomogeneous pseudodifferential equation on the nonperturbed free surface of the liquid, (2) a representation of the localized right-hand side in the form of a Maslov canonical operator on a special Lagrangian manifold and the subsequent application of a generalization to evolution problems of an approach, which was recently suggested in the paper [A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, and M. Rouleux, Dokl. Ross. Akad. Nauk 475 (6), 624-628 (2017); Engl. transl.: Dokl. Math. 96 (1), 406-410 (2017)], to solving stationary problems with localized right-hand sides and its combination with "nonstandard" characteristics. A method of calculation (generalizing long-standing results of Dobrokhotov and Zhevandrov) of an analog of the Kelvin wedge and the wave fields inside the wedge and in its neighborhood is suggested, which uses the consideration that this method is the projection to the extended configuration space of a Lagrangian manifold formed by the trajectories of the Hamiltonian vector field issuing from the intersection of the set of zeros of the extended Hamiltonian of the problem with conormal bundle to the graph of the vector function defining the trajectory of motion of an equivalent source on the surface of the liquid.

A quantum dot close to Stoner instability: The role of the Berry phase

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

Saha, Arijit, E-mail: arijitsahahri@gmail.com; Gefen, Yuval; Burmistrov, Igor

2012-10-15

The physics of a quantum dot with electron-electron interactions is well captured by the so called 'Universal Hamiltonian' if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are represented by three spatially independent terms which describe the charging energy, the spin-exchange and the interaction in the Cooper channel. In this paper we concentrate on the exchange interaction and generalize the functional bosonization formalism developed earlier for the charging energy. This turned out to be challenging as the effective bosonic action is formulated in terms of a vector field and is non-abelian due tomore » the non-commutativity of the spin operators. Here we develop a geometric approach which is particularly useful in the mesoscopic Stoner regime, i.e., when the strong exchange interaction renders the system close to the Stoner instability. We show that it is sufficient to sum over the adiabatic paths of the bosonic vector field and, for these paths, the crucial role is played by the Berry phase. Using these results we were able to calculate the magnetic susceptibility of the dot. The latter, in close vicinity of the Stoner instability point, matches very well with the exact solution [I.S. Burmistrov, Y. Gefen, M.N. Kiselev, JETP Lett. 92 (2010) 179]. - Highlights: Black-Right-Pointing-Pointer We consider a conducting QD whose dynamics is governed by exchange interaction. Black-Right-Pointing-Pointer We study the model within the 'Universal Hamiltonian' framework. Black-Right-Pointing-Pointer The ensuing bosonic action is non-abelian (hence non-trivial). Black-Right-Pointing-Pointer We find that the low energy dynamics is governed by a fluctuating Berry phase term. Black-Right-Pointing-Pointer We calculate the partition function and the zero frequency magnetic susceptibility.« less

Eisenhart lifts and symmetries of time-dependent systems

NASA Astrophysics Data System (ADS)

Cariglia, M.; Duval, C.; Gibbons, G. W.; Horváthy, P. A.

2016-10-01

Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with n degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in n + 2 dimensions, equipped with its covariantly constant null Killing vector field. Reparametrisation of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schrödinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaître and Bianchi cosmologies and how it fits in with our previous discussion in the non-relativistic limit.

The Lagrangian-Hamiltonian formalism for higher order field theories

NASA Astrophysics Data System (ADS)

Vitagliano, Luca

2010-06-01

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.

PubMed

Pang, Shengshi; Jordan, Andrew N

2017-03-09

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T 2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T 4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

PubMed Central

Pang, Shengshi; Jordan, Andrew N.

2017-01-01

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case. PMID:28276428

Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

NASA Astrophysics Data System (ADS)

Risser, Steven Michael

This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb interactions in the Huckel Hamiltonian results in calculated hyperpolarizabilities that are much larger than the experimentally determined values. Comparison of hyperpolarizabilities calculated for small benzene derivatives using both the Huckel and PPP Hamiltonians shows that inclusion of explicit Coulomb interactions is not as significant for aromatic molecules. This assertion is supported by comparison of the calculated results to the experimentally determined values. This allows for predictions of the hyperpolarizability of various liquid crystal molecules to be made.

Illustrating dynamical symmetries in classical mechanics: The Laplace-Runge-Lenz vector revisited

NASA Astrophysics Data System (ADS)

O'Connell, Ross C.; Jagannathan, Kannan

2003-03-01

The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and degeneracy associated with this vector and with analogous dynamical symmetries. We define a conserved dynamical variable α that characterizes the orientation of the orbit in two-dimensional configuration space for the Kepler problem and an analogous variable β for the isotropic harmonic oscillator. This orbit orientation variable is canonically conjugate to the angular momentum component normal to the plane of motion. We explore the canonical one-parameter group of transformations generated by α(β). Because we have an obvious pair of conserved canonically conjugate variables, it is desirable to use them as a coordinate-momentum pair. In terms of these phase space coordinates, the form of the Hamiltonian is nearly trivial because neither member of the pair can occur explicitly in the Hamiltonian. From these considerations we gain a simple picture of dynamics in phase space. The procedure we use is in the spirit of the Hamilton-Jacobi method.

Hamiltonian structure of Dubrovin's equation of associativity in 2-d topological field theory

NASA Astrophysics Data System (ADS)

Galvão, C. A. P.; Nutku, Y.

1996-12-01

A third order Monge-Ampère type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac's theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra.

Conservation laws and evolution schemes in geodesic, hydrodynamic, and magnetohydrodynamic flows

NASA Astrophysics Data System (ADS)

Markakis, Charalampos; Uryū, Kōji; Gourgoulhon, Eric; Nicolas, Jean-Philippe; Andersson, Nils; Pouri, Athina; Witzany, Vojtěch

2017-09-01

Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton's principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. In this framework, Ertel's potential vorticity theorem for baroclinic fluids arises as a special case of a conservation law valid for any Hamiltonian system. Moreover, conserved circulation laws, such as those of Kelvin, Alfvén and Bekenstein-Oron, emerge simply as special cases of the Poincaré-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin's theorem to baroclinic (nonisentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space.

Spherical type integrable classical systems in a magnetic field

NASA Astrophysics Data System (ADS)

Marchesiello, A.; Šnobl, L.; Winternitz, P.

2018-04-01

We show that four classes of second order spherical type integrable classical systems in a magnetic field exist in the Euclidean space {E}3 , and construct the Hamiltonian and two second order integrals of motion in involution for each of them. For one of the classes the Hamiltonian depends on four arbitrary functions of one variable. This class contains the magnetic monopole as a special case. Two further classes have Hamiltonians depending on one arbitrary function of one variable and four or six constants, respectively. The magnetic field in these cases is radial. The remaining system corresponds to a constant magnetic field and the Hamiltonian depends on two constants. Questions of superintegrability—i.e. the existence of further integrals—are discussed.

Hamiltonian description of closed configurations of the vacuum magnetic field

NASA Astrophysics Data System (ADS)

Skovoroda, A. A.

2015-05-01

Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov'ev, and V.D. Shafranov.

First-order dipolar phase transition in the Dicke model with infinitely coordinated frustrating interaction

NASA Astrophysics Data System (ADS)

Mukhin, S. I.; Gnezdilov, N. V.

2018-05-01

We found analytically a first-order quantum phase transition in a Cooper pair box array of N low-capacitance Josephson junctions capacitively coupled to resonant photons in a microwave cavity. The Hamiltonian of the system maps on the extended Dicke Hamiltonian of N spins 1 /2 with infinitely coordinated antiferromagnetic (frustrating) interaction. This interaction arises from the gauge-invariant coupling of the Josephson-junction phases to the vector potential of the resonant photons field. In the N ≫1 semiclassical limit, we found a critical coupling at which the ground state of the system switches to one with a net collective electric dipole moment of the Cooper pair boxes coupled to a super-radiant equilibrium photonic condensate. This phase transition changes from the first to second order if the frustrating interaction is switched off. A self-consistently "rotating" Holstein-Primakoff representation for the Cartesian components of the total superspin is proposed, that enables one to trace both the first- and the second-order quantum phase transitions in the extended and standard Dicke models, respectively.

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

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

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra ismore » later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a rotating quadrupole field ion trap are presented. •Exact solutions for magneto-transport in variable electromagnetic fields are shown.« less

Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling

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

Damour, Thibault; Jaranowski, Piotr; Schaefer, Gerhard

2008-07-15

Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the effective one body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the 'effective' Hamiltonian and the 'real' one; (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta; (iii) a Kerr-type effective metric (with Pade-resummed coefficients) which depends on the choice of some basic 'effective spin vector' S{sub eff}, and which is deformed by comparable-mass effects; and (iv)more » an additional effective spin-orbit interaction term involving another spin vector {sigma}. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter a{sub LSO}{identical_to}cJ{sub LSO}/(G(H{sub LSO}/c{sup 2}){sup 2}). We find that the inclusion of NLO spin-orbit terms has a significant 'moderating' effect on the dynamical characteristics of the circular orbits for large and parallel spins.« less

Capillary wave theory of adsorbed liquid films and the structure of the liquid-vapor interface

NASA Astrophysics Data System (ADS)

MacDowell, Luis G.

2017-08-01

In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of the capillary wave spectrum obtained recently in computer simulations, and the predicted translation mode of surface fluctuations reproduces to linear order in field strength an exact solution of the density correlation function for the Landau-Ginzburg-Wilson Hamiltonian in an external field.

The quantization of the chiral Schwinger model based on the BFT - BFV formalism

NASA Astrophysics Data System (ADS)

Kim, Won T.; Kim, Yong-Wan; Park, Mu-In; Park, Young-Jai; Yoon, Sean J.

1997-03-01

We apply the newly improved Batalin - Fradkin - Tyutin (BFT) Hamiltonian method to the chiral Schwinger model in the case of the regularization ambiguity a>1. We show that one can systematically construct the first class constraints by the BFT Hamiltonian method, and also show that the well-known Dirac brackets of the original phase space variables are exactly the Poisson brackets of the corresponding modified fields in the extended phase space. Furthermore, we show that the first class Hamiltonian is simply obtained by replacing the original fields in the canonical Hamiltonian by these modified fields. Performing the momentum integrations, we obtain the corresponding first class Lagrangian in the configuration space.

Cauchy problem as a two-surface based ‘geometrodynamics’

NASA Astrophysics Data System (ADS)

Rácz, István

2015-01-01

Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1 + (1 + 2) decomposition, the canonical form of the spacetime metric and a suitable specification of the conformal structure of the foliating two-surfaces, a gauge fixing is introduced. It is shown that, in terms of the chosen geometrically distinguished variables, the 1 + 3 Hamiltonian and momentum constraints can be recast into the form of a parabolic equation and a first order symmetric hyperbolic system, respectively. Initial data to this system can be given on one of the two-surfaces foliating the three-dimensional initial data surface. The 1 + 3 reduced Einstein's equations are also determined. By combining the 1 + 3 momentum constraint with the reduced system of the secondary 1 + 2 decomposition, a mixed hyperbolic-hyperbolic system is formed. It is shown that solutions to this mixed hyperbolic-hyperbolic system are also solutions to the full set of Einstein's equations provided that the 1 + 3 Hamiltonian constraint is solved on the initial data surface {{Σ }0} and the 1 + 2 Hamiltonian and momentum type expressions vanish on a world-tube yielded by the Lie transport of one of the two-surfaces foliating {{Σ }0} along the time evolution vector field. Whenever the foliating two-surfaces are compact without boundary in the spacetime and a regular origin exists on the time-slices—this is the location where the foliating two-surfaces smoothly reduce to a point—it suffices to guarantee that the 1 + 3 Hamiltonian constraint holds on the initial data surface. A short discussion on the use of the geometrically distinguished variables in identifying the degrees of freedom of gravity are also included. Dedicated to Zoltán Cseke on the occasion of his 70th birthday.

Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

NASA Astrophysics Data System (ADS)

Weinstein, Marvin; Chandra, Ravi; Auerbach, Assa

2012-02-01

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements. In contrast to variational approaches and most implementations of DMRG, Lanczos rotations towards the ground state do not involve incremental minimizations, (e.g. sweeping procedures) which may get stuck in false local minima. The lattice of size N is partitioned into two subclusters. At each iteration the rotating Lanczos vector is compressed into two sets of nsvd small subcluster vectors using singular value decomposition. For low entanglement entropy See, (satisfied by short range Hamiltonians), the truncation error is bounded by (-nsvd^1/See). Convergence is tested for the Heisenberg model on Kagom'e clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given. Reference: arXiv:1105.0007

Systems of conservation laws with third-order Hamiltonian structures

NASA Astrophysics Data System (ADS)

Ferapontov, Evgeny V.; Pavlov, Maxim V.; Vitolo, Raffaele F.

2018-06-01

We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in P^{n+2} satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension n+2, classify n-tuples of skew-symmetric 2-forms A^{α } \\in Λ^2(W) such that φ _{β γ }A^{β }\\wedge A^{γ }=0, for some non-degenerate symmetric φ.

Symmetry and Circularization in the Damped Kepler Problem

NASA Astrophysics Data System (ADS)

Crescimanno, Michael; Hamilton, Brian

2007-05-01

Generically, a Hamiltonian system to which damping (non-Hamiltonian) forces are added loses its symmetry. It is a non-trivial fact that the eccentricity vector of lightly damped Kepler orbits is a constant for linear damping only. We describe the group theoretic background necessary to understand this fact and to relate it to that analogue of the Landau criterion for superfluidity associated with the general problem of orbit circularization. To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2007.OSS07.C2.4

Quasiperiodicity in time evolution of the Bloch vector under the thermal Jaynes-Cummings model

NASA Astrophysics Data System (ADS)

Azuma, Hiroo; Ban, Masashi

2014-07-01

We study a quasiperiodic structure in the time evolution of the Bloch vector, whose dynamics is governed by the thermal Jaynes-Cummings model (JCM). Putting the two-level atom into a certain pure state and the cavity field into a mixed state in thermal equilibrium at initial time, we let the whole system evolve according to the JCM Hamiltonian. During this time evolution, motion of the Bloch vector seems to be in disorder. Because of the thermal photon distribution, both a norm and a direction of the Bloch vector change hard at random. In this paper, taking a different viewpoint compared with ones that we have been used to, we investigate quasiperiodicity of the Bloch vector’s trajectories. Introducing the concept of the quasiperiodic motion, we can explain the confused behaviour of the system as an intermediate state between periodic and chaotic motions. More specifically, we discuss the following two facts: (1) If we adjust the time interval Δt properly, figures consisting of plotted dots at the constant time interval acquire scale invariance under replacement of Δt by sΔt, where s(>1) is an arbitrary real but not transcendental number. (2) We can compute values of the time variable t, which let |Sz(t)| (the absolute value of the z-component of the Bloch vector) be very small, with the Diophantine approximation (a rational approximation of an irrational number).

Quantum Finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2007-09-01

Foreword; Preface; Acknowledgements; 1. Synopsis; Part I. Fundamental Concepts of Finance: 2. Introduction to finance; 3. Derivative securities; Part II. Systems with Finite Number of Degrees of Freedom: 4. Hamiltonians and stock options; 5. Path integrals and stock options; 6. Stochastic interest rates' Hamiltonians and path integrals; Part III. Quantum Field Theory of Interest Rates Models: 7. Quantum field theory of forward interest rates; 8. Empirical forward interest rates and field theory models; 9. Field theory of Treasury Bonds' derivatives and hedging; 10. Field theory Hamiltonian of forward interest rates; 11. Conclusions; Appendix A: mathematical background; Brief glossary of financial terms; Brief glossary of physics terms; List of main symbols; References; Index.

RPA treatment of a motivated QCD Hamiltonian in the SO(4) (2 + 1)-flavor limit: Light and strange mesons

NASA Astrophysics Data System (ADS)

Yepez-Martinez, Tochtli; Civitarese, Osvaldo; Hess, Peter O.

The SO(4) symmetry of a sector of the quantum chromodynamics (QCD) Hamiltonian was analyzed in a previous work. The numerical calculations were then restricted to a particle-hole (ph) space and the comparison with experimental data was reasonable in spite of the complexity of the QCD spectrum at low energy. Here on, we continue along this line of research and show our new results of the treatment of the QCD Hamiltonian in the SO(4) representation, including ground state correlations by means of the Random Phase Approximation (RPA). We are able to identify, within this model, states which may be associated to physical pseudo-scalar and vector mesons, like η,η‧,K,ρ,ω,ϕ, as well as the pion (π).

Hamiltonian Cycle Enumeration via Fermion-Zeon Convolution

NASA Astrophysics Data System (ADS)

Staples, G. Stacey

2017-12-01

Beginning with a simple graph having finite vertex set V, operators are induced on fermion and zeon algebras by the action of the graph's adjacency matrix and combinatorial Laplacian on the vector space spanned by the graph's vertices. When the graph is simple (undirected with no loops or multiple edges), the matrices are symmetric and the induced operators are self-adjoint. The goal of the current paper is to recover a number of known graph-theoretic results from quantum observables constructed as linear operators on fermion and zeon Fock spaces. By considering an "indeterminate" fermion/zeon Fock space, a fermion-zeon convolution operator is defined whose trace recovers the number of Hamiltonian cycles in the graph. This convolution operator is a quantum observable whose expectation reveals the number of Hamiltonian cycles in the graph.

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

NASA Astrophysics Data System (ADS)

Lampart, Jonas; Schmidt, Julian; Teufel, Stefan; Tumulka, Roderich

2018-06-01

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cut-off (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC.

First integrals of motion in a gauge covariant framework, Killing-Maxwell system and quantum anomalies

NASA Astrophysics Data System (ADS)

Visinescu, M.

2012-10-01

Hidden symmetries in a covariant Hamiltonian framework are investigated. The special role of the Stackel-Killing and Killing-Yano tensors is pointed out. The covariant phase-space is extended to include external gauge fields and scalar potentials. We investigate the possibility for a higher-order symmetry to survive when the electromagnetic interactions are taken into account. Aconcrete realization of this possibility is given by the Killing-Maxwell system. The classical conserved quantities do not generally transfer to the quantized systems producing quantum gravitational anomalies. As a rule the conformal extension of the Killing vectors and tensors does not produce symmetry operators for the Klein-Gordon operator.

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

Hamiltonian structure of Dubrovin{close_quote}s equation of associativity in 2-d topological field theory

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

Galvao, C.A.; Nutku, Y.

1996-12-01

mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}

Quantum transport and the Wigner distribution function for Bloch electrons in spatially homogeneous electric and magnetic fields

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Sokolov, V. N.; Krieger, J. B.

2017-10-01

The theory of Bloch electron dynamics for carriers in homogeneous electric and magnetic fields of arbitrary time dependence is developed in the framework of the Liouville equation. The Wigner distribution function (WDF) is determined from the single-particle density matrix in the ballistic regime, i.e., collision effects are excluded. In the theory, the single-particle transport equation is established with the electric field described in the vector potential gauge, and the magnetic field is treated in the symmetric gauge. No specific assumptions are made concerning the form of the initial distribution in momentum or configuration space. The general approach is to employ the accelerated Bloch state representation (ABR) as a basis so that the dependence upon the electric field, including multiband Zener tunneling, is treated exactly. Further, in the formulation of the WDF, we transform to a new set of variables so that the final WDF is gauge invariant and is expressed explicitly in terms of the position, kinetic momentum, and time. The methodology for developing the WDF is illustrated by deriving the exact WDF equation for free electrons in homogeneous electric and magnetic fields resulting in the same form as given by the collisionless Boltzmann transport equation (BTE). The methodology is then extended to the case of electrons described by an effective Hamiltonian corresponding to an arbitrary energy band function; the exact WDF equation results for the effective Hamiltonian case are shown to approximate the free electron results when taken to second order in the magnetic field. As a corollary, in these cases, it is shown that if the WDF is a wave packet, then the time rate of change of the electron quasimomentum is given by the Lorentz force. In treating the problem of Bloch electrons in a periodic potential in the presence of homogeneous electric and magnetic fields, the methodology for deriving the WDF reveals a multiband character due to the inherent nature of the Bloch states. The K0 representation of the Bloch envelope functions is employed to express the multiband WDF in a useful form. In examining the single-band WDF, it is found that the collisionless WDF equation matches the equivalent BTE to first order in the magnetic field. These results are necessarily extended to second order in the magnetic field by employing a unitary transformation that diagonalizes the Hamiltonian using the ABR to second order. The unitary transformation process includes a discussion of the multiband WDF transport analysis and the identification of the combined Zener-magnetic-field induced tunneling.

Hamiltonian vs Lagrangian Embedding of a Massive Spin-One Theory Involving Two-Form Field

NASA Astrophysics Data System (ADS)

Harikumar, E.; Sivakumar, M.

We consider the Hamiltonian and Lagrangian embedding of a first-order, massive spin-one, gauge noninvariant theory involving antisymmetric tensor field. We apply the BFV-BRST generalized canonical approach to convert the model to a first class system and construct nilpotent BFV-BRST charge and a unitarizing Hamiltonian. The canonical analysis of the Stückelberg formulation of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the Lagrangian embedded model. We show that to obtain manifestly covariant Stückelberg Lagrangian from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.

A Green's function formulation of the k→ ·p→ theory in the presence of spin-orbit interaction and magnetic field: Application to the electronic structure and related properties of w-GaN

NASA Astrophysics Data System (ADS)

Shadangi, Subrat K.; Mishra, Sambit R.; Tripathi, Gouri S.

2018-01-01

We use a Green's function perturbation formalism in the presence of an applied magnetic field and spin-orbit effects in the effective mass representation (EMR). The lack of lattice translational symmetry of the vector potential in the presence of the magnetic field is considered by redefining the Green's function in terms of the Peierls' phase factor. The equation of motion of the Green's function as a function of a magnetic wave vector was solved using perturbation theory, leading to expressions for the effective mass and the g-factor. We study the electronic structure of wurtzite GaN theoretically using the resulting k→ ·π→ method, where k→ is the electronic wave vector and π→ is the relativistic momentum operator by considering the conduction band edge and three valence bands. The k→ ·π→ Hamiltonians for the conduction band edge and the valence bands are diagonalized, considering the conduction band and one valence band at a time. We obtain electron and hole dispersions. Effects of other bands are considered by using perturbation theory. Resulting dispersions agree with the results of other calculations. In order to study the effective mass and the g-factor, we use the eigenvalues and eigenfunctions obtained after the diagonalization. Our results for the effective masses and the g-factors agree fairly well with available theoretical and experimental results, Temperature dependence of both the electronic effective mass and g-factor is studied and trends obtained agree with the existing experimental data.

Finite Nilpotent BRST Transformations in Hamiltonian Formulation

NASA Astrophysics Data System (ADS)

Rai, Sumit Kumar; Mandal, Bhabani Prasad

2013-10-01

We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformations in the sector of Lagrange multiplier and its corresponding momenta.

Field-antifield and BFV formalisms for quadratic systems with open gauge algebras

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

Nirov, K.S.; Razumov, A.V.

1992-09-20

In this paper the Lagrangian field-antifield (BV) and Hamiltonian (BFV) BRST formalisms for the general quadratic systems with open gauge algebra are considered. The equivalence between the Lagrangian and Hamiltonian formalisms is proven.

Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system

NASA Astrophysics Data System (ADS)

Gong, Z. R.; Ian, H.; Liu, Yu-Xi; Sun, C. P.; Nori, Franco

2009-12-01

Using the Born-Oppenheimer approximation, we derive an effective Hamiltonian for an optomechanical system that leads to a nonlinear Kerr effect in the system’s vacuum. The oscillating mirror at one edge of the optomechanical system induces a squeezing effect in the intensity spectrum of the cavity field. A near-resonant laser field is applied at the other edge to drive the cavity field in order to enhance the Kerr effect. We also propose a quantum-nondemolition-measurement setup to monitor a system with two cavities separated by a common oscillating mirror based on our effective Hamiltonian approach.

Compactly supported Wannier functions and algebraic K -theory

NASA Astrophysics Data System (ADS)

Read, N.

2017-03-01

In a tight-binding lattice model with n orbitals (single-particle states) per site, Wannier functions are n -component vector functions of position that fall off rapidly away from some location, and such that a set of them in some sense span all states in a given energy band or set of bands; compactly supported Wannier functions are such functions that vanish outside a bounded region. They arise not only in band theory, but also in connection with tensor-network states for noninteracting fermion systems, and for flat-band Hamiltonians with strictly short-range hopping matrix elements. In earlier work, it was proved that for general complex band structures (vector bundles) or general complex Hamiltonians—that is, class A in the tenfold classification of Hamiltonians and band structures—a set of compactly supported Wannier functions can span the vector bundle only if the bundle is topologically trivial, in any dimension d of space, even when use of an overcomplete set of such functions is permitted. This implied that, for a free-fermion tensor network state with a nontrivial bundle in class A, any strictly short-range parent Hamiltonian must be gapless. Here, this result is extended to all ten symmetry classes of band structures without additional crystallographic symmetries, with the result that in general the nontrivial bundles that can arise from compactly supported Wannier-type functions are those that may possess, in each of d directions, the nontrivial winding that can occur in the same symmetry class in one dimension, but nothing else. The results are obtained from a very natural usage of algebraic K -theory, based on a ring of polynomials in e±i kx,e±i ky,..., which occur as entries in the Fourier-transformed Wannier functions.

Hamiltonian closures in fluid models for plasmas

NASA Astrophysics Data System (ADS)

Tassi, Emanuele

2017-11-01

This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and connections with previously discussed fluid models are pointed out.

Mean-field description of topological charge 4e superconductors

NASA Astrophysics Data System (ADS)

Gabriele, Victoria; Luo, Jing; Teo, Jeffrey C. Y.

BCS superconductors can be understood by a mean-field approximation of two-body interacting Hamiltonians, whose ground states break charge conservation spontaneously by allowing non-vanishing expectation values of charge 2e Cooper pairs. Topological superconductors, such as one-dimensional p-wave wires, have non-trivial ground states that support robust gapless boundary excitations. We construct a four-body Hamiltonian in one dimension and perform a mean-field analysis. The mean-field Hamiltonian is now quartic in fermions but is still exactly solvable. The ground state exhibits 4-fermion expectation values instead of Cooper pair ones. There also exists a topological phase, where the charge 4e superconductor carries exotic zero energy boundary excitations.

Mean-field theory for multipole ordering in f-electron systems on the basis of a j-j coupling scheme

NASA Astrophysics Data System (ADS)

Yamamura, Ryosuke; Hotta, Takashi

2018-05-01

We develop a microscopic theory for multipole ordering, applicable to the system with plural numbers of f electrons per ion, from an itinerant picture on the basis of a j-j coupling scheme. For the purpose, by introducing the Γ8 Hubbard Hamiltonian as the minimum model to discuss the multipole ordering in f-electron systems, we describe the mean-field approximation in terms of the multipole operators. For the case of n = 2 , where n denotes the average f-electron number per ion, we analyze the model on a simple cubic lattice to obtain the multipole phase diagram. In particular, we find the order of non-Kramers Γ3 quadrupoles, O20 and O22 , with different ordering vectors. We attempt to explain the phase diagram from the discussion on the interaction energy.

The gravity duals of modular Hamiltonians

DOE PAGES

Jafferis, Daniel L.; Suh, S. Josephine

2016-09-12

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-likemore » to the causal completion of the region.« less

The gravity duals of modular Hamiltonians

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

Jafferis, Daniel L.; Suh, S. Josephine

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-likemore » to the causal completion of the region.« less

Superintegrability on N-dimensional spaces of constant curvature from so( N + 1) and its contractions

NASA Astrophysics Data System (ADS)

Herranz, F. J.; Ballesteros, Á.

2008-05-01

The Lie—Poisson algebra so( N + 1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the N-dimensional spherical, Euclidean, hyperbolic, Minkowskian, and (anti-)de Sitter spaces. We firstly present a Hamiltonian which is a superposition of an arbitrary central potential with N arbitrary centrifugal terms. Such a system is quasi-maximally superintegrable since this is endowed with 2 N — 3 functionally independent constants of motion (plus the Hamiltonian). Secondly, we identify two maximally superintegrable Hamiltonians by choosing a specific central potential and finding at the same time the remaining integral. The former is the generalization of the Smorodinsky—Winternitz system to the above six spaces, while the latter is a generalization of the Kepler—Coulomb potential, for which the Laplace—Runge—Lenz N vector is also given. All the systems and constants of motion are explicitly expressed in a unified form in terms of ambient and polar coordinates as they are parametrized by two contraction parameters (curvature and signature of the metric).

The Artificial Hamiltonian, First Integrals, and Closed-Form Solutions of Dynamical Systems for Epidemics

NASA Astrophysics Data System (ADS)

Naz, Rehana; Naeem, Imran

2018-03-01

The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.

Foundations of Quantum Mechanics: Derivation of a dissipative Schrödinger equation from first principles

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

Gonçalves, L.A.; Olavo, L.S.F., E-mail: olavolsf@gmail.com

Dissipation in Quantum Mechanics took some time to become a robust field of investigation after the birth of the field. The main issue hindering developments in the field is that the Quantization process was always tightly connected to the Hamiltonian formulation of Classical Mechanics. In this paper we present a quantization process that does not depend upon the Hamiltonian formulation of Classical Mechanics (although still departs from Classical Mechanics) and thus overcome the problem of finding, from first principles, a completely general Schrödinger equation encompassing dissipation. This generalized process of quantization is shown to be nothing but an extension ofmore » a more restricted version that is shown to produce the Schrödinger equation for Hamiltonian systems from first principles (even for Hamiltonian velocity dependent potential). - Highlights: • A Quantization process independent of the Hamiltonian formulation of quantum Mechanics is proposed. • This quantization method is applied to dissipative or absorptive systems. • A Dissipative Schrödinger equation is derived from first principles.« less

Ratios of Vector and Pseudoscalar B Meson Decay Constants in the Light-Cone Quark Model

NASA Astrophysics Data System (ADS)

Dhiman, Nisha; Dahiya, Harleen

2018-05-01

We study the decay constants of pseudoscalar and vector B meson in the framework of light-cone quark model. We apply the variational method to the relativistic Hamiltonian with the Gaussian-type trial wave function to obtain the values of β (scale parameter). Then with the help of known values of constituent quark masses, we obtain the numerical results for the decay constants f_P and f_V, respectively. We compare our numerical results with the existing experimental data.

Symmetry analysis of strain, electric and magnetic fields in the Bi2Se3-class of topological insulators

NASA Astrophysics Data System (ADS)

Rosdahl Brems, Mathias; Paaske, Jens; Lunde, Anders Mathias; Willatzen, Morten

2018-05-01

Based on group theoretical arguments we derive the most general Hamiltonian for the Bi2Se3-class of materials including terms to third order in the wave vector, first order in electric and magnetic fields, first order in strain and first order in both strain and wave vector. We determine analytically the effects of strain on the electronic structure of Bi2Se3. For the most experimentally relevant surface termination we analytically derive the surface state (SS) spectrum, revealing an anisotropic Dirac cone with elliptical constant energy contours giving rise to a direction-dependent group velocity. The spin-momentum locking of strained Bi2Se3 is shown to be modified. Hence, strain control can be used to manipulate the spin degree of freedom via the spin–orbit coupling. We show that for a thin film of Bi2Se3 the SS band gap induced by coupling between the opposite surfaces changes opposite to the bulk band gap under strain. Tuning the SS band gap by strain, gives new possibilities for the experimental investigation of the thickness dependent gap and optimization of optical properties relevant for, e.g., photodetector and energy harvesting applications. We finally derive analytical expressions for the effective mass tensor of the Bi2Se3 class of materials as a function of strain and electric field.

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.

Exponential propagators for the Schrödinger equation with a time-dependent potential.

PubMed

Bader, Philipp; Blanes, Sergio; Kopylov, Nikita

2018-06-28

We consider the numerical integration of the Schrödinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential propagators that have shown to be highly efficient for general time-dependent Hamiltonians. We propose new CF propagators that are tailored for Hamiltonians of the said structure, showing a considerably improved performance. We obtain new fourth- and sixth-order CF propagators as well as a novel sixth-order propagator that incorporates a double commutator that only depends on coordinates, so this term can be considered as cost-free. The algorithms require the computation of the action of exponentials on a vector similar to the well-known exponential midpoint propagator, and this is carried out using the Lanczos method. We illustrate the performance of the new methods on several numerical examples.

Transitionless driving on adiabatic search algorithm

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

Oh, Sangchul, E-mail: soh@qf.org.qa; Kais, Sabre, E-mail: kais@purdue.edu; Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907

We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian,more » approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.« less

First principles of Hamiltonian medicine.

PubMed

Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

2014-05-19

We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.

Poisson structure of dynamical systems with three degrees of freedom

NASA Astrophysics Data System (ADS)

Gümral, Hasan; Nutku, Yavuz

1993-12-01

It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one-form in three dimensions. Advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability. Techniques for finding Poisson structures are presented and applied to various examples such as the Halphen system which has been studied as the two-monopole problem by Atiyah and Hitchin. It is shown that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a nontrivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of three-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the SL(2,R) structure is a quadratic unfolding of an integrable one-form in 3+1 dimensions. It is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of Poisson structure and some new techniques for incorporating arbitrary constants into the Poisson one-form are presented herein. This leads to some extensions, analogous to q extensions, of Poisson structure. The Kermack-McKendrick model and some of its generalizations describing the spread of epidemics, as well as the integrable cases of the Lorenz, Lotka-Volterra, May-Leonard, and Maxwell-Bloch systems admit globally integrable bi-Hamiltonian structure.

Algebraic Bethe ansatz for the sℓ (2) Gaudin model with boundary

NASA Astrophysics Data System (ADS)

Cirilo António, N.; Manojlović, N.; Ragoucy, E.; Salom, I.

2015-04-01

Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations.

Scaling Limit for a Generalization of the Nelson Model and its Application to Nuclear Physics

NASA Astrophysics Data System (ADS)

Suzuki, Akito

We study a mathematically rigorous derivation of a quantum mechanical Hamiltonian in a general framework. We derive such a Hamiltonian by taking a scaling limit for a generalization of the Nelson model, which is an abstract interaction model between particles and a Bose field with some internal degrees of freedom. Applying it to a model for the field of the nuclear force with isospins, we obtain a Schrödinger Hamiltonian with a matrix-valued potential, the one pion exchange potential, describing an effective interaction between nucleons.

Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

NASA Astrophysics Data System (ADS)

Balajany, Hamideh; Mehrafarin, Mohammad

2018-06-01

In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis-Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et al. (2013) [21] for these Berry phases, which is resolved to yield agreement with our results.

Flux qubit interaction with rapid single-flux quantum logic circuits: Control and readout

NASA Astrophysics Data System (ADS)

Klenov, N. V.; Kuznetsov, A. V.; Soloviev, I. I.; Bakurskiy, S. V.; Denisenko, M. V.; Satanin, A. M.

2017-07-01

We present the results of an analytical study and numerical simulation of the dynamics of a superconducting three-Josephson-junction (3JJ) flux qubit magnetically coupled with rapid single-flux quantum (RSFQ) logic circuit, which demonstrate the fundamental possibility of implementing the simplest logic operations at picosecond times, as well as rapid non-destructive readout. It is shown that when solving optimization problems, the qubit dynamics can be conveniently interpreted as a precession of the magnetic moment vector around the direction of the magnetic field. In this case, the role of magnetic field components is played by combinations of the Hamiltonian matrix elements, and the role of the magnetic moment is played by the Bloch vector. Features of the 3JJ qubit model are discussed during the analysis of how the qubit is affected by exposure to a short control pulse, as are the similarities between the Bloch and Landau-Lifshitz-Gilbert equations. An analysis of solutions to the Bloch equations made it possible to develop recommendations for the use of readout RSFQ circuits in implementing an optimal interface between the classical and quantum parts of the computer system, as well as to justify the use of single-quantum logic in order to control superconducting quantum circuits on a chip.

Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices.

PubMed

Leclerc, Arnaud; Carrington, Tucker

2014-05-07

We propose an iterative method for computing vibrational spectra that significantly reduces the memory cost of calculations. It uses a direct product primitive basis, but does not require storing vectors with as many components as there are product basis functions. Wavefunctions are represented in a basis each of whose functions is a sum of products (SOP) and the factorizable structure of the Hamiltonian is exploited. If the factors of the SOP basis functions are properly chosen, wavefunctions are linear combinations of a small number of SOP basis functions. The SOP basis functions are generated using a shifted block power method. The factors are refined with a rank reduction algorithm to cap the number of terms in a SOP basis function. The ideas are tested on a 20-D model Hamiltonian and a realistic CH3CN (12 dimensional) potential. For the 20-D problem, to use a standard direct product iterative approach one would need to store vectors with about 10(20) components and would hence require about 8 × 10(11) GB. With the approach of this paper only 1 GB of memory is necessary. Results for CH3CN agree well with those of a previous calculation on the same potential.

Terrorism/Criminalogy/Sociology via Magnetism-Hamiltonian ``Models''?!: Black Swans; What Secrets Lie Buried in Magnetism?; ``Magnetism Will Conquer the Universe?''(Charles Middleton, aka ``His Imperial Majesty The Emperior Ming `The Merciless!!!''

NASA Astrophysics Data System (ADS)

Carrott, Anthony; Siegel, Edward Carl-Ludwig; Hoover, John-Edgar; Ness, Elliott

2013-03-01

Terrorism/Criminalogy//Sociology : non-Linear applied-mathematician (``nose-to-the grindstone / ``gearheadism'') ''modelers'': Worden,, Short, ...criminologists/counter-terrorists/sociologists confront [SIAM Conf. on Nonlinearity, Seattle(12); Canadian Sociology Conf,. Burnaby(12)]. ``The `Sins' of the Fathers Visited Upon the Sons'': Zeno vs Ising vs Heisenberg vs Stoner vs Hubbard vs Siegel ''SODHM''(But NO Y!!!) vs ...??? Magntism and it turn are themselves confronted BY MAGNETISM,via relatively magnetism/metal-insulator conductivity / percolation-phase-transitions critical-phenomena -illiterate non-linear applied-mathematician (nose-to-the-grindstone/ ``gearheadism'')''modelers''. What Secrets Lie Buried in Magnetism?; ``Magnetism Will Conquer the Universe!!!''[Charles Middleton, aka ``His Imperial Majesty The Emperior Ming `The Merciless!!!']'' magnetism-Hamiltonian phase-transitions percolation-``models''!: Zeno(~2350 BCE) to Peter the Pilgrim(1150) to Gilbert(1600) to Faraday(1815-1820) to Tate (1870-1880) to Ewing(1882) hysteresis to Barkhausen(1885) to Curie(1895)-Weiss(1895) to Ising-Lenz(r-space/Localized-Scalar/ Discrete/1911) to Heisenberg(r-space/localized-vector/discrete/1927) to Priesich(1935) to Stoner (electron/k-space/ itinerant-vector/discrete/39) to Stoner-Wohlfarth (technical-magnetism hysteresis /r-space/ itinerant-vector/ discrete/48) to Hubbard-Longuet-Higgins (k-space versus r-space/

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.

Quantum mechanics of a photon

NASA Astrophysics Data System (ADS)

Babaei, Hassan; Mostafazadeh, Ali

2017-08-01

A first-quantized free photon is a complex massless vector field A =(Aμ ) whose field strength satisfies Maxwell's equations in vacuum. We construct the Hilbert space H of the photon by endowing the vector space of the fields A in the temporal-Coulomb gauge with a positive-definite and relativistically invariant inner product. We give an explicit expression for this inner product, identify the Hamiltonian for the photon with the generator of time translations in H , determine the operators representing the momentum and the helicity of the photon, and introduce a chirality operator whose eigenfunctions correspond to fields having a definite sign of energy. We also construct a position operator for the photon whose components commute with each other and with the chirality and helicity operators. This allows for the construction of the localized states of the photon with a definite sign of energy and helicity. We derive an explicit formula for the latter and compute the corresponding electric and magnetic fields. These turn out to diverge not just at the point where the photon is localized but on a plane containing this point. We identify the axis normal to this plane with an associated symmetry axis and show that each choice of this axis specifies a particular position operator, a corresponding position basis, and a position representation of the quantum mechanics of a photon. In particular, we examine the position wave functions determined by such a position basis, elucidate their relationship with the Riemann-Silberstein and Landau-Peierls wave functions, and give an explicit formula for the probability density of the spatial localization of the photon.

Quantum and classical dissipation of charged particles

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

Ibarra-Sierra, V.G.; Anzaldo-Meneses, A.; Cardoso, J.L.

2013-08-15

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail. -- Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle.more » •Classical and quantum dynamics of a damped electric charge.« less

Modular Hamiltonians on the null plane and the Markov property of the vacuum state

NASA Astrophysics Data System (ADS)

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-09-01

We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.

Hamiltonian of Mean Force and Dissipative Scalar Field Theory

NASA Astrophysics Data System (ADS)

Jafari, Marjan; Kheirandish, Fardin

2018-04-01

Quantum dynamics of a dissipative scalar field is investigated. Using the Hamiltonian of mean force, internal energy, free energy and entropy of a dissipative scalar field are obtained. It is shown that a dissipative massive scalar field can be considered as a free massive scalar field described by an effective mass and dispersion relation. Internal energy of the scalar field, as the subsystem, is found in the limit of low temperature and weak and strong couplings to an Ohimc heat bath. Correlation functions for thermal and coherent states are derived.

Analysis of Raman lasing without inversion

NASA Astrophysics Data System (ADS)

Sheldon, Paul Martin

1999-12-01

Properties of lasing without inversion were studied analytically and numerically using Maple computer assisted algebra software. Gain for probe electromagnetic field without population inversion in detuned three level atomic schemes has been found. Matter density matrix dynamics and coherence is explored using Pauli matrices in 2-level systems and Gell-Mann matrices in 3-level systems. It is shown that extreme inversion produces no coherence and hence no lasing. Unitary transformation from the strict field-matter Hamiltonian to an effective two-photon Raman Hamiltonian for multilevel systems has been derived. Feynman diagrams inherent in the derivation show interesting physics. An additional picture change was achieved and showed cw gain possible. Properties of a Raman-like laser based on injection of 3- level coherently driven Λ-type atoms whose Hamiltonian contains the Raman Hamiltonian and microwave coupling the two bottom states have been studied in the limits of small and big photon numbers in the drive field. Another picture change removed the microwave coupler to all orders and simplified analysis. New possibilities of inversionless generation were found.

Might god toss coins?

NASA Astrophysics Data System (ADS)

Pearle, Philip

1982-03-01

In the problem of the gambler's ruin, a classic problem in probability theory, a number of gamblers play against each other until all but one of them is “wiped out.” It is shown that this problem is identical to a previously presented formulation of the reduction of the state vector, so that the state vectors in a linear superposition may be regarded as “playing” against each other until all but one of them is “wiped out.” This is a useful part of the description of an objectively real universe represented by a state vector that is a superposition of macroscopically distinguishable states dynamically created by the Hamiltonian and destroyed by the reduction mechanism.

Hamiltonian formulation of the KdV equation

NASA Astrophysics Data System (ADS)

Nutku, Y.

1984-06-01

We consider the canonical formulation of Whitham's variational principle for the KdV equation. This Lagrangian is degenerate and we have found it necessary to use Dirac's theory of constrained systems in constructing the Hamiltonian. Earlier discussions of the Hamiltonian structure of the KdV equation were based on various different decompositions of the field which is avoided by this new approach.

Hamiltonian Anomalies from Extended Field Theories

NASA Astrophysics Data System (ADS)

Monnier, Samuel

2015-09-01

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.

Form of the manifestly covariant Lagrangian

NASA Astrophysics Data System (ADS)

Johns, Oliver Davis

1985-10-01

The preferred form for the manifestly covariant Lagrangian function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' Lagrangian and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant Lagrangian theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' Lagrangian, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives Lagrangian theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' Lagrangian is a completely adequate basis for covariant Lagrangian theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the Lagrangian and other four-vector equations.

The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach

ERIC Educational Resources Information Center

Likar, A.; Razpet, N.

2009-01-01

The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is…

Landau problem with time dependent mass in time dependent electric and harmonic background fields

NASA Astrophysics Data System (ADS)

Lawson, Latévi M.; Avossevou, Gabriel Y. H.

2018-04-01

The spectrum of a Hamiltonian describing the dynamics of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field is obtained. The configuration space wave function of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian, we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce a unitary transformation in the framework of the algebraic formalism to construct the invariant operator of the system and then to obtain the exact solution of the Hamiltonian. We recover the solutions of the ordinary Landau problem in the absence of the electric and harmonic fields for a constant particle mass.

Vector-valued Jack polynomials and wavefunctions on the torus

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

2017-06-01

The Hamiltonian of the quantum Calogero-Sutherland model of N identical particles on the circle with 1/r 2 interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials taking values in modules of the symmetric group and the matrix solution of a system of linear differential equations one constructs novel eigenfunctions of the Hamiltonian. Like the usual wavefunctions each eigenfunction determines a symmetric probability density on the N-torus. The construction applies to any irreducible representation of the symmetric group. The methods depend on the theory of generalized Jack polynomials due to Griffeth, and the Yang-Baxter graph approach of Luque and the author.

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations

NASA Astrophysics Data System (ADS)

Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

2012-06-01

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics.

The universal propagator

NASA Technical Reports Server (NTRS)

Klauder, John R.

1993-01-01

For a general Hamiltonian appropriate to a single canonical degree of freedom, a universal propagator with the property that it correctly evolves the coherent-state Hilbert space representatives for an arbitrary fiducial vector is characterized and defined. The universal propagator is explicitly constructed for the harmonic oscillator, with a result that differs from the conventional propagators for this system.

Perspective: Quantum Hamiltonians for optical interactions

NASA Astrophysics Data System (ADS)

Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy

2018-01-01

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Alternative bi-Hamiltonian structures for WDVV equations of associativity

NASA Astrophysics Data System (ADS)

Kalayci, J.; Nutku, Y.

1998-01-01

The WDVV equations of associativity in two-dimensional topological field theory are completely integrable third-order Monge-Ampère equations which admit bi-Hamiltonian structure. The time variable plays a distinguished role in the discussion of Hamiltonian structure, whereas in the theory of WDVV equations none of the independent variables merits such a distinction. WDVV equations admit very different alternative Hamiltonian structures under different possible choices of the time variable, but all these various Hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure. They can be identified as different components of the covariant Witten-Zuckerman symplectic 2-form current density where a variational formulation of the WDVV equation that leads to the Hamiltonian operator through the Dirac bracket is available.

Boson mapping techniques applied to constant gauge fields in QCD

NASA Technical Reports Server (NTRS)

Hess, Peter Otto; Lopez, J. C.

1995-01-01

Pairs of coordinates and derivatives of the constant gluon modes are mapped to new gluon-pair fields and their derivatives. Applying this mapping to the Hamiltonian of constant gluon fields results for large coupling constants into an effective Hamiltonian which separates into one describing a scalar field and another one for a field with spin two. The ground state is dominated by pairs of gluons coupled to color and spin zero with slight admixtures of color zero and spin two pairs. As color group we used SU(2).

Hamiltonian Effective Field Theory Study of the N^{*}(1535) Resonance in Lattice QCD.

PubMed

Liu, Zhan-Wei; Kamleh, Waseem; Leinweber, Derek B; Stokes, Finn M; Thomas, Anthony W; Wu, Jia-Jun

2016-02-26

Drawing on experimental data for baryon resonances, Hamiltonian effective field theory (HEFT) is used to predict the positions of the finite-volume energy levels to be observed in lattice QCD simulations of the lowest-lying J^{P}=1/2^{-} nucleon excitation. In the initial analysis, the phenomenological parameters of the Hamiltonian model are constrained by experiment and the finite-volume eigenstate energies are a prediction of the model. The agreement between HEFT predictions and lattice QCD results obtained on volumes with spatial lengths of 2 and 3 fm is excellent. These lattice results also admit a more conventional analysis where the low-energy coefficients are constrained by lattice QCD results, enabling a determination of resonance properties from lattice QCD itself. Finally, the role and importance of various components of the Hamiltonian model are examined.

HO2 rovibrational eigenvalue studies for nonzero angular momentum

NASA Astrophysics Data System (ADS)

Wu, Xudong T.; Hayes, Edward F.

1997-08-01

An efficient parallel algorithm is reported for determining all bound rovibrational energy levels for the HO2 molecule for nonzero angular momentum values, J=1, 2, and 3. Performance tests on the CRAY T3D indicate that the algorithm scales almost linearly when up to 128 processors are used. Sustained performance levels of up to 3.8 Gflops have been achieved using 128 processors for J=3. The algorithm uses a direct product discrete variable representation (DVR) basis and the implicitly restarted Lanczos method (IRLM) of Sorensen to compute the eigenvalues of the polyatomic Hamiltonian. Since the IRLM is an iterative method, it does not require storage of the full Hamiltonian matrix—it only requires the multiplication of the Hamiltonian matrix by a vector. When the IRLM is combined with a formulation such as DVR, which produces a very sparse matrix, both memory and computation times can be reduced dramatically. This algorithm has the potential to achieve even higher performance levels for larger values of the total angular momentum.

A sparse matrix-vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

NASA Astrophysics Data System (ADS)

Ghale, Purnima; Johnson, Harley T.

2018-06-01

We present an efficient sparse matrix-vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev-Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix-matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev-Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix-vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

Self-consistent chaos in a mean-field Hamiltonian model of fluids and plasmas

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, D.; Firpo, Marie-Christine

2002-11-01

We present a mean-field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas. In plasmas, the model describes the self-consistent evolution of electron holes and clumps in phase space. In fluids, the model describes the dynamics of vortices with negative and positive circulation in shear flows. The mean-field nature of the system makes it a tractable model to study the dynamics of large degrees-of-freedom, coupled Hamiltonian systems. Here we focus in the role of self-consistent chaos in the formation and destruction of phase space coherent structures. Numerical simulations in the finite N and in the Narrow kinetic limit (where N is the number of particles) show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles, and show that the N = 2 limit has a family of rotating integrable solutions described by a one degree-of-freedom nontwist Hamiltonian. The coherence of the dipole is explained in terms of a parametric resonance between the rotation frequency of the macroparticles and the oscillation frequency of the self-consistent mean field. For a class of initial conditions, the mean field exhibits a self-consistent, elliptic-hyperbolic bifurcation that leads to the destruction of the dipole and violent mixing of the phase space.

Beyond the Unified Model

NASA Astrophysics Data System (ADS)

Frauendorf, S.

2018-04-01

The key elements of the Unified Model are reviewed. The microscopic derivation of the Bohr Hamiltonian by means of adiabatic time-dependent mean field theory is presented. By checking against experimental data the limitations of the Unified Model are delineated. The description of the strong coupling between the rotational and intrinsic degrees of freedom in framework of the rotating mean field is presented from a conceptual point of view. The classification of rotational bands as configurations of rotating quasiparticles is introduced. The occurrence of uniform rotation about an axis that differs from the principle axes of the nuclear density distribution is discussed. The physics behind this tilted-axis rotation, unknown in molecular physics, is explained on a basic level. The new symmetries of the rotating mean field that arise from the various orientations of the angular momentum vector with respect to the triaxial nuclear density distribution and their manifestation by the level sequence of rotational bands are discussed. Resulting phenomena, as transverse wobbling, rotational chirality, magnetic rotation and band termination are discussed. Using the concept of spontaneous symmetry breaking the microscopic underpinning of the rotational degrees is refined.

Possible treatment of the ghost states in the Lee-Wick standard model

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

Shalaby, Abouzeid M.; Physics Department, Faculty of Science, Qassim University

2009-07-15

In this work, we employ the techniques used to cure the indefinite norm problem in pseudo-Hermitian Hamiltonians to show that the ghost states in a higher derivative scalar field theory are not real ghosts. For the model under investigation, an imaginary auxiliary field is introduced to have an equivalent non-Hermitian two-field scalar theory. We were able to calculate exactly the positive definite metric operator {eta} for the quantum mechanical as well as the quantum field versions of the theory. While the equivalent Hamiltonian is non-Hermitian in a Hilbert space characterized by the Dirac sense inner product, it is, however, amore » Hermitian in a Hilbert space endowed with the inner product . The main feature of the latter Hilbert space is that the propagator has the correct sign (no Lee-Wick fields). Moreover, the calculated metric operator diagonalizes the Hamiltonian in the two fields (no mixing). We found that the Hermiticity of the calculated metric operator to lead to the constrain M>2m for the two Higgs masses, in agreement with other calculations in the literature. Besides, our mass formulas coincide with those obtained in other works (obtained by a very different regime but with the existence of ghost states), which means that our positive normed Hamiltonian form preserves the mass spectra.« less

Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models

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

Perin, M.; Chandre, C.; Tassi, E.

2015-09-15

Moment closures of the Vlasov-Ampère system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two, and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary numbermore » of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed.« less

Scaling with System Size of the Lyapunov Exponents for the Hamiltonian Mean Field Model

NASA Astrophysics Data System (ADS)

Manos, Thanos; Ruffo, Stefano

2011-12-01

The Hamiltonian Mean Field model is a prototype for systems with long-range interactions. It describes the motion of N particles moving on a ring, coupled with an infinite-range potential. The model has a second-order phase transition at the energy density Uc =3/4 and its dynamics is exactly described by the Vlasov equation in the N→∞ limit. Its chaotic properties have been investigated in the past, but the determination of the scaling with N of the Lyapunov Spectrum (LS) of the model remains a challenging open problem. Here we show that the N -1/3 scaling of the Maximal Lyapunov Exponent (MLE), found in previous numerical and analytical studies, extends to the full LS; scaling is "precocious" for the LS, meaning that it becomes manifest for a much smaller number of particles than the one needed to check the scaling for the MLE. Besides that, the N -1/3 scaling appears to be valid not only for U>Uc , as suggested by theoretical approaches based on a random matrix approximation, but also below a threshold energy Ut ≈0.2. Using a recently proposed method (GALI) devised to rapidly check the chaotic or regular nature of an orbit, we find that Ut is also the energy at which a sharp transition from weak to strong chaos is present in the phase-space of the model. Around this energy the phase of the vector order parameter of the model becomes strongly time dependent, inducing a significant untrapping of particles from a nonlinear resonance.

Hamiltonian structures for systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Olver, Peter J.; Nutku, Yavuz

1988-07-01

The bi-Hamiltonian structure for a large class of one-dimensional hyberbolic systems of conservation laws in two field variables, including the equations of gas dynamics, shallow water waves, one-dimensional elastic media, and the Born-Infeld equation from nonlinear electrodynamics, is exhibited. For polytropic gas dynamics, these results lead to a quadri-Hamiltonian structure. New higher-order entropy-flux pairs (conservation laws) and higher-order symmetries are exhibited.

Can model Hamiltonians describe the electron-electron interaction in π-conjugated systems?: PAH and graphene

NASA Astrophysics Data System (ADS)

Chiappe, G.; Louis, E.; San-Fabián, E.; Vergés, J. A.

2015-11-01

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser-Parr-Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree-Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree-Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an ‘effective’ Hamiltonian including only on-site interactions (Hubbard)? The performance of CI will be checked on small molecules. The electronic structure of azulene and fused azulene will be used to illustrate several aspects of the method. As regards graphene, several questions will be considered: (i) paramagnetic versus antiferromagnetic solutions, (ii) forbidden gap versus dot size, (iii) graphene nano-ribbons, and (iv) optical properties.

Algebraic integrability: a survey.

PubMed

Vanhaecke, Pol

2008-03-28

We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems.

Monte Carlo simulations of spin transport in a strained nanoscale InGaAs field effect transistor

NASA Astrophysics Data System (ADS)

Thorpe, B.; Kalna, K.; Langbein, F. C.; Schirmer, S.

2017-12-01

Spin-based logic devices could operate at a very high speed with a very low energy consumption and hold significant promise for quantum information processing and metrology. We develop a spintronic device simulator by combining an in-house developed, experimentally verified, ensemble self-consistent Monte Carlo device simulator with spin transport based on a Bloch equation model and a spin-orbit interaction Hamiltonian accounting for Dresselhaus and Rashba couplings. It is employed to simulate a spin field effect transistor operating under externally applied voltages on a gate and a drain. In particular, we simulate electron spin transport in a 25 nm gate length In0.7Ga0.3As metal-oxide-semiconductor field-effect transistor with a CMOS compatible architecture. We observe a non-uniform decay of the net magnetization between the source and the gate and a magnetization recovery effect due to spin refocusing induced by a high electric field between the gate and the drain. We demonstrate a coherent control of the polarization vector of the drain current via the source-drain and gate voltages, and show that the magnetization of the drain current can be increased twofold by the strain induced into the channel.

Local modular Hamiltonians from the quantum null energy condition

NASA Astrophysics Data System (ADS)

Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin

2018-03-01

The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .

Hamiltonian analysis of higher derivative scalar-tensor theories

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

Langlois, David; Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr

2016-07-01

We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of themore » dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.« less

Spin squeezing a cold molecule

NASA Astrophysics Data System (ADS)

Bhattacharya, M.

2015-12-01

In this article we present a concrete proposal for spin squeezing the cold ground-state polar paramagnetic molecule OH, a system currently under fine control in the laboratory. In contrast to existing work, we consider a single, noninteracting molecule with angular momentum greater than 1 /2 . Starting from an experimentally relevant effective Hamiltonian, we identify an adiabatic regime where different combinations of static electric and magnetic fields can be used to realize the single-axis twisting Hamiltonian of Kitagawa and Ueda [M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993), 10.1103/PhysRevA.47.5138], the uniform field Hamiltonian proposed by Law et al. [C. K. Law, H. T. Ng, and P. T. Leung, Phys. Rev. A 63, 055601 (2001), 10.1103/PhysRevA.63.055601], and a model of field propagation in a Kerr medium considered by Agarwal and Puri [G. S. Agarwal and R. R. Puri, Phys. Rev. A 39, 2969 (1989), 10.1103/PhysRevA.39.2969]. We then consider the situation in which nonadiabatic effects are quite large and show that the effective Hamiltonian supports spin squeezing even in this case. We provide analytical expressions as well as numerical calculations, including optimization of field strengths and accounting for the effects of field misalignment. Our results have consequences for applications such as precision spectroscopy, techniques such as magnetometry, and stereochemical effects such as the orientation-to-alignment transition.

Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems

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

Barnich, Glenn; Troessaert, Cedric

2009-04-15

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity, and massless higher spin gauge fields.

Stability of Inhomogeneous Equilibria of Hamiltonian Continuous Media Field Theories

NASA Astrophysics Data System (ADS)

Hagstrom, George

2013-10-01

There are a wide variety of 1 + 1 Hamiltonian continuous media field theories that exhibit phase space pattern formation. In plasma physics, the most famous of these is the Vlasov-Poisson equation, but other examples include the incompressible Euler equation in two-dimensions and the Hamiltonian Mean Field (or XY) model. One of the characteristic phenomenon that occurs in systems described by these equations is the formation of cat's eye patterns in phase space as a result of the nonlinear saturation of instabilities. Corresponding to each of these cat's eyes is a spatially inhomogeneous equilibrium solution of the underlying model, in plasma physics these are called BGK modes, but analogous solutions exist in all of the above systems. Here we analyze the stability of inhomogeneous equilibria in the Hamiltonian Mean Field model and in the Single Wave model, which is an equation that was derived to provide a model of the formation of electron holes in plasmas. We use action angle variables and the properties of elliptic functions to analyze the resulting dispersion relation construct linearly stable inhomogeneous equilibria for in the limit of small numbers of particles and study the behavior of solutions near these equilibria. Work supported by USDOE grant no. DE-FG02-ER53223.

Navier-Stokes dynamics on a differential one-form

NASA Astrophysics Data System (ADS)

Story, Troy L.

2006-11-01

After transforming the Navier-Stokes dynamic equation into a characteristic differential one-form on an odd-dimensional differentiable manifold, exterior calculus is used to construct a pair of differential equations and tangent vector(vortex vector) characteristic of Hamiltonian geometry. A solution to the Navier-Stokes dynamic equation is then obtained by solving this pair of equations for the position x^k and the conjugate to the position bk as functions of time. The solution bk is shown to be divergence-free by contracting the differential 3-form corresponding to the divergence of the gradient of the velocity with a triple of tangent vectors, implying constraints on two of the tangent vectors for the system. Analysis of the solution bk shows it is bounded since it remains finite as | x^k | ->,, and is physically reasonable since the square of the gradient of the principal function is bounded. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian is obtained.

Ultracold atoms in strong synthetic magnetic fields

NASA Astrophysics Data System (ADS)

Ketterle, Wolfgang

2015-03-01

The Harper Hofstadter Hamiltonian describes charged particles in the lowest band of a lattice at high magnetic fields. This Hamiltonian can be realized with ultracold atoms using laser assisted tunneling which imprints the same phase into the wavefunction of neutral atoms as a magnetic field dose for electrons. I will describe our observation of a bosonic superfluid in a magnetic field with half a flux quantum per lattice unit cell, and discuss new possibilities for implementing spin-orbit coupling. Work done in collaboration with C.J. Kennedy, G.A. Siviloglou, H. Miyake, W.C. Burton, and Woo Chang Chung.

Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems

NASA Astrophysics Data System (ADS)

Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2011-09-01

The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.

Geometric phase of cosmological scalar and tensor perturbations in f(R) gravity

NASA Astrophysics Data System (ADS)

Balajany, Hamideh; Mehrafarin, Mohammad

2018-05-01

By using the conformal equivalence of f(R) gravity in vacuum and the usual Einstein theory with scalar-field matter, we derive the Hamiltonian of the linear cosmological scalar and tensor perturbations in f(R) gravity in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes as a Lewis-Riesenfeld phase.

Hamiltonian surface charges using external sources

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

Troessaert, Cédric, E-mail: troessaert@cecs.cl

2016-05-15

In this work, we interpret part of the boundary conditions as external sources in order to partially solve the integrability problem present in the computation of surface charges associated to gauge symmetries in the hamiltonian formalism. We start by describing the hamiltonian structure of external symmetries preserving the action up to a transformation of the external sources of the theory. We then extend these results to the computation of surface charges for field theories with non-trivial boundary conditions.

The quantum n-body problem in dimension d ⩾ n – 1: ground state

NASA Astrophysics Data System (ADS)

Miller, Willard, Jr.; Turbiner, Alexander V.; Escobar-Ruiz, M. A.

2018-05-01

We employ generalized Euler coordinates for the n body system in dimensional space, which consists of the centre-of-mass vector, relative (mutual) mass-independent distances r ij and angles as remaining coordinates. We prove that the kinetic energy of the quantum n-body problem for can be written as the sum of three terms: (i) kinetic energy of centre-of-mass, (ii) the second order differential operator which depends on relative distances alone and (iii) the differential operator which annihilates any angle-independent function. The operator has a large reflection symmetry group and in variables is an algebraic operator, which can be written in terms of generators of the hidden algebra . Thus, makes sense of the Hamiltonian of a quantum Euler–Arnold top in a constant magnetic field. It is conjectured that for any n, the similarity-transformed is the Laplace–Beltrami operator plus (effective) potential; thus, it describes a -dimensional quantum particle in curved space. This was verified for . After de-quantization the similarity-transformed becomes the Hamiltonian of the classical top with variable tensor of inertia in an external potential. This approach allows a reduction of the dn-dimensional spectral problem to a -dimensional spectral problem if the eigenfunctions depend only on relative distances. We prove that the ground state function of the n body problem depends on relative distances alone.

Reverse ray tracing for transformation optics.

PubMed

Hu, Chia-Yu; Lin, Chun-Hung

2015-06-29

Ray tracing is an important technique for predicting optical system performance. In the field of transformation optics, the Hamiltonian equations of motion for ray tracing are well known. The numerical solutions to the Hamiltonian equations of motion are affected by the complexities of the inhomogeneous and anisotropic indices of the optical device. Based on our knowledge, no previous work has been conducted on ray tracing for transformation optics with extreme inhomogeneity and anisotropicity. In this study, we present the use of 3D reverse ray tracing in transformation optics. The reverse ray tracing is derived from Fermat's principle based on a sweeping method instead of finding the full solution to ordinary differential equations. The sweeping method is employed to obtain the eikonal function. The wave vectors are then obtained from the gradient of that eikonal function map in the transformed space to acquire the illuminance. Because only the rays in the points of interest have to be traced, the reverse ray tracing provides an efficient approach to investigate the illuminance of a system. This approach is useful in any form of transformation optics where the material property tensor is a symmetric positive definite matrix. The performance and analysis of three transformation optics with inhomogeneous and anisotropic indices are explored. The ray trajectories and illuminances in these demonstration cases are successfully solved by the proposed reverse ray tracing method.

Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model

NASA Astrophysics Data System (ADS)

Manojlović, N.; Salom, I.

2017-10-01

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.

Anomalous Rashba spin-orbit interaction in electrically controlled topological insulator based on InN/GaN quantum wells

NASA Astrophysics Data System (ADS)

Łepkowski, Sławomir P.; Bardyszewski, Witold

2017-05-01

We study theoretically the topological phase transition and the Rashba spin-orbit interaction in electrically biased InN/GaN quantum wells. We show that that for properly chosen widths of quantum wells and barriers, one can effectively tune the system through the topological phase transition applying an external electric field perpendicular to the QW plane. We find that in InN/GaN quantum wells with the inverted band structure, when the conduction band s-type level is below the heavy hole and light hole p-type levels, the spin splitting of the subbands decreases with increasing the amplitude of the electric field in the quantum wells, which reveals the anomalous Rashba effect. Derived effective Rashba Hamiltonians can describe the subband spin splitting only for very small wave vectors due to strong coupling between the subbands. Furthermore, we demonstrate that for InN/GaN quantum wells in a Hall bar geometry, the critical voltage for the topological phase transition depends distinctly on the width of the structure and a significant spin splitting of the edge states lying in the 2D band gap can be almost switched off by increasing the electric field in quantum wells only by a few percent. We show that the dependence of the spin splitting of the upper branch of the edge state dispersion curve on the wave vector has a threshold-like behavior with the on/off spin splitting ratio reaching two orders of magnitude for narrow Hall bars. The threshold wave vector depends weakly on the Hall bar width, whereas it increases significantly with the bias voltage due to an increase of the energetic distance between the s-type and p-type quantum well energy levels and a reduction of the coupling between the subbands.

Anomalous Rashba spin-orbit interaction in electrically controlled topological insulator based on InN/GaN quantum wells.

PubMed

Łepkowski, Sławomir P; Bardyszewski, Witold

2017-05-17

We study theoretically the topological phase transition and the Rashba spin-orbit interaction in electrically biased InN/GaN quantum wells. We show that that for properly chosen widths of quantum wells and barriers, one can effectively tune the system through the topological phase transition applying an external electric field perpendicular to the QW plane. We find that in InN/GaN quantum wells with the inverted band structure, when the conduction band s-type level is below the heavy hole and light hole p-type levels, the spin splitting of the subbands decreases with increasing the amplitude of the electric field in the quantum wells, which reveals the anomalous Rashba effect. Derived effective Rashba Hamiltonians can describe the subband spin splitting only for very small wave vectors due to strong coupling between the subbands. Furthermore, we demonstrate that for InN/GaN quantum wells in a Hall bar geometry, the critical voltage for the topological phase transition depends distinctly on the width of the structure and a significant spin splitting of the edge states lying in the 2D band gap can be almost switched off by increasing the electric field in quantum wells only by a few percent. We show that the dependence of the spin splitting of the upper branch of the edge state dispersion curve on the wave vector has a threshold-like behavior with the on/off spin splitting ratio reaching two orders of magnitude for narrow Hall bars. The threshold wave vector depends weakly on the Hall bar width, whereas it increases significantly with the bias voltage due to an increase of the energetic distance between the s-type and p-type quantum well energy levels and a reduction of the coupling between the subbands.

An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1994-01-01

The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.

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.

Model many-body Stoner Hamiltonian for binary FeCr alloys

NASA Astrophysics Data System (ADS)

Nguyen-Manh, D.; Dudarev, S. L.

2009-09-01

We derive a model tight-binding many-body d -electron Stoner Hamiltonian for FeCr binary alloys and investigate the sensitivity of its mean-field solutions to the choice of hopping integrals and the Stoner exchange parameters. By applying the local charge-neutrality condition within a self-consistent treatment we show that the negative enthalpy-of-mixing anomaly characterizing the alloy in the low chromium concentration limit is due entirely to the presence of the on-site exchange Stoner terms and that the occurrence of this anomaly is not specifically related to the choice of hopping integrals describing conventional chemical bonding between atoms in the alloy. The Bain transformation pathway computed, using the proposed model Hamiltonian, for the Fe15Cr alloy configuration is in excellent agreement with ab initio total-energy calculations. Our investigation also shows how the parameters of a tight-binding many-body model Hamiltonian for a magnetic alloy can be derived from the comparison of its mean-field solutions with other, more accurate, mean-field approximations (e.g., density-functional calculations), hence stimulating the development of large-scale computational algorithms for modeling radiation damage effects in magnetic alloys and steels.

Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional

NASA Astrophysics Data System (ADS)

Chacón, Enrique; Tarazona, Pedro

2016-06-01

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional.

PubMed

Chacón, Enrique; Tarazona, Pedro

2016-06-22

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

The direct reaction field hamiltonian: Analysis of the dispersion term and application to the water dimer

NASA Astrophysics Data System (ADS)

Thole, B. T.; Van Duijnen, P. Th.

1982-10-01

The induction and dispersion terms obtained from quantum-mechanical calculations with a direct reaction field hamiltonian are compared to second order perturbation theory expressions. The dispersion term is shown to give an upper bound which is a generalization of Alexander's upper bound. The model is illustrated by a calculation on the interactions in the water dimer. The long range Coulomb, induction and dispersion interactions are reasonably reproduced.

Effective lattice Hamiltonian for monolayer tin disulfide: Tailoring electronic structure with electric and magnetic fields

NASA Astrophysics Data System (ADS)

Yu, Jin; van Veen, Edo; Katsnelson, Mikhail I.; Yuan, Shengjun

2018-06-01

The electronic properties of monolayer tin dilsulfide (ML -Sn S2 ), a recently synthesized metal dichalcogenide, are studied by a combination of first-principles calculations and tight-binding (TB) approximation. An effective lattice Hamiltonian based on six hybrid s p -like orbitals with trigonal rotation symmetry are proposed to calculate the band structure and density of states for ML -Sn S2 , which demonstrates good quantitative agreement with relativistic density-functional-theory calculations in a wide energy range. We show that the proposed TB model can be easily applied to the case of an external electric field, yielding results consistent with those obtained from full Hamiltonian results. In the presence of a perpendicular magnetic field, highly degenerate equidistant Landau levels are obtained, showing typical two-dimensional electron gas behavior. Thus, the proposed TB model provides a simple way in describing properties in ML -Sn S2 .

Canonical gravity, diffeomorphisms and objective histories

NASA Astrophysics Data System (ADS)

Samuel, Joseph

2000-11-01

This paper discusses the implementation of diffeomorphism invariance in purely Hamiltonian formulations of general relativity. We observe that, if a constrained Hamiltonian formulation derives from a manifestly covariant Lagrangian, the diffeomorphism invariance of the Lagrangian results in the following properties of the constrained Hamiltonian theory: the diffeomorphisms are generated by constraints on the phase space so that: (a) the algebra of the generators reflects the algebra of the diffeomorphism group; (b) the Poisson brackets of the basic fields with the generators reflects the spacetime transformation properties of these basic fields. This suggests that in a purely Hamiltonian approach the requirement of diffeomorphism invariance should be interpreted to include (b) and not just (a) as one might naively suppose. Giving up (b) amounts to giving up objective histories, even at the classical level. This observation has implications for loop quantum gravity which are spelled out in a companion paper. We also describe an analogy between canonical gravity and relativistic particle dynamics to illustrate our main point.

Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems

NASA Astrophysics Data System (ADS)

Si, Wen; Si, Jianguo

2018-06-01

This paper includes two parts. In the first part, we first focus on quasi-periodic time dependent perturbations of one-dimensional quasi-periodically forced systems with degenerate equilibrium. We study the system in two cases, for one of which system admits a response solution under a non-resonant condition on the frequency vector weaker than Brjuno–Rüssmann’s and for another of which system also admits a response solution without any non-resonant conditions. Next, we investigate the existence of response solutions of a quasi-periodic perturbed system with degenerate (including completely degenerate) equilibrium under Brjuno–Rüssmann’s non-resonant condition by using the Herman method. In the second part, we consider, firstly, the quasi-periodic perturbation of a universal unfolding of one-dimensional degenerate vector field . Secondly, we consider the perturbation of a universal unfolding of normal two-dimensional Hamiltonian system with completely degenerate equilibrium. With KAM theory and singularity theory, we show that these two classes of universal unfolding can persist on large Cantor sets under Brjuno–Rüssmann’s non-resonant condition, which implies all the invariant tori in the integrable part and all the bifurcation scenario can survive on large Cantor sets. The result for Hamiltonian system can apply directly to the response context for quasi-periodically forced systems. Our results in this paper can be regarded as an improvement with respect to several results in various literature (Broer et al 2005 Nonlinearity 18 1735–69 Broer et al 2006 J. Differ. Equ. 222 233–62 Wagener 2005 J. Differ. Equ. 216 216–81 Xu 2010 J. Differ. Equ. 250 551–71 Xu and Jiang 2010 Ergod. Theor. Dynam. Syst. 31 599–611 Lu and Xu 2014 Nonlinear Differ. Equ. Appl. 21 361–70). This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11171185, 11571201).

Fermion bag approach to Hamiltonian lattice field theories in continuous time

NASA Astrophysics Data System (ADS)

Huffman, Emilie; Chandrasekharan, Shailesh

2017-12-01

We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the 3 d Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find η =0.54 (6 ) and ν =0.88 (2 ) using lattices up to N =2304 sites. We argue that even sizes up to N =10 ,000 sites should be accessible with supercomputers available today.

Theoretical estimates of the width of light-meson states in the SO(4) (2+1)-flavor limit

NASA Astrophysics Data System (ADS)

Yépez-Martínez, Tochtli; Civitarese, Osvaldo; Hess, Peter Otto

The low-energy sector of the mesonic spectrum exhibits some features which may be understood in terms of the SO(4) symmetry contained in the QCD-Hamiltonian written in the Coulomb Gauge. In our previous work, we have shown that this is indeed the case when the Instantaneous Color-Charge Interaction (ICCI) is treated by means of nonperturbative many-body techniques. Continuing along this line of description, in this work we calculate the width of meson states belonging to the low portion of the spectrum (E < 1 GeV). In spite of the rather simple structure of the Hamiltonian used to calculate the spectra of pseudoscalar and vector mesons, the results for the width of these states follow the pattern of the data.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

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

Park, Jae Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr; Department of Chemistry, Pohang University of Science and Technology

2014-04-28

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabaticmore » transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.« less

Time and a physical Hamiltonian for quantum gravity.

PubMed

Husain, Viqar; Pawłowski, Tomasz

2012-04-06

We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society

Quasi-stationary states and fermion pair creation from a vacuum in supercritical Coulomb field

NASA Astrophysics Data System (ADS)

Khalilov, V. R.

2017-12-01

Creation of charged fermion pair from a vacuum in so-called supercritical Coulomb potential is examined for the case when fermions can move only in the same (one) plane. In which case, quantum dynamics of charged massive or massless fermions can be described by the two-dimensional Dirac Hamiltonians with an usual (-a/r) Coulomb potential. These Hamiltonians are singular and require the additional definition in order for them to be treated as self-adjoint quantum-mechanical operators. We construct the self-adjoint two-dimensional Dirac Hamiltonians with a Coulomb potential and determine the quantum-mechanical states for such Hamiltonians in the corresponding Hilbert spaces of square-integrable functions. We determine the scattering amplitude in which the self-adjoint extension parameter is incorporated and then obtain equations implicitly defining possible discrete energy spectra of the self-adjoint Dirac Hamiltonians with a Coulomb potential. It is shown that this quantum system becomes unstable in the presence of a supercritical Coulomb potential which manifests in the appearance of quasi-stationary states in the lower (negative) energy continuum. The energy spectrum of those states is quasi-discrete, consists of broadened levels with widths related to the inverse lifetimes of the quasi-stationary states as well as the probability of creation of charged fermion pair by a supercritical Coulomb field. Explicit analytical expressions for the creation probabilities of charged (massive or massless) fermion pair are obtained in a supercritical Coulomb field.

Transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Hiday, L. A.; Howell, K. C.

The present time-fixed impulsive transfers between 3D libration point orbits in the vicinity of the interior L(1) libration point of the sun-earth-moon barycenter system are 'optimal' in that the total characteristic velocity required for implementation of the transfer exhibits a local minimum. The conditions necessary for a time-fixed, two-impulse transfer trajectory to be optimal are stated in terms of the primer vector, and the conditions necessary for satisfying the local optimality of a transfer trajectory containing additional impulses are addressed by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses.

A general approach to the electronic spin relaxation of Gd(III) complexes in solutions. Monte Carlo simulations beyond the Redfield limit

NASA Astrophysics Data System (ADS)

Rast, S.; Fries, P. H.; Belorizky, E.; Borel, A.; Helm, L.; Merbach, A. E.

2001-10-01

The time correlation functions of the electronic spin components of a metal ion without orbital degeneracy in solution are computed. The approach is based on the numerical solution of the time-dependent Schrödinger equation for a stochastic perturbing Hamiltonian which is simulated by a Monte Carlo algorithm using discrete time steps. The perturbing Hamiltonian is quite general, including the superposition of both the static mean crystal field contribution in the molecular frame and the usual transient ligand field term. The Hamiltonian of the static crystal field can involve the terms of all orders, which are invariant under the local group of the average geometry of the complex. In the laboratory frame, the random rotation of the complex is the only source of modulation of this Hamiltonian, whereas an additional Ornstein-Uhlenbeck process is needed to describe the time fluctuations of the Hamiltonian of the transient crystal field. A numerical procedure for computing the electronic paramagnetic resonance (EPR) spectra is proposed and discussed. For the [Gd(H2O)8]3+ octa-aqua ion and the [Gd(DOTA)(H2O)]- complex [DOTA=1,4,7,10-tetrakis(carboxymethyl)-1,4,7,10-tetraazacyclo dodecane] in water, the predictions of the Redfield relaxation theory are compared with those of the Monte Carlo approach. The Redfield approximation is shown to be accurate for all temperatures and for electronic resonance frequencies at and above X-band, justifying the previous interpretations of EPR spectra. At lower frequencies the transverse and longitudinal relaxation functions derived from the Redfield approximation display significantly faster decays than the corresponding simulated functions. The practical interest of this simulation approach is underlined.

Second rank direction cosine spherical tensor operators and the nuclear electric quadrupole hyperfine structure Hamiltonian of rotating molecules

NASA Astrophysics Data System (ADS)

di Lauro, C.

2018-03-01

Transformations of vector or tensor properties from a space-fixed to a molecule-fixed axis system are often required in the study of rotating molecules. Spherical components λμ,ν of a first rank irreducible tensor can be obtained from the direction cosines between the two axis systems, and a second rank tensor with spherical components λμ,ν(2) can be built from the direct product λ × λ. It is shown that the treatment of the interaction between molecular rotation and the electric quadrupole of a nucleus is greatly simplified, if the coefficients in the axis-system transformation of the gradient of the electric field of the outer charges at the coupled nucleus are arranged as spherical components λμ,ν(2). Then the reduced matrix elements of the field gradient operators in a symmetric top eigenfunction basis, including their dependence on the molecule-fixed z-angular momentum component k, can be determined from the knowledge of those of λ(2) . The hyperfine structure Hamiltonian Hq is expressed as the sum of terms characterized each by a value of the molecule-fixed index ν, whose matrix elements obey the rule Δk = ν. Some of these terms may vanish because of molecular symmetry, and the specific cases of linear and symmetric top molecules, orthorhombic molecules, and molecules with symmetry lower than orthorhombic are considered. Each ν-term consists of a contraction of the rotational tensor λ(2) and the nuclear quadrupole tensor in the space-fixed frame, and its matrix elements in the rotation-nuclear spin coupled representation can be determined by the standard spherical tensor methods.

Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints

NASA Astrophysics Data System (ADS)

Krasovskii, A. A.; Lebedev, P. D.; Tarasyev, A. M.

2017-05-01

We consider a neoclassical (economic) growth model. A nonlinear Ramsey equation, modeling capital dynamics, in the case of Cobb-Douglas production function is reduced to the linear differential equation via a Bernoulli substitution. This considerably facilitates the search for a solution to the optimal growth problem with logarithmic preferences. The study deals with solving the corresponding infinite horizon optimal control problem. We consider a vector field of the Hamiltonian system in the Pontryagin maximum principle, taking into account control constraints. We prove the existence of two alternative steady states, depending on the constraints. A proposed algorithm for constructing growth trajectories combines methods of open-loop control and closed-loop regulatory control. For some levels of constraints and initial conditions, a closed-form solution is obtained. We also demonstrate the impact of technological change on the economic equilibrium dynamics. Results are supported by computer calculations.

Four-dimensional gravity as an almost-Poisson system

NASA Astrophysics Data System (ADS)

Ita, Eyo Eyo

2015-04-01

In this paper, we examine the phase space structure of a noncanonical formulation of four-dimensional gravity referred to as the Instanton representation of Plebanski gravity (IRPG). The typical Hamiltonian (symplectic) approach leads to an obstruction to the definition of a symplectic structure on the full phase space of the IRPG. We circumvent this obstruction, using the Lagrange equations of motion, to find the appropriate generalization of the Poisson bracket. It is shown that the IRPG does not support a Poisson bracket except on the vector constraint surface. Yet there exists a fundamental bilinear operation on its phase space which produces the correct equations of motion and induces the correct transformation properties of the basic fields. This bilinear operation is known as the almost-Poisson bracket, which fails to satisfy the Jacobi identity and in this case also the condition of antisymmetry. We place these results into the overall context of nonsymplectic systems.

Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes

NASA Astrophysics Data System (ADS)

Marvian, Milad; Lidar, Daniel A.

2017-01-01

We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.

Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes.

PubMed

Marvian, Milad; Lidar, Daniel A

2017-01-20

We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.

Simulating electric field interactions with polar molecules using spectroscopic databases

NASA Astrophysics Data System (ADS)

Owens, Alec; Zak, Emil J.; Chubb, Katy L.; Yurchenko, Sergei N.; Tennyson, Jonathan; Yachmenev, Andrey

2017-03-01

Ro-vibrational Stark-associated phenomena of small polyatomic molecules are modelled using extensive spectroscopic data generated as part of the ExoMol project. The external field Hamiltonian is built from the computed ro-vibrational line list of the molecule in question. The Hamiltonian we propose is general and suitable for any polar molecule in the presence of an electric field. By exploiting precomputed data, the often prohibitively expensive computations associated with high accuracy simulations of molecule-field interactions are avoided. Applications to strong terahertz field-induced ro-vibrational dynamics of PH3 and NH3, and spontaneous emission data for optoelectrical Sisyphus cooling of H2CO and CH3Cl are discussed.

Global Melnikov Theory in Hamiltonian Systems with General Time-Dependent Perturbations

NASA Astrophysics Data System (ADS)

Gidea, Marian; de la Llave, Rafael

2018-04-01

We consider a mechanical system consisting of n-penduli and a d-degree-of-freedom rotator. The phase space of the rotator defines a normally hyperbolic invariant manifold Λ _0 . We apply a time-dependent perturbation, which is not assumed to be either Hamiltonian, or periodic, or quasi-periodic, as we allow for rather general time dependence. The strength of the perturbation is given by a parameter ɛ \\in R . For all |ɛ | sufficiently small, the augmented flow—obtained by making the time into a new variable—has a normally hyperbolic locally invariant manifold \\tilde{Λ }_ɛ . For ɛ =0 , \\tilde{Λ }_0=Λ _0× R . We define a Melnikov-type vector, which gives the first-order expansion of the displacement of the stable and unstable manifolds of \\tilde{Λ }_0 under the perturbation. We provide an explicit formula for the Melnikov vector in terms of convergent improper integrals of the perturbation along homoclinic orbits of the unperturbed system. We show that if the perturbation satisfies some explicit non-degeneracy conditions, then the stable and unstable manifolds of \\tilde{Λ }_ɛ , W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) , respectively, intersect along a transverse homoclinic manifold, and, moreover, the splitting of W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) can be explicitly computed, up to the first order, in terms of the Melnikov-type vector. This implies that the excursions along some homoclinic trajectories yield a non-trivial increase of order O(ɛ ) in the action variables of the rotator, for all sufficiently small perturbations. The formulas that we obtain are independent of the unperturbed motions in Λ _0 , and give, at the same time, the effects on periodic, quasi-periodic, or general-type orbits. When the perturbation is Hamiltonian, we express the effects of the perturbation, up to the first order, in terms of a Melnikov potential. In addition, if the perturbation is periodic, we obtain that the non-degeneracy conditions on the Melnikov potential are generic.

Effective Hamiltonians for correlated narrow energy band systems and magnetic insulators: Role of spin-orbit interactions in metal-insulator transitions and magnetic phase transitions

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

Chakraborty, Subrata; Vijay, Amrendra, E-mail: avijay@iitm.ac.in

Using a second-quantized many-electron Hamiltonian, we obtain (a) an effective Hamiltonian suitable for materials whose electronic properties are governed by a set of strongly correlated bands in a narrow energy range and (b) an effective spin-only Hamiltonian for magnetic materials. The present Hamiltonians faithfully include phonon and spin-related interactions as well as the external fields to study the electromagnetic response properties of complex materials and they, in appropriate limits, reduce to the model Hamiltonians due to Hubbard and Heisenberg. With the Hamiltonian for narrow-band strongly correlated materials, we show that the spin-orbit interaction provides a mechanism for metal-insulator transition, whichmore » is distinct from the Mott-Hubbard (driven by the electron correlation) and the Anderson mechanism (driven by the disorder). Next, with the spin-only Hamiltonian, we demonstrate the spin-orbit interaction to be a reason for the existence of antiferromagnetic phase in materials which are characterized by a positive isotropic spin-exchange energy. This is distinct from the Néel-VanVleck-Anderson paradigm which posits a negative spin-exchange for the existence of antiferromagnetism. We also find that the Néel temperature increases as the absolute value of the spin-orbit coupling increases.« less

Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, Diego

We study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and N-> infty kinetic limit (where N is the number of particles). The linear stability of equilibria in the kinetic model is studied as well as the initial value problem including Landau damping . Numerical simulations show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles and show that the N=2 limit has a family of rotating integrable solutions that provide an accurate description of the dynamics. We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.

Force Analysis and Energy Operation of Chaotic System of Permanent-Magnet Synchronous Motor

NASA Astrophysics Data System (ADS)

Qi, Guoyuan; Hu, Jianbing

2017-12-01

The disadvantage of a nondimensionalized model of a permanent-magnet synchronous Motor (PMSM) is identified. The original PMSM model is transformed into a Kolmogorov system to aid dynamic force analysis. The vector field of the PMSM is analogous to the force field including four types of torque — inertial, internal, dissipative, and generalized external. Using the feedback thought, the error torque between external torque and dissipative torque is identified. The pitchfork bifurcation of the PMSM is performed. Four forms of energy are identified for the system — kinetic, potential, dissipative, and supplied. The physical interpretations of the decomposition of force and energy exchange are given. Casimir energy is stored energy, and its rate of change is the error power between the dissipative energy and the energy supplied to the motor. Error torque and error power influence the different types of dynamic modes. The Hamiltonian energy and Casimir energy are compared to find the function of each in producing the dynamic modes. A supremum bound for the chaotic attractor is proposed using the error power and Lagrange multiplier.

Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians.

PubMed

Ghassemi Tabrizi, Shadan; Arbuznikov, Alexei V; Kaupp, Martin

2018-03-26

Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl] 4 ('Ni 4 ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp - is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni 4 , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Functional level-set derivative for a polymer self consistent field theory Hamiltonian

NASA Astrophysics Data System (ADS)

Ouaknin, Gaddiel; Laachi, Nabil; Bochkov, Daniil; Delaney, Kris; Fredrickson, Glenn H.; Gibou, Frederic

2017-09-01

We derive functional level-set derivatives for the Hamiltonian arising in self-consistent field theory, which are required to solve free boundary problems in the self-assembly of polymeric systems such as block copolymer melts. In particular, we consider Dirichlet, Neumann and Robin boundary conditions. We provide numerical examples that illustrate how these shape derivatives can be used to find equilibrium and metastable structures of block copolymer melts with a free surface in both two and three spatial dimensions.

The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

DOE PAGES

Dubček, Tena; Lelas, Karlo; Jukić, Dario; ...

2015-12-07

Here we propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. Lastly, we compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.

Explicitly-correlated non-born-oppenheimer calculations of the HD molecule in a strong magnetic field

NASA Astrophysics Data System (ADS)

Adamowicz, Ludwik; Stanke, Monika; Tellgren, Erik; Helgaker, Trygve

2017-08-01

Explicitly correlated all-particle Gaussian functions with shifted centers (ECGs) are implemented within the earlier proposed effective variational non-Born-Oppenheimer method for calculating bound states of molecular systems in magnetic field (Adamowicz et al., 2015). The Hamiltonian used in the calculations is obtained by subtracting the operator representing the kinetic energy of the center-of-mass motion from the total laboratory-frame Hamiltonian. Test ECG calculations are performed for the HD molecule.

Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Tavan, Paul; Mathias, Gerald

2014-03-01

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call "Hamiltonian dielectric solvent" (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

Diagonalizing the Hamiltonian of λϕ4 theory in 2 space-time dimensions

NASA Astrophysics Data System (ADS)

Christensen, Neil

2018-01-01

We propose a new non-perturbative technique for calculating the scattering amplitudes of field-theory directly from the eigenstates of the Hamiltonian. Our method involves a discretized momentum space and a momentum cutoff, thereby truncating the Hilbert space and making numerical diagonalization of the Hamiltonian achievable. We show how to do this in the context of a simplified λϕ4 theory in two space-time dimensions. We present the results of our diagonalization, its dependence on time, its dependence on the parameters of the theory and its renormalization.

Exploring Hamiltonian dielectric solvent molecular dynamics

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Tavan, Paul; Mathias, Gerald

2014-09-01

Hamiltonian dielectric solvent (HADES) is a recent method [7,25], which enables Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric continua. Sample simulations of an α-helical decapeptide with and without explicit solvent demonstrate the high efficiency of HADES-MD. Addressing the folding of this peptide by replica exchange MD we study the properties of HADES by comparing melting curves, secondary structure motifs and salt bridges with explicit solvent results. Despite the unoptimized ad hoc parametrization of HADES, calculated reaction field energies correlate well with numerical grid solutions of the dielectric Poisson equation.

Steepest entropy ascent for two-state systems with slowly varying Hamiltonians

NASA Astrophysics Data System (ADS)

Militello, Benedetto

2018-05-01

The steepest entropy ascent approach is considered and applied to two-state systems. When the Hamiltonian of the system is time-dependent, the principle of maximum entropy production can still be exploited; arguments to support this fact are given. In the limit of slowly varying Hamiltonians, which allows for the adiabatic approximation for the unitary part of the dynamics, the system exhibits significant robustness to the thermalization process. Specific examples such as a spin in a rotating field and a generic two-state system undergoing an avoided crossing are considered.

Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes

NASA Astrophysics Data System (ADS)

Kowalski, A. M.; Rossignoli, R.

2018-04-01

We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian, and possesses stable and unstable regimes. The dynamics of the whole system is shown to be strongly influenced by the quantum subsystem. In particular, chaos is seen to arise in the vicinity of a quantum critical case, which separates the stable and unstable regimes of the bosonic system.

A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate an arbitrary finite change of gauge-fixing functions in the path integral.

An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

NASA Astrophysics Data System (ADS)

Turkington, Bruce

2013-08-01

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter.

Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches

NASA Astrophysics Data System (ADS)

Antonowicz, Marek; Szczyrba, Wiktor

1985-06-01

We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.

Unidirectional Wave Vector Manipulation in Two-Dimensional Space with an All Passive Acoustic Parity-Time-Symmetric Metamaterials Crystal

NASA Astrophysics Data System (ADS)

Liu, Tuo; Zhu, Xuefeng; Chen, Fei; Liang, Shanjun; Zhu, Jie

2018-03-01

Exploring the concept of non-Hermitian Hamiltonians respecting parity-time symmetry with classical wave systems is of great interest as it enables the experimental investigation of parity-time-symmetric systems through the quantum-classical analogue. Here, we demonstrate unidirectional wave vector manipulation in two-dimensional space, with an all passive acoustic parity-time-symmetric metamaterials crystal. The metamaterials crystal is constructed through interleaving groove- and holey-structured acoustic metamaterials to provide an intrinsic parity-time-symmetric potential that is two-dimensionally extended and curved, which allows the flexible manipulation of unpaired wave vectors. At the transition point from the unbroken to broken parity-time symmetry phase, the unidirectional sound focusing effect (along with reflectionless acoustic transparency in the opposite direction) is experimentally realized over the spectrum. This demonstration confirms the capability of passive acoustic systems to carry the experimental studies on general parity-time symmetry physics and further reveals the unique functionalities enabled by the judiciously tailored unidirectional wave vectors in space.

Spin Hamiltonian Analysis of the SMM V15 Using High Field ESR

NASA Astrophysics Data System (ADS)

Martens, Mathew; van Tol, Hans; Bertaina, Sylvain; Barbara, Bernard; Muller, Achim; Chiorescu, Irinel

2014-03-01

We have studied molecular magnets using high field / high frequency Electron Spin Resonance. Such molecular structures contain many quantum spins linked by exchange interactions and consequently their energy structure is often complex and require a good understanding of the molecular spin Hamiltonian. In particular, we studied the V15 molecule, comprised of 15 spins 1/2 and a total spin 1/2, which is a system that recently showed quantum Rabi oscillations of its total quantum spin. This type of molecule is an essential system for advancing molecular structures into quantum computing. We used high frequency characterization techniques (of hundreds of GHz) to gain insight into the exchange anisotropy interactions, crystal field, and anti-symmetric interactions present in this system. We analyzed the data using a detailed numerical analysis of spin interactions and our findings regarding the V15 spin Hamiltonian will be discussed. Supported by the NSF Cooperative Agreement Grant No. DMR-0654118 and No. NHMFL UCGP 5059, NSF grant No. DMR-0645408.

Higher spin conformal geometry in three dimensions and prepotentials for higher spin gauge fields

NASA Astrophysics Data System (ADS)

Henneaux, Marc; Hörtner, Sergio; Leonard, Amaury

2016-01-01

We study systematically the conformal geometry of higher spin bosonic gauge fields in three spacetime dimensions. We recall the definition of the Cotton tensor for higher spins and establish a number of its properties that turn out to be key in solving in terms of prepotentials the constraint equations of the Hamiltonian (3 + 1) formulation of four-dimensional higher spin gauge fields. The prepotentials are shown to exhibit higher spin conformal symmetry. Just as for spins 1 and 2, they provide a remarkably simple, manifestly duality invariant formulation of the theory. While the higher spin conformal geometry is developed for arbitrary bosonic spin, we explicitly perform the Hamiltonian analysis and derive the solution of the constraints only in the illustrative case of spin 3. In a separate publication, the Hamiltonian analysis in terms of prepotentials is extended to all bosonic higher spins using the conformal tools of this paper, and the same emergence of higher spin conformal symmetry is confirmed.

Gravitational Field as a Pressure Force from Logarithmic Lagrangians and Non-Standard Hamiltonians: The Case of Stellar Halo of Milky Way

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2018-03-01

Recently, the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations. Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties. One interesting form related to the inverse variational problem is the logarithmic Lagrangian, which has a number of motivating features related to the Liénard-type and Emden nonlinear differential equations. Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians. In this communication, we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians. One interesting consequence concerns the emergence of an extra pressure term, which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field. The case of the stellar halo of the Milky Way is considered.

Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

NASA Astrophysics Data System (ADS)

Cirilo António, N.; Manojlović, N.; Salom, I.

2014-12-01

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

Phase separation in solution of worm-like micelles: a dilute ? spin-vector model

NASA Astrophysics Data System (ADS)

Panizza, Pascal; Cristobal, Galder; Curély, Jacques

1998-12-01

We show how the dilute 0953-8984/10/50/006/img2 spin vector model introduced originally by Wheeler and co-workers for describing the polymerization phenomenon in solutions of liquid sulphur and of living polymers may be conveniently adapted for studying phase separation in systems containing long flexible micelles. We draw an isomorphism between the coupling constant appearing in the exchange Hamiltonian and the surfactant energies in the micellar problem. We solve this problem within the mean-field approximation and compare the main results we have obtained with respect to polymer theory and previous theories of phase separation in micellar solutions. We show that the attractive interaction term 0953-8984/10/50/006/img3 between monomers renormalizes the aggregation energy and subsequently the corresponding size distribution. Under these conditions, we observe that the general aspect of the phase diagram in the 0953-8984/10/50/006/img4 plane (where 0953-8984/10/50/006/img5 is the surfactant concentration) is different from previous results. The spinodal line shows a re-entrant behaviour and, at low concentrations, we point out the possibility of specific nucleation phenomena related to the existence of a metastable transition line between a region composed of spherical micelles and another one corresponding to a dilute solution of long flexible micelles.

Kondo effect in systems with dynamical symmetries

NASA Astrophysics Data System (ADS)

Kuzmenko, T.; Kikoin, K.; Avishai, Y.

2004-05-01

This paper is devoted to a systematic exposure of the Kondo physics in quantum dots for which the low-energy spin excitations consist of a few different spin multiplets |SiMi>. Under certain conditions (to be explained below), some of the lowest energy levels ESi are nearly degenerate. The dot in its ground state cannot then be regarded as a simple quantum top, in the sense that beside its spin operator other dot (vector) operators Rn are needed (in order to fully determine its quantum states), which have nonzero matrix elements between states of different spin multiplets ≠0. These Runge-Lenz operators do not appear in the isolated dot Hamiltonian (so in some sense they are “hidden”). Yet, they are exposed when tunneling between dot and leads is switched on. The effective spin Hamiltonian which couples the metallic electron spin s with the operators of the dot then contains exchange terms JnsṡRn besides the ubiquitous ones JisṡSi. The operators Si and Rn generate a dynamical group [usually SO(n)]. Remarkably, the value of n can be controlled by gate voltages, indicating that abstract concepts such as dynamical symmetry groups are experimentally realizable. Moreover, when an external magnetic field is applied, under favorable circumstances the exchange interaction involves solely the Runge-Lenz operators Rn and the corresponding dynamical symmetry group is SU(n). For example, the celebrated group SU(3) is realized in a triple quantum dot with four electrons.

Valley- and spin-filter in monolayer MoS2

NASA Astrophysics Data System (ADS)

Majidi, Leyla; Zare, Moslem; Asgari, Reza

2014-12-01

We propose a valley- and spin-filter based on a normal/ferromagnetic/normal molybdenum disulfide (MoS2) junction where the polarizations of the valley and the spin can be inverted by reversing the direction of the exchange field in the ferromagnetic region. By using a modified Dirac Hamiltonian and the scattering formalism, we find that the polarizations can be tuned by applying a gate voltage and changing the exchange field in the structure. We further demonstrate that the presence of a topological term (β) in the Hamiltonian results in an enhancement or a reduction of the charge conductance depending on the value of the exchange field.

A systematic study of finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.

Higher Order First Integrals of Motion in a Gauge Covariant Hamiltonian Framework

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out.

Higher-dimensional Wannier functions of multiparameter Hamiltonians

NASA Astrophysics Data System (ADS)

Hanke, Jan-Philipp; Freimuth, Frank; Blügel, Stefan; Mokrousov, Yuriy

2015-05-01

When using Wannier functions to study the electronic structure of multiparameter Hamiltonians H(k ,λ ) carrying a dependence on crystal momentum k and an additional periodic parameter λ , one usually constructs several sets of Wannier functions for a set of values of λ . We present the concept of higher-dimensional Wannier functions (HDWFs), which provide a minimal and accurate description of the electronic structure of multiparameter Hamiltonians based on a single set of HDWFs. The obstacle of nonorthogonality of Bloch functions at different λ is overcome by introducing an auxiliary real space, which is reciprocal to the parameter λ . We derive a generalized interpolation scheme and emphasize the essential conceptual and computational simplifications in using the formalism, for instance, in the evaluation of linear response coefficients. We further implement the necessary machinery to construct HDWFs from ab initio within the full potential linearized augmented plane-wave method (FLAPW). We apply our implementation to accurately interpolate the Hamiltonian of a one-dimensional magnetic chain of Mn atoms in two important cases of λ : (i) the spin-spiral vector q and (ii) the direction of the ferromagnetic magnetization m ̂. Using the generalized interpolation of the energy, we extract the corresponding values of magnetocrystalline anisotropy energy, Heisenberg exchange constants, and spin stiffness, which compare very well with the values obtained from direct first principles calculations. For toy models we demonstrate that the method of HDWFs can also be used in applications such as the virtual crystal approximation, ferroelectric polarization, and spin torques.

Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

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

Tronko, Natalia; Brizard, Alain J.

A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint onmore » the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.« less

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.

Hamiltonian models for topological phases of matter in three spatial dimensions

NASA Astrophysics Data System (ADS)

Williamson, Dominic J.; Wang, Zhenghan

2017-02-01

We present commuting projector Hamiltonian realizations of a large class of (3 + 1)D topological models based on mathematical objects called unitary G-crossed braided fusion categories. This construction comes with a wealth of examples from the literature of symmetry-enriched topological phases. The spacetime counterparts to our Hamiltonians are unitary state sum topological quantum fields theories (TQFTs) that appear to capture all known constructions in the literature, including the Crane-Yetter-Walker-Wang and 2-Group gauge theory models. We also present Hamiltonian realizations of a state sum TQFT recently constructed by Kashaev whose relation to existing models was previously unknown. We argue that this TQFT is captured as a special case of the Crane-Yetter-Walker-Wang model, with a premodular input category in some instances.

Communication: Relativistic Fock-space coupled cluster study of small building blocks of larger uranium complexes.

PubMed

Tecmer, Paweł; Gomes, André Severo Pereira; Knecht, Stefan; Visscher, Lucas

2014-07-28

We present a study of the electronic structure of the [UO2](+), [UO2](2 +), [UO2](3 +), NUO, [NUO](+), [NUO](2 +), [NUN](-), NUN, and [NUN](+) molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin-orbit coupling and Gaunt interactions are compared to results obtained with the Dirac-Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity).

Communication: Relativistic Fock-space coupled cluster study of small building blocks of larger uranium complexes

NASA Astrophysics Data System (ADS)

Tecmer, Paweł; Severo Pereira Gomes, André; Knecht, Stefan; Visscher, Lucas

2014-07-01

We present a study of the electronic structure of the [UO2]+, [UO2]2 +, [UO2]3 +, NUO, [NUO]+, [NUO]2 +, [NUN]-, NUN, and [NUN]+ molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin-orbit coupling and Gaunt interactions are compared to results obtained with the Dirac-Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity).

Multi-Lagrangians for integrable systems

NASA Astrophysics Data System (ADS)

Nutku, Y.; Pavlov, M. V.

2002-03-01

We propose a general scheme to construct multiple Lagrangians for completely integrable nonlinear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit N-fold first order local Hamiltonian structure can be cast into variational form with 2N-1 Lagrangians which will be local functionals of Clebsch potentials. This number increases to 3N-2 when the Miura transformation is invertible. Furthermore we construct a new Lagrangian for polytropic gas dynamics in 1+1 dimensions which is a free, local functional of the physical field variables, namely density and velocity, thus dispensing with the necessity of introducing Clebsch potentials entirely. This is a consequence of bi-Hamiltonian structure with a compatible pair of first and third order Hamiltonian operators derived from Sheftel's recursion operator.

Reducing the two-body problem in scalar-tensor theories to the motion of a test particle: A scalar-tensor effective-one-body approach

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis

2018-01-01

Starting from the second post-Keplerian (2PK) Hamiltonian describing the conservative part of the two-body dynamics in massless scalar-tensor (ST) theories, we build an effective-one-body (EOB) Hamiltonian which is a ν deformation (where ν =0 is the test mass limit) of the analytically known ST Hamiltonian of a test particle. This ST-EOB Hamiltonian leads to a simple (yet canonically equivalent) formulation of the conservative 2PK two-body problem, but also defines a resummation of the dynamics which is well-suited to ST regimes that depart strongly from general relativity (GR) and which may provide information on the strong field dynamics; in particular, the ST innermost stable circular orbit location and associated orbital frequency. Results will be compared and contrasted with those deduced from the ST-deformation of the (5PN) GR-EOB Hamiltonian previously obtained in [Phys. Rev. D 95, 124054 (2017), 10.1103/PhysRevD.95.124054].

Reducible boundary conditions in coupled channels

NASA Astrophysics Data System (ADS)

Pankrashkin, Konstantin

2005-10-01

We study Hamiltonians with point interactions in spaces of vector-valued functions. Using some information from the theory of quantum graphs, we describe a class of the operators which can be reduced to the direct sum of several one-dimensional problems. It shown that such a reduction is closely connected with the invariance under channel permutations. Examples are provided by some 'model' interactions, in particular, the so-called δ, δ' and the Kirchhoff couplings.

Effective field theory for triaxially deformed nuclei

NASA Astrophysics Data System (ADS)

Chen, Q. B.; Kaiser, N.; Meißner, Ulf-G.; Meng, J.

2017-10-01

Effective field theory is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. The Hamiltonian for the triaxial rotor is obtained up to next-to-leading order within the effective field theory formalism. Its applicability is examined by comparing with a five-dimensional rotor-vibrator Hamiltonian for the description of the energy spectra of the ground state and γ band in Ru isotopes. It is found that by taking into account the next-to-leading order corrections, the ground state band in the whole spin region and the γ band in the low spin region are well described. The deviations for high-spin states in the γ bands point towards the importance of including vibrational degrees of freedom in the effective field theory formulation.

Entanglement Dynamics of Linear and Nonlinear Interaction of Two Two-Level Atoms with a Quantized Phase-Damped Field in the Dispersive Regime

NASA Astrophysics Data System (ADS)

Tavassoly, M. K.; Daneshmand, R.; Rustaee, N.

2018-06-01

In this paper we study the linear and nonlinear (intensity-dependent) interactions of two two-level atoms with a single-mode quantized field far from resonance, while the phase-damping effect is also taken into account. To find the analytical solution of the atom-field state vector corresponding to the considered model, after deducing the effective Hamiltonian we evaluate the time-dependent elements of the density operator using the master equation approach and superoperator method. Consequently, we are able to study the influences of the special nonlinearity function f (n) = √ {n}, the intensity of the initial coherent state field and the phase-damping parameter on the degree of entanglement of the whole system as well as the field and atom. It is shown that in the presence of damping, by passing time, the amount of entanglement of each subsystem with the rest of system, asymptotically reaches to its stationary and maximum value. Also, the nonlinear interaction does not have any effect on the entanglement of one of the atoms with the rest of system, but it changes the amplitude and time period of entanglement oscillations of the field and the other atom. Moreover, this may cause that, the degree of entanglement which may be low (high) at some moments of time becomes high (low) by entering the intensity-dependent function in the atom-field coupling.

Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems

NASA Astrophysics Data System (ADS)

Tonni, Erik; Rodríguez-Laguna, Javier; Sierra, Germán

2018-04-01

Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.

Exponentially-Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians

NASA Technical Reports Server (NTRS)

Mandra, Salvatore

2017-01-01

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated to a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.

Two-color Fermi-liquid theory for transport through a multilevel Kondo impurity

NASA Astrophysics Data System (ADS)

Karki, D. B.; Mora, Christophe; von Delft, Jan; Kiselev, Mikhail N.

2018-05-01

We consider a quantum dot with K ≥2 orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multilevel Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel S =1 Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fermi liquid. Using nonequilibrium (Keldysh) perturbation theory around the strong-coupling fixed point we analyze the transport properties of the model at finite temperature, Zeeman magnetic field, and source-drain voltage applied across the quantum dot. We compute the Fermi-liquid transport constants and discuss different universality classes associated with emergent symmetries.

Quantitative conditions for time evolution in terms of the von Neumann equation

NASA Astrophysics Data System (ADS)

Wang, WenHua; Cao, HuaiXin; Chen, ZhengLi; Wang, Lie

2018-07-01

The adiabatic theorem describes the time evolution of the pure state and gives an adiabatic approximate solution to the Schödinger equation by choosing a single eigenstate of the Hamiltonian as the initial state. In quantum systems, states are divided into pure states (unite vectors) and mixed states (density matrices, i.e., positive operators with trace one). Accordingly, mixed states have their own corresponding time evolution, which is described by the von Neumann equation. In this paper, we discuss the quantitative conditions for the time evolution of mixed states in terms of the von Neumann equation. First, we introduce the definitions for uniformly slowly evolving and δ-uniformly slowly evolving with respect to mixed states, then we present a necessary and sufficient condition for the Hamiltonian of the system to be uniformly slowly evolving and we obtain some upper bounds for the adiabatic approximate error. Lastly, we illustrate our results in an example.

Computing resonance energies, widths, and wave functions using a Lanczos method in real arithmetic.

PubMed

Tremblay, Jean Christophe; Carrington, Tucker

2005-06-22

We introduce new ideas for calculating resonance energies and widths. It is shown that a non-Hermitian-Lanczos approach can be used to compute eigenvalues of H+W, where H is the Hamiltonian and W is a complex absorbing potential (CAP), without evaluating complex matrix-vector products. This is done by exploiting the link between a CAP-modified Hamiltonian matrix and a real but nonsymmetric matrix U suggested by Mandelshtam and Neumaier [J. Theor. Comput. Chem. 1, 1 (2002)] and using a coupled-two-term Lanczos procedure. We use approximate resonance eigenvectors obtained from the non-Hermitian-Lanczos algorithm and a very good CAP to obtain very accurate energies and widths without solving eigenvalue problems for many values of the CAP strength parameter and searching for cusps. The method is applied to the resonances of HCO. We compare properties of the method with those of established approaches.

Improved Spectral Calculations for Discrete Schrődinger Operators

NASA Astrophysics Data System (ADS)

Puelz, Charles

This work details an O(n2) algorithm for computing spectra of discrete Schrődinger operators with periodic potentials. Spectra of these objects enhance our understanding of fundamental aperiodic physical systems and contain rich theoretical structure of interest to the mathematical community. Previous work on the Harper model led to an O(n2) algorithm relying on properties not satisfied by other aperiodic operators. Physicists working with the Fibonacci Hamiltonian, a popular quasicrystal model, have instead used a problematic dynamical map approach or a sluggish O(n3) procedure for their calculations. The algorithm presented in this work, a blend of well-established eigenvalue/vector algorithms, provides researchers with a more robust computational tool of general utility. Application to the Fibonacci Hamiltonian in the sparsely studied intermediate coupling regime reveals structure in canonical coverings of the spectrum that will prove useful in motivating conjectures regarding band combinatorics and fractal dimensions.

On the definition of the time evolution operator for time-independent Hamiltonians in non-relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.

2017-09-01

The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.

Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme

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

Levi, Michele; Steinhoff, Jan, E-mail: michele.levi@upmc.fr, E-mail: jan.steinhoff@aei.mpg.de

2016-01-01

We implement the effective field theory for gravitating spinning objects in the post-Newtonian scheme at the next-to-next-to-leading order level to derive the gravitational spin-orbit interaction potential at the third and a half post-Newtonian order for rapidly rotating compact objects. From the next-to-next-to-leading order interaction potential, which we obtain here in a Lagrangian form for the first time, we derive straightforwardly the corresponding Hamiltonian. The spin-orbit sector constitutes the most elaborate spin dependent sector at each order, and accordingly we encounter a proliferation of the relevant Feynman diagrams, and a significant increase of the computational complexity. We present in detail themore » evaluation of the interaction potential, going over all contributing Feynman diagrams. The computation is carried out in terms of the ''nonrelativistic gravitational'' fields, which are advantageous also in spin dependent sectors, together with the various gauge choices included in the effective field theory for gravitating spinning objects, which also optimize the calculation. In addition, we automatize the effective field theory computations, and carry out the automated computations in parallel. Such automated effective field theory computations would be most useful to obtain higher order post-Newtonian corrections. We compare our Hamiltonian to the ADM Hamiltonian, and arrive at a complete agreement between the ADM and effective field theory results. Finally, we provide Hamiltonians in the center of mass frame, and complete gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to third and a half post-Newtonian order. The derivation presented here is essential to obtain further higher order post-Newtonian corrections, and to reach the accuracy level required for the successful detection of gravitational radiation.« less

Hamiltonian methods: BRST, BFV

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

Garcia, J. Antonio

2006-09-25

The range of applicability of Hamiltonian methods to gauge theories is very diverse and cover areas of research from phenomenology to mathematical physics. We review some of the areas developed in Mexico in the last decades. They cover the study of symplectic methods, BRST-BFV and BV approaches, Klauder projector program, and non perturbative technics used in the study of bound states in relativistic field theories.

Hamiltonian methods: BRST, BFV

NASA Astrophysics Data System (ADS)

García, J. Antonio

2006-09-01

The range of applicability of Hamiltonian methods to gauge theories is very diverse and cover areas of research from phenomenology to mathematical physics. We review some of the areas developed in México in the last decades. They cover the study of symplectic methods, BRST-BFV and BV approaches, Klauder projector program, and non perturbative technics used in the study of bound states in relativistic field theories.

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

Mouchet, Amaury, E-mail: mouchet@phys.univ-tours.fr

The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.

Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields

NASA Astrophysics Data System (ADS)

Grimaudo, R.; Belousov, Yu.; Nakazato, H.; Messina, A.

2018-05-01

The quantum dynamics of a Jˆ2 =(jˆ1 +jˆ2) 2-conserving Hamiltonian model describing two coupled spins jˆ1 and jˆ2 under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of Jˆ2 is dynamically invariant and the Hamiltonian of the total system restricted to any one of such (j1 +j2) - |j1 -j2 | + 1 eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical properties of the noise, here represented as a classical fluctuating magnetic field. The time evolution of the joint transition probabilities of the two spins jˆ1 and jˆ2 between two prefixed factorized states is examined, bringing to light peculiar dynamical properties of the system under scrutiny. When the noise-induced non-unitary dynamics of the two coupled spins is properly taken into account, analytical expressions for the joint Landau-Zener transition probabilities are reported. The possibility of extending the applicability of our results to other time-dependent spin models is pointed out.

Extended Quantum Field Theory, Index Theory, and the Parity Anomaly

NASA Astrophysics Data System (ADS)

Müller, Lukas; Szabo, Richard J.

2018-06-01

We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit construction of a geometric cobordism bicategory which incorporates general background fields in a stack, and together with the theory of symmetric monoidal bicategories we use it to provide the concrete forms of invertible extended quantum field theories which capture anomalies in both the path integral and Hamiltonian frameworks. Specialising this situation by using the extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners due to Loya and Melrose, we obtain a new Hamiltonian perspective on the parity anomaly. We compute explicitly the 2-cocycle of the projective representation of the gauge symmetry on the quantum state space, which is defined in a parity-symmetric way by suitably augmenting the standard chiral fermionic Fock spaces with Lagrangian subspaces of zero modes of the Dirac Hamiltonian that naturally appear in the index theorem. We describe the significance of our constructions for the bulk-boundary correspondence in a large class of time-reversal invariant gauge-gravity symmetry-protected topological phases of quantum matter with gapless charged boundary fermions, including the standard topological insulator in 3 + 1 dimensions.

High-precision calculations in strongly coupled quantum field theory with next-to-leading-order renormalized Hamiltonian Truncation

NASA Astrophysics Data System (ADS)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-10-01

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d = 2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d ≥ 3.

Long-distance Lienard-Wiechert potentials and qq-bar spin dependence

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

Childers, R.W.

1987-12-15

The long-range spin dependence of the qq interaction is considered in a model in which the confining potential is required to be the static limit of retarded scalar and vector potentials analogous to the Lienard-Wiechert potentials of classical electrodynamics. A generalization of Darwin's method is used to obtain the corresponding Hamiltonian. The long-distance spin-dependent interaction is found to be determined completely by only two potentials: namely, the static scalar and vector potentials. This is to be compared with the four potentials required in Eichten and Feinberg's general formulation. Two different solutions are allowed by Gromes's theorem. In one, the scalarmore » potential can be linear; in the other, it must be logarithmic.« less

Anisotropic optical absorption induced by Rashba spin-orbit coupling in monolayer phosphorene

NASA Astrophysics Data System (ADS)

Li, Yuan; Li, Xin; Wan, Qi; Bai, R.; Wen, Z. C.

2018-04-01

We obtain the effective Hamiltonian of the phosphorene including the effect of Rashba spin-orbit coupling in the frame work of the low-energy theory. The spin-splitting energy bands show an anisotropy feature for the wave vectors along kx and ky directions, where kx orients to ΓX direction in the k space. We numerically study the optical absorption of the electrons for different wave vectors with Rashba spin-orbit coupling. We find that the spin-flip transition from the valence band to the conduction band induced by the circular polarized light closes to zero with increasing the x-component wave vector when ky equals to zero, while it can be significantly increased to a large value when ky gets a small value. When the wave vector varies along the ky direction, the spin-flip transition can also increase to a large value, however, which shows an anisotropy feature for the optical absorption. Especially, the spin-conserved transitions keep unchanged and have similar varying trends for different wave vectors. This phenomenon provides a novel route for the manipulation of the spin-dependent property of the fermions in the monolayer phosphorene.

Particles with nonlinear electric response: Suppressing van der Waals forces by an external field.

PubMed

Soo, Heino; Dean, David S; Krüger, Matthias

2017-01-01

We study the classical thermal component of Casimir, or van der Waals, forces between point particles with highly anharmonic dipole Hamiltonians when they are subjected to an external electric field. Using a model for which the individual dipole moments saturate in a strong field (a model that mimics the charges in a neutral, perfectly conducting sphere), we find that the resulting Casimir force depends strongly on the strength of the field, as demonstrated by analytical results. For a certain angle between the external field and center-to-center axis, the fluctuation force can be tuned and suppressed to arbitrarily small values. We compare the forces between these particles with those between particles with harmonic Hamiltonians and also provide a simple formula for asymptotically large external fields, which we expect to be generally valid for the case of saturating dipole moments.

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

Miyao, Tadahiro; Spohn, Herbert

The retarded van der Waals potential, as first obtained by Casimir and Polder, is usually computed on the basis of nonrelativistic quantum electrodynamics . The Hamiltonian describes two infinitely heavy nuclei, charge e, separated by a distance R and two spinless electrons, charge -e, nonrelativistically coupled to the quantized radiation field. Casimir and Polder used the dipole approximation and small coupling to the Maxwell field. We employ here the full Hamiltonian and determine the asymptotic strength of the leading -R{sup -7} potential, which is valid for all e. Our computation is based on a path integral representation and expands inmore » 1/R, rather than in e.« less

On the existence of touch points for first-order state inequality constraints

NASA Technical Reports Server (NTRS)

Seywald, Hans; Cliff, Eugene M.

1993-01-01

The appearance of touch points in state constrained optimal control problems with general vector-valued control is studied. Under the assumption that the Hamiltonian is regular, touch points for first-order state inequalities are shown to exist only under very special conditions. In many cases of practical importance these conditions can be used to exclude touch points a priori without solving an optimal control problem. The results are demonstrated on a simple example.

Hamiltonian theory of guiding-center motion

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

Littlejohn, R.G.

1980-05-01

A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.

Model independent new physics analysis in Λ _b→ Λ μ ^+μ ^- decay

NASA Astrophysics Data System (ADS)

Das, Diganta

2018-03-01

We study the rare Λ _b→ Λ μ ^+μ ^- decay in the Standard Model and beyond. Beyond the Standard Model we include new vector and axial-vector operators, scalar and pseudo-scalar operators, and tensor operators in the effective Hamiltonian. Working in the helicity basis and using appropriate parametrization of the Λ _b → Λ hadronic matrix elements, we give expressions of hadronic and leptonic helicity amplitudes and derive expression of double differential branching ratio with respect to dilepton invariant mass squared and cosine of lepton angle. Appropriately integrating the differential branching ratio over the lepton angle, we obtain the longitudinal polarization fraction and the leptonic forward-backward asymmetry and sequentially study the observables in the presence of the new couplings. To analyze the implications of the new vector and axial-vector couplings, we follow the current global fits to b→ sμ ^+μ ^- data. While the impacts of scalar couplings can be significant, exclusive \\bar{B}→ X_sμ ^+μ ^- data imply stringent constraints on the tensor couplings and hence the effects on Λ _b→ Λ μ ^+μ ^- are negligible.

On the Stark effect in open shell complexes exhibiting partially quenched electronic angular momentum: Infrared laser Stark spectroscopy of OH–C 2H 2, OH–C 2H 4, and OH–H 2O

DOE PAGES

Moradi, Christopher P.; Douberly, Gary E.

2015-06-22

The Stark effect is considered for polyatomic open shell complexes that exhibit partially quenched electronic angular momentum. Matrix elements of the Stark Hamiltonian represented in a parity conserving Hund's case (a) basis are derived for the most general case, in which the permanent dipole moment has projections on all three inertial axes of the system. Transition intensities are derived, again for the most general case, in which the laser polarization has projections onto axes parallel and perpendicular to the Stark electric field, and the transition dipole moment vector is projected onto all three inertial axes in the molecular frame. Asmore » a result, simulations derived from this model are compared to experimental rovibrational Stark spectra of OH-C 2H 2, OH-C 2H 4, and OH-H 2O complexes formed in helium nanodroplets.« less

Variables separation and superintegrability of the nine-dimensional MICZ-Kepler problem

NASA Astrophysics Data System (ADS)

Phan, Ngoc-Hung; Le, Dai-Nam; Thoi, Tuan-Quoc N.; Le, Van-Hoang

2018-03-01

The nine-dimensional MICZ-Kepler problem is of recent interest. This is a system describing a charged particle moving in the Coulomb field plus the field of a SO(8) monopole in a nine-dimensional space. Interestingly, this problem is equivalent to a 16-dimensional harmonic oscillator via the Hurwitz transformation. In the present paper, we report on the multiseparability, a common property of superintegrable systems, and the superintegrability of the problem. First, we show the solvability of the Schrödinger equation of the problem by the variables separation method in different coordinates. Second, based on the SO(10) symmetry algebra of the system, we construct explicitly a set of seventeen invariant operators, which are all in the second order of the momentum components, satisfying the condition of superintegrability. The found number 17 coincides with the prediction of (2n - 1) law of maximal superintegrability order in the case n = 9. Until now, this law is accepted to apply only to scalar Hamiltonian eigenvalue equations in n-dimensional space; therefore, our results can be treated as evidence that this definition of superintegrability may also apply to some vector equations such as the Schrödinger equation for the nine-dimensional MICZ-Kepler problem.

Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems

NASA Astrophysics Data System (ADS)

Vogl, M.; Pankratov, O.; Shallcross, S.

2017-07-01

We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

Rapid convergence of optimal control in NMR using numerically-constructed toggling frames

NASA Astrophysics Data System (ADS)

Coote, Paul; Anklin, Clemens; Massefski, Walter; Wagner, Gerhard; Arthanari, Haribabu

2017-08-01

We present a numerical method for rapidly solving the Bloch equation for an arbitrary time-varying spin-1/2 Hamiltonian. The method relies on fast, vectorized computations such as summation and quaternion multiplication, rather than slow computations such as matrix exponentiation. A toggling frame is constructed in which the Hamiltonian is time-invariant, and therefore has a simple analytical solution. The key insight is that constructing this frame is faster than solving the system dynamics in the original frame. Rapidly solving the Bloch equations for an arbitrary Hamiltonian is particularly useful in the context of NMR optimal control. Optimal control theory can be used to design pulse shapes for a range of tasks in NMR spectroscopy. However, it requires multiple simulations of the Bloch equations at each stage of the algorithm, and for each relevant set of parameters (e.g. chemical shift frequencies). This is typically time consuming. We demonstrate that by working in an appropriate toggling frame, optimal control pulses can be generated much faster. We present a new alternative to the well-known GRAPE algorithm to continuously update the toggling-frame as the optimal pulse is generated, and demonstrate that this approach is extremely fast. The use and benefit of rapid optimal pulse generation is demonstrated for 19F fragment screening experiments.

NLO renormalization in the Hamiltonian truncation

NASA Astrophysics Data System (ADS)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-09-01

Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

Quantum finance Hamiltonian for coupon bond European and barrier options.

PubMed

Baaquie, Belal E

2008-03-01

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb_{2}Ti_{2}O_{7} in a Magnetic Field.

PubMed

Thompson, J D; McClarty, P A; Prabhakaran, D; Cabrera, I; Guidi, T; Coldea, R

2017-08-04

The frustrated pyrochlore magnet Yb_{2}Ti_{2}O_{7} has the remarkable property that it orders magnetically but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe, in addition to dispersive magnons, a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measurements we find that the low- and high-field regions are smoothly connected with no sharp phase transition, with the spin gap increasing monotonically in field. Through fits to an extensive data set of dispersion relations combined with magnetization measurements, we reevaluate the spin Hamiltonian, finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields.

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.

Characterization of the hyperfine interaction of the excited D50 state of Eu3 +:Y2SiO5

NASA Astrophysics Data System (ADS)

Cruzeiro, Emmanuel Zambrini; Etesse, Jean; Tiranov, Alexey; Bourdel, Pierre-Antoine; Fröwis, Florian; Goldner, Philippe; Gisin, Nicolas; Afzelius, Mikael

2018-03-01

We characterize the europium (Eu3 +) hyperfine interaction of the excited state (D50) and determine its effective spin Hamiltonian parameters for the Zeeman and quadrupole tensors. An optical free induction decay method is used to measure all hyperfine splittings under a weak external magnetic field (up to 10 mT) for various field orientations. On the basis of the determined Hamiltonian, we discuss the possibility to predict optical transition probabilities between hyperfine levels for the F70⟷D50 transition. The obtained results provide necessary information to realize an optical quantum memory scheme which utilizes long spin coherence properties of 3 + 151Eu :Y2SiO5 material under external magnetic fields.

Ordinary versus PT-symmetric Φ³ quantum field theory

DOE PAGES

Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele

2012-04-02

A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum fieldmore » theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.« less

Mean energy of some interacting bosonic systems derived by virtue of the generalized Hellmann-Feynman theorem

NASA Astrophysics Data System (ADS)

Fan, Hong-yi; Xu, Xue-xiang

2009-06-01

By virtue of the generalized Hellmann-Feynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann-Feynman theorem and may enrich the theory of quantum statistics.

Retrieving the ground state of spin glasses using thermal noise: Performance of quantum annealing at finite temperatures.

PubMed

Nishimura, Kohji; Nishimori, Hidetoshi; Ochoa, Andrew J; Katzgraber, Helmut G

2016-09-01

We study the problem to infer the ground state of a spin-glass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spin-glass generalization of a well-established result that the ground state of a purely ferromagnetic Hamiltonian is best inferred at a finite temperature in the sense of smallest Hamming distance when the original ferromagnetic interactions are disturbed by noise. We use the numerical transfer-matrix method to establish the existence of an optimal finite temperature in one- and two-dimensional systems. Our numerical results are supported by mean-field calculations, which give an explicit expression of the optimal temperature to infer the spin-glass ground state as a function of variances of the distributions of the original interactions and the noise. The mean-field prediction is in qualitative agreement with numerical data. Implications on postprocessing of quantum annealing on a noisy device are discussed.

Complete Hamiltonian analysis of cosmological perturbations at all orders

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

Nandi, Debottam; Shankaranarayanan, S., E-mail: debottam@iisertvm.ac.in, E-mail: shanki@iisertvm.ac.in

2016-06-01

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the 'gauge-fixing' issues and extend the analysis to scalar field models and show that our approach can be applied to any order of perturbation for any first order derivative fields. In the case of Galilean scalar fields, our procedure can extract constrained relations at all orders in perturbations leading to the fact that there is no extra degrees of freedom due to the presence of higher time derivatives of the field in themore » Lagrangian. We compare and contrast our approach to the Lagrangian approach (Chen et al. [2006]) for extracting higher order correlations and show that our approach is efficient and robust and can be applied to any model of gravity and matter fields without invoking slow-roll approximation.« less

Recursion Relations for Double Ramification Hierarchies

NASA Astrophysics Data System (ADS)

Buryak, Alexandr; Rossi, Paolo

2016-03-01

In this paper we study various properties of the double ramification hierarchy, an integrable hierarchy of hamiltonian PDEs introduced in Buryak (CommunMath Phys 336(3):1085-1107, 2015) using intersection theory of the double ramification cycle in the moduli space of stable curves. In particular, we prove a recursion formula that recovers the full hierarchy starting from just one of the Hamiltonians, the one associated to the first descendant of the unit of a cohomological field theory. Moreover, we introduce analogues of the topological recursion relations and the divisor equation both for the Hamiltonian densities and for the string solution of the double ramification hierarchy. This machinery is very efficient and we apply it to various computations for the trivial and Hodge cohomological field theories, and for the r -spin Witten's classes. Moreover, we prove the Miura equivalence between the double ramification hierarchy and the Dubrovin-Zhang hierarchy for the Gromov-Witten theory of the complex projective line (extended Toda hierarchy).

GEMPIC: geometric electromagnetic particle-in-cell methods

NASA Astrophysics Data System (ADS)

Kraus, Michael; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

2017-08-01

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

A comparison of force fields and calculation methods for vibration intervals of isotopic H3(+) molecules

NASA Astrophysics Data System (ADS)

Carney, G. D.; Adler-Golden, S. M.; Lesseski, D. C.

1986-04-01

This paper reports (1) improved values for low-lying vibration intervals of H3(+), H2D(+), D2H(+), and D3(+) calculated using the variational method and Simons-Parr-Finlan (1973) representations of the Carney-Porter (1976) and Dykstra-Swope (1979) ab initio H3(+) potential energy surfaces, (2) quartic normal coordinate force fields for isotopic H3(+) molecules, (3) comparisons of variational and second-order perturbation theory, and (4) convergence properties of the Lai-Hagstrom internal coordinate vibrational Hamiltonian. Standard deviations between experimental and ab initio fundamental vibration intervals of H3(+), H2D(+), D2H(+), and D3(+) for these potential surfaces are 6.9 (Carney-Porter) and 1.2/cm (Dykstra-Swope). The standard deviations between perturbation theory and exact variational fundamentals are 5 and 10/cm for the respective surfaces. The internal coordinate Hamiltonian is found to be less efficient than the previously employed 't' coordinate Hamiltonian for these molecules, except in the case of H2D(+).

Sequential Feedback Scheme Outperforms the Parallel Scheme for Hamiltonian Parameter Estimation.

PubMed

Yuan, Haidong

2016-10-14

Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find the highest achievable precision with the given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in the quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter, we show that the sequential feedback scheme has a threefold improvement over the parallel scheme for Hamiltonian parameter estimations on two-dimensional systems, and an order of O(d+1) improvement for Hamiltonian parameter estimation on d-dimensional systems. We also show that, contrary to the conventional belief, it is possible to simultaneously achieve the highest precision for estimating all three components of a magnetic field, which sets a benchmark on the local precision limit for the estimation of a magnetic field.

BRST theory without Hamiltonian and Lagrangian

NASA Astrophysics Data System (ADS)

Lyakhovich, S. L.; Sharapov, A. A.

2005-03-01

We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure or action principle is supposed to exist. For such a generic gauge system we construct a consistent BRST formulation, which includes the conventional BV Lagrangian and BFV Hamiltonian schemes as particular cases. If the original manifold carries a weak Poisson structure (a bivector field giving rise to a Poisson bracket on the space of physical observables) the generic gauge system is shown to admit deformation quantization by means of the Kontsevich formality theorem. A sigma-model interpretation of this quantization algorithm is briefly discussed.

A lattice approach to spinorial quantum gravity

NASA Technical Reports Server (NTRS)

Renteln, Paul; Smolin, Lee

1989-01-01

A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.

Elliptic-symmetry vector optical fields.

PubMed

Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Kong, Ling-Jun; Tu, Chenghou; Wang, Hui-Tian

2014-08-11

We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.

Voltage-induced switching of an antiferromagnetically ordered topological Dirac semimetal

NASA Astrophysics Data System (ADS)

Kim, Youngseok; Kang, Kisung; Schleife, André; Gilbert, Matthew J.

2018-04-01

An antiferromagnetic semimetal has been recently identified as a new member of topological semimetals that may host three-dimensional symmetry-protected Dirac fermions. A reorientation of the Néel vector may break the underlying symmetry and open a gap in the quasiparticle spectrum, inducing the (semi)metal-insulator transition. Here, we predict that such a transition may be controlled by manipulating the chemical potential location of the material. We perform both analytical and numerical analysis on the thermodynamic potential of the model Hamiltonian and find that the gapped spectrum is preferred when the chemical potential is located at the Dirac point. As the chemical potential deviates from the Dirac point, the system shows a possible transition from the gapped to the gapless phase and switches the corresponding Néel vector configuration. We perform density functional theory calculations to verify our analysis using a realistic material and discuss a two terminal transport measurement as a possible route to identify the voltage-induced switching of the Néel vector.

Canonical quantization of constrained systems and coadjoint orbits of Diff(S sup 1 )

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

Scherer, W.M.

It is shown that Dirac's treatment of constrained Hamiltonian systems and Schwinger's action principle quantization lead to identical commutations relations. An explicit relation between the Lagrange multipliers in the action principle approach and the additional terms in the Dirac bracket is derived. The equivalence of the two methods is demonstrated in the case of the non-linear sigma model. Dirac's method is extended to superspace and this extension is applied to the chiral superfield. The Dirac brackets of the massive interacting chiral superfluid are derived and shown to give the correct commutation relations for the component fields. The Hamiltonian of themore » theory is given and the Hamiltonian equations of motion are computed. They agree with the component field results. An infinite sequence of differential operators which are covariant under the coadjoint action of Diff(S{sup 1}) and analogues to Hill's operator is constructed. They map conformal fields of negative integer and half-integer weight to their dual space. Some properties of these operators are derived and possible applications are discussed. The Korteweg-de Vries equation is formulated as a coadjoint orbit of Diff(S{sup 1}).« less

Chern-Simons improved Hamiltonians for strings in three space dimensions

NASA Astrophysics Data System (ADS)

Gordeli, Ivan; Melnikov, Dmitry; Niemi, Antti J.; Sedrakyan, Ara

2016-07-01

In the case of a structureless string the extrinsic curvature and torsion determine uniquely its shape in three-dimensional ambient space, by way of solution of the Frenet equation. In many physical scenarios there are in addition symmetries that constrain the functional form of the ensuing energy function. For example, the energy of a structureless string should be independent of the way the string is framed in the Frenet equation. Thus the energy should only involve the curvature and torsion as dynamical variables, in a manner that resembles the Hamiltonian of the Abelian Higgs model. Here we investigate the effect of symmetry principles in the construction of Hamiltonians for structureless strings. We deduce from the concept of frame independence that in addition to extrinsic curvature and torsion, the string can also engage a three-dimensional Abelian bulk gauge field as a dynamical variable. We find that the presence of a bulk gauge field gives rise to a long-range interaction between different strings. Moreover, when this gauge field is subject to Chern-Simons self-interaction, it becomes plausible that interacting strings are subject to fractional statistics in three space dimensions.

Rigged String Configurations, Bethe Ansatz Qubits, and Conservation of Parity

NASA Astrophysics Data System (ADS)

Lulek, T.

Bethe Ansatz solutions for the Heisenberg Hamiltonian of a one - dimensional magnetic ring of N nodes, each with the spin 1/2, within the XXX model, have been presented as some composite systems, in a spirit of quantum information theory. The constituents are single - node spin states, which organize into strings of various length, and "seas of holes". The former are responsible for dynamics, whereas the latter determine the range of riggings for strings. Another aim was to demonstrate a unification of Bethe Ansatz eigenstates by means of Galois symmetries of finite field extensions. The key observation is that the original eigenproblem is expressible in integers, and thus, for a finite fixed N, the splitting field of the characteristic polynom of the Heisenberg Hamiltonian is also finite. The Galois group of the latter field permutes, by definition, roots of this polynom, which implies permutation of eigenstates. General considerations are demonstrated on the example of heptagon (N = 7), which admits an implementation of a collection of arithmetic qubits, and also demonstrates a special case of degeneration of the spectrum of the Hamiltonian, resulting from conservation of parity, within the realm of rigged string configurations.

Versatile generation of optical vector fields and vector beams using a non-interferometric approach.

PubMed

Tripathi, Santosh; Toussaint, Kimani C

2012-05-07

We present a versatile, non-interferometric method for generating vector fields and vector beams which can produce all the states of polarization represented on a higher-order Poincaré sphere. The versatility and non-interferometric nature of this method is expected to enable exploration of various exotic properties of vector fields and vector beams. To illustrate this, we study the propagation properties of some vector fields and find that, in general, propagation alters both their intensity and polarization distribution, and more interestingly, converts some vector fields into vector beams. In the article, we also suggest a modified Jones vector formalism to represent vector fields and vector beams.

Approximation methods in relativistic eigenvalue perturbation theory

NASA Astrophysics Data System (ADS)

Noble, Jonathan Howard

In this dissertation, three questions, concerning approximation methods for the eigenvalues of quantum mechanical systems, are investigated: (i) What is a pseudo--Hermitian Hamiltonian, and how can its eigenvalues be approximated via numerical calculations? This is a fairly broad topic, and the scope of the investigation is narrowed by focusing on a subgroup of pseudo--Hermitian operators, namely, PT--symmetric operators. Within a numerical approach, one projects a PT--symmetric Hamiltonian onto an appropriate basis, and uses a straightforward two--step algorithm to diagonalize the resulting matrix, leading to numerically approximated eigenvalues. (ii) Within an analytic ansatz, how can a relativistic Dirac Hamiltonian be decoupled into particle and antiparticle degrees of freedom, in appropriate kinematic limits? One possible answer is the Foldy--Wouthuysen transform; however, there are alter- native methods which seem to have some advantages over the time--tested approach. One such method is investigated by applying both the traditional Foldy--Wouthuysen transform and the "chiral" Foldy--Wouthuysen transform to a number of Dirac Hamiltonians, including the central-field Hamiltonian for a gravitationally bound system; namely, the Dirac-(Einstein-)Schwarzschild Hamiltonian, which requires the formal- ism of general relativity. (iii) Are there are pseudo--Hermitian variants of Dirac Hamiltonians that can be approximated using a decoupling transformation? The tachyonic Dirac Hamiltonian, which describes faster-than-light spin-1/2 particles, is gamma5--Hermitian, i.e., pseudo-Hermitian. Superluminal particles remain faster than light upon a Lorentz transformation, and hence, the Foldy--Wouthuysen program is unsuited for this case. Thus, inspired by the Foldy--Wouthuysen program, a decoupling transform in the ultrarelativistic limit is proposed, which is applicable to both sub- and superluminal particles.

Experiments in Quantum Coherence and Computation With Single Cooper-Pair Electronics

DTIC Science & Technology

2006-01-22

through the cavity. In the absence of damping, exact diagonalization of the Jaynes - Cumming Hamiltonian yields the excited eigenstates (dressed states...neglecting rapidly oscillating terms and omitting damping for the moment, Eq. (16) reduces to the Jaynes - Cummings Hamiltonian (1) with V=EJ /" and cou...is therefore little entanglement between the field and qubit in this situation and the rotation fidelity is high. To model the effect of the drive on

A modified symplectic PRK scheme for seismic wave modeling

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Ma, Jian

2017-02-01

A new scheme for the temporal discretization of the seismic wave equation is constructed based on symplectic geometric theory and a modified strategy. The ordinary differential equation in terms of time, which is obtained after spatial discretization via the spectral-element method, is transformed into a Hamiltonian system. A symplectic partitioned Runge-Kutta (PRK) scheme is used to solve the Hamiltonian system. A term related to the multiplication of the spatial discretization operator with the seismic wave velocity vector is added into the symplectic PRK scheme to create a modified symplectic PRK scheme. The symplectic coefficients of the new scheme are determined via Taylor series expansion. The positive coefficients of the scheme indicate that its long-term computational capability is more powerful than that of conventional symplectic schemes. An exhaustive theoretical analysis reveals that the new scheme is highly stable and has low numerical dispersion. The results of three numerical experiments demonstrate the high efficiency of this method for seismic wave modeling.

TDA and RPA pseudoscalar and vector solutions for the low energy regime of a motivated QCD Hamiltonian.

NASA Astrophysics Data System (ADS)

Yépez-Martínez, T.; Amor Quiroz, D. A.; Hess, P. O.; Civitarese, O.

2017-07-01

We present the low energy meson spectrum of a Coulomb gauge QCD motivated Hamiltonian for light and strange quarks. We have used the harmonic oscillator as a trial basis and performed a pre-diagonalization of the kinetic energy term in order to get an effective basis where quark and anti-quark degrees of freedom are defined. For the relevant interactions between quarks and anti-quarks, we have implemented a confining interaction between color sources, in order to account in an effective way for the gluonic degrees of freedom. The low energy meson spectrum is obtained from the implementation of the TDA and RPA many-body-methods. The physical states have been described as TDA and RPA collective states with a relatively good agreement. Particularly, the particle-hole correlations of the RPA ground state improve the RPA pion-like state (159.7 MeV) close to its physical value while the TDA one remains at a higher energy (269.2 MeV).

Semiflexible polymer dynamics with a bead-spring model

NASA Astrophysics Data System (ADS)

Barkema, Gerard T.; Panja, Debabrata; van Leeuwen, J. M. J.

2014-11-01

We study the dynamical properties of semiflexible polymers with a recently introduced bead-spring model. We focus on double-stranded DNA (dsDNA). The two parameters of the model, T* and ν, are chosen to match its experimental force-extension curve. In comparison to its groundstate value, the bead-spring Hamiltonian is approximated in the first order by the Hessian that is quadratic in the bead positions. The eigenmodes of the Hessian provide the longitudinal (stretching) and transverse (bending) eigenmodes of the polymer, and the corresponding eigenvalues match well with the established phenomenology of semiflexible polymers. At the Hessian approximation of the Hamiltonian, the polymer dynamics is linear. Using the longitudinal and transverse eigenmodes, for the linearized problem, we obtain analytical expressions of (i) the autocorrelation function of the end-to-end vector, (ii) the autocorrelation function of a bond (i.e. a spring, or a tangent) vector at the middle of the chain, and (iii) the mean-square displacement of a tagged bead in the middle of the chain, as the sum over the contributions from the modes—the so-called ‘mode sums’. We also perform simulations with the full dynamics of the model. The simulations yield numerical values of the correlations functions (i-iii) that agree very well with the analytical expressions for the linearized dynamics. This does not however mean that the nonlinearities are not present. In fact, we also study the mean-square displacement of the longitudinal component of the end-to-end vector that showcases strong nonlinear effects in the polymer dynamics, and we identify at least an effective t7/8 power-law regime in its time-dependence. Nevertheless, in comparison to the full mean-square displacement of the end-to-end vector the nonlinear effects remain small at all times—it is in this sense we state that our results demonstrate that the linearized dynamics suffices for dsDNA fragments that are shorter than or comparable to the persistence length. Our results are consistent with those of the wormlike chain (WLC) model, the commonly used descriptive tool of semiflexible polymers.

The parity-violating asymmetry in the 3He(n,p)3H reaction

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

M. Viviani, R. Schiavilla, L. Girlanda, A. Kievsky, L.E. Marcucci

2010-10-01

The longitudinal asymmetry induced by parity-violating (PV) components in the nucleon-nucleon potential is studied in the charge-exchange reaction 3He(n,p)3H at vanishing incident neutron energies. An expression for the PV observable is derived in terms of T-matrix elements for transitions from the {2S+1}L_J=1S_0 and 3S_1 states in the incoming n-3He channel to states with J=0 and 1 in the outgoing p-3H channel. The T-matrix elements involving PV transitions are obtained in first-order perturbation theory in the hadronic weak-interaction potential, while those connecting states of the same parity are derived from solutions of the strong-interaction Hamiltonian with the hyperspherical-harmonics method. The coupled-channelmore » nature of the scattering problem is fully accounted for. Results are obtained corresponding to realistic or chiral two- and three-nucleon strong-interaction potentials in combination with either the DDH or pionless EFT model for the weak-interaction potential. The asymmetries, predicted with PV pion and vector-meson coupling constants corresponding (essentially) to the DDH "best values" set, range from -9.44 to -2.48 in units of 10^{-8}, depending on the input strong-interaction Hamiltonian. This large model dependence is a consequence of cancellations between long-range (pion) and short-range (vector-meson) contributions, and is of course sensitive to the assumed values for the PV coupling constants.« less

Superradiant phase transition in a model of three-level-Λ systems interacting with two bosonic modes

NASA Astrophysics Data System (ADS)

Hayn, Mathias; Emary, Clive; Brandes, Tobias

2012-12-01

We consider an ensemble of three-level particles in Lambda configuration interacting with two bosonic modes. The Hamiltonian has the form of a generalized Dicke model. We show that in the thermodynamic limit this model supports a superradiant quantum phase transition. Remarkably, this can be both a first- and a second-order phase transition. A connection of the phase diagram to the symmetries of the Hamiltonian is also given. In addition, we show that this model can describe atoms interacting with an electromagnetic field in which the microscopic Hamiltonian includes a diamagnetic contribution. Even though the parameters of the atomic system respect the Thomas-Reiche-Kuhn sum rule, the system still shows a superradiant phase transition.

Multisymplectic unified formalism for Einstein-Hilbert gravity

NASA Astrophysics Data System (ADS)

Gaset, Jordi; Román-Roy, Narciso

2018-03-01

We present a covariant multisymplectic formulation for the Einstein-Hilbert model of general relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified Lagrangian-Hamiltonian formalism is particularly interesting when it is applied to these kinds of theories, since it simplifies the treatment of them, in particular, the implementation of the constraint algorithm, the retrieval of the Lagrangian description, and the construction of the covariant Hamiltonian formalism. In order to apply this algorithm to the covariant field equations, they must be written in a suitable geometrical way, which consists of using integrable distributions, represented by multivector fields of a certain type. We apply all these tools to the Einstein-Hilbert model without and with energy-matter sources. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomentum (covariant) Hamiltonian formalisms in both cases. As a consequence of the gauge freedom and the constraint algorithm, we see how this model is equivalent to a first-order regular theory, without gauge freedom. In the case of the presence of energy-matter sources, we show how some relevant geometrical and physical characteristics of the theory depend on the type of source. In all the cases, we obtain explicitly multivector fields which are solutions to the gravitational field equations. Finally, a brief study of symmetries and conservation laws is done in this context.

Excitation spectrum and staggering transformations in lattice quantum models.

PubMed

Faria da Veiga, Paulo A; O'Carroll, Michael; Schor, Ricardo

2002-08-01

We consider the energy-momentum excitation spectrum of diverse lattice Hamiltonian operators: the generator of the Markov semigroup of Ginzburg-Landau models with Langevin stochastic dynamics, the Hamiltonian of a scalar quantum field theory, and the Hamiltonian associated with the transfer matrix of a classical ferromagnetic spin system at high temperature. The low-lying spectrum consists of a one-particle state and a two-particle band. The two-particle spectrum is determined using a lattice version of the Bethe-Salpeter equation. In addition to the two-particle band, depending on the lattice dimension and on the attractive or repulsive character of the interaction between the particles of the system, there is, respectively, a bound state below or above the two-particle band. We show how the existence or nonexistence of these bound states can be understood in terms of a nonrelativistic single-particle lattice Schrödinger Hamiltonian with a delta potential. A staggering transformation relates the spectra of the attractive and the repulsive cases.

An ensemble of paired spin(-1/2) nuclei in a rotating solid: Polarization evolution and NMR spectrum in a wobbling frame.

PubMed

Kundla, Enn

2007-04-01

The evolution of the magnetic polarization of an ensemble of paired spin(-1/2) nuclei in an MAS NMR (nuclear magnetic resonance) experiment and the induced spectrum are described theoretically by means of a Liouville-von Neumann equation representation in a wobbling rotating frame in combination with the averaged Hamiltonian theory. In this method, the effect of a high-intensity external static magnetic field and the effects of the leftover interaction components of the Hamiltonian that commute with the approximate Hamiltonian are taken into account simultaneously and equivalently. This method reproduces details that really exist in the recorded spectra, caused by secular terms in the Hamiltonian, which might otherwise be smoothed out owing to the approximate treatment of the effects of the secular terms. Complete analytical expressions, which describe the whole NMR spectrum including the rotational sideband sets, and which consider all the relevant intermolecular interactions, are obtained.

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

NASA Astrophysics Data System (ADS)

Hermes, Matthew R.; Dukelsky, Jorge; Scuseria, Gustavo E.

2017-06-01

The failures of single-reference coupled-cluster theory for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled-cluster theory fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled-cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a test bed [J. Chem. Phys. 146, 054110 (2017), 10.1063/1.4974989]. We generalize the concept of a symmetry-projected mean-field wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled-cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled-cluster theory is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.

Ground State of the Universe and the Cosmological Constant. A Nonperturbative Analysis.

PubMed

Husain, Viqar; Qureshi, Babar

2016-02-12

The physical Hamiltonian of a gravity-matter system depends on the choice of time, with the vacuum naturally identified as its ground state. We study the expanding Universe with scalar field in the volume time gauge. We show that the vacuum energy density computed from the resulting Hamiltonian is a nonlinear function of the cosmological constant and time. This result provides a new perspective on the relation between time, the cosmological constant, and vacuum energy.

Creation of a magnetic barrier at a noble q close to physical midpoint between two resonant surfaces in the ASDEX UG tokamak

NASA Astrophysics Data System (ADS)

Vazquez, Justin; Ali, Halima; Punjabi, Alkesh

2009-11-01

Ciraolo, Vittot and Chandre method of building invariant manifolds inside chaos in Hamiltonian systems [Ali H. and Punjabi A, Plasma Phys. Control. Fusion, 49, 1565--1582 (2007)] is used in the ASDEX UG tokamak. In this method, a second order perturbation is added to the perturbed Hamiltonian [op cit]. It creates an invariant torus inside the chaos, and reduces the plasma transport. The perturbation that is added to the equilibrium Hamiltonian is at least an order of magnitude smaller than the perturbation that causes chaos. This additional term has a finite, limited number of Fourier modes. Resonant magnetic perturbations (m,n) = (3,2)+(4,3) are added to the field line Hamiltonian for the ASDEX UG. An area-preserving map for the field line trajectories in the ASDEX UG is used. The common amplitude δ of these modes that gives complete chaos between the resonant surfaces ψ43 and ψ32 is determined. A magnetic barrier is built at a surface with noble q that is very nearly equals to the q at the physical midpoint between the two resonant surfaces. The maximum amplitude of magnetic perturbation for which this barrier can be sustained is determined. This work is supported by US Department of Energy grants DE-FG02-07ER54937, DE-FG02-01ER54624 and DE-FG02-04ER54793.

Topological BF Theories

NASA Astrophysics Data System (ADS)

Sǎraru, Silviu-Constantin

Topological field theories originate in the papers of Schwarz and Witten. Initially, Schwarz shown that one of the topological invariants, namely the Ray-Singer torsion, can be represented as the partition function of a certain quantum field theory. Subsequently, Witten constructed a framework for understanding Morse theory in terms of supersymmetric quantum mechanics. These two constructions represent the prototypes of all topological field theories. The model used by Witten has been applied to classical index theorems and, moreover, suggested some generalizations that led to new mathematical results on holomorphic Morse inequalities. Starting with these results, further developments in the domain of topological field theories have been achieved. The Becchi-Rouet-Stora-Tyutin (BRST) symmetry allowed for a new definition of topological ...eld theories as theories whose BRST-invariant Hamiltonian is also BRST-exact. An important class of topological theories of Schwarz type is the class of BF models. This type of models describes three-dimensional quantum gravity and is useful at the study of four-dimensional quantum gravity in Ashtekar-Rovelli-Smolin formulation. Two-dimensional BF models are correlated to Poisson sigma models from various two-dimensional gravities. The analysis of Poisson sigma models, including their relationship to two-dimensional gravity and the study of classical solutions, has been intensively studied in the literature. In this thesis we approach the problem of construction of some classes of interacting BF models in the context of the BRST formalism. In view of this, we use the method of the deformation of the BRST charge and BRST-invariant Hamiltonian. Both methods rely on specific techniques of local BRST cohomology. The main hypotheses in which we construct the above mentioned interactions are: space-time locality, Poincare invariance, smoothness of deformations in the coupling constant and the preservation of the number of derivatives on each field. The first two hypotheses implies that the resulting interacting theory must be local in space-time and Poincare invariant. The smoothness of deformations means that the deformed objects that contribute to the construction of interactions must be smooth in the coupling constant and reduce to the objects corresponding to the free theory in the zero limit of the coupling constant. The preservation of the number of derivatives on each field imp! lies two aspects that must be simultaneously fulfilled: (i) the differential order of each free field equation must coincide with that of the corresponding interacting field equation; (ii) the maximum number of space-time derivatives from the interacting vertices cannot exceed the maximum number of derivatives from the free Lagrangian. The main results obtained can be synthesized into: obtaining self-interactions for certain classes of BF models; generation of couplings between some classes of BF theories and matter theories; construction of interactions between a class of BF models and a system of massless vector fields.

Small traveling clusters in attractive and repulsive Hamiltonian mean-field models.

PubMed

Barré, Julien; Yamaguchi, Yoshiyuki Y

2009-03-01

Long-lasting small traveling clusters are studied in the Hamiltonian mean-field model by comparing between attractive and repulsive interactions. Nonlinear Landau damping theory predicts that a Gaussian momentum distribution on a spatially homogeneous background permits the existence of traveling clusters in the repulsive case, as in plasma systems, but not in the attractive case. Nevertheless, extending the analysis to a two-parameter family of momentum distributions of Fermi-Dirac type, we theoretically predict the existence of traveling clusters in the attractive case; these findings are confirmed by direct N -body numerical simulations. The parameter region with the traveling clusters is much reduced in the attractive case with respect to the repulsive case.

Equivalent Hamiltonian for the Lee model

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

Jones, H. F.

2008-03-15

Using the techniques of quasi-Hermitian quantum mechanics and quantum field theory we use a similarity transformation to construct an equivalent Hermitian Hamiltonian for the Lee model. In the field theory confined to the V/N{theta} sector it effectively decouples V, replacing the three-point interaction of the original Lee model by an additional mass term for the V particle and a four-point interaction between N and {theta}. While the construction is originally motivated by the regime where the bare coupling becomes imaginary, leading to a ghost, it applies equally to the standard Hermitian regime where the bare coupling is real. In thatmore » case the similarity transformation becomes a unitary transformation.« less

Adiabatic perturbation theory for atoms and molecules in the low-frequency regime

NASA Astrophysics Data System (ADS)

Martiskainen, Hanna; Moiseyev, Nimrod

2017-12-01

There is an increasing interest in the photoinduced dynamics in the low frequency, ω, regime. The multiphoton absorptions by molecules in strong laser fields depend on the polarization of the laser and on the molecular structure. The unique properties of the interaction of atoms and molecules with lasers in the low-frequency regime imply new concepts and directions in strong-field light-matter interactions. Here we represent a perturbational approach for the calculations of the quasi-energy spectrum in the low-frequency regime, which avoids the construction of the Floquet operator with extremely large number of Floquet channels. The zero-order Hamiltonian in our perturbational approach is the adiabatic Hamiltonian where the atoms/molecules are exposed to a dc electric field rather than to ac-field. This is in the spirit of the first step in the Corkum three-step model. The second-order perturbation correction terms are obtained when i ℏ ω ∂/∂ τ serves as a perturbation and τ is a dimensionless variable. The second-order adiabatic perturbation scheme is found to be an excellent approach for calculating the ac-field Floquet solutions in our test case studies of a simple one-dimensional time-periodic model Hamiltonian. It is straightforward to implement the perturbation approach presented here for calculating atomic and molecular energy shifts (positions) due to the interaction with low-frequency ac-fields using high-level electronic structure methods. This is enabled since standard quantum chemistry packages allow the calculations of atomic and molecular energy shifts due to the interaction with dc-fields. In addition to the shift of the energy positions, the energy widths (inverse lifetimes) can be obtained at the same level of theory. These energy shifts are functions of the laser parameters (low frequency, intensity, and polarization).

Spin Relaxation and Manipulation in Spin-orbit Qubits

NASA Astrophysics Data System (ADS)

Borhani, Massoud; Hu, Xuedong

2012-02-01

We derive a generalized form of the Electric Dipole Spin Resonance (EDSR) Hamiltonian in the presence of the spin-orbit interaction for single spins in an elliptic quantum dot (QD) subject to an arbitrary (in both direction and magnitude) applied magnetic field. We predict a nonlinear behavior of the Rabi frequency as a function of the magnetic field for sufficiently large Zeeman energies, and present a microscopic expression for the anisotropic electron g-tensor. Similarly, an EDSR Hamiltonian is devised for two spins confined in a double quantum dot (DQD). Finally, we calculate two-electron-spin relaxation rates due to phonon emission, for both in-plane and perpendicular magnetic fields. Our results have immediate applications to current EDSR experiments on nanowire QDs, g-factor optimization of confined carriers, and spin decay measurements in DQD spin-orbit qubits.

Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations.

PubMed

Banerjee, Amartya S; Lin, Lin; Suryanarayana, Phanish; Yang, Chao; Pask, John E

2018-06-12

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).

Extending geometrical optics: A Lagrangian theory for vector waves

NASA Astrophysics Data System (ADS)

Ruiz, D. E.

2016-10-01

Even diffraction aside, the commonly known equations of geometrical optics (GO) are not entirely accurate. GO considers wave rays as classical particles, which are completely described by their coordinates and momenta, but rays have another degree of freedom, namely, polarization. As a result, wave rays can behave as particles with spin. A well-known example of polarization dynamics is wave-mode conversion, which can be interpreted as rotation of the (classical) ``wave spin.'' However, there are other less-known manifestations of the wave spin, such as polarization precession and polarization-driven bending of ray trajectories. This talk presents recent advances in extending and reformulating GO as a first-principle Lagrangian theory, whose effective-gauge Hamiltonian governs both mentioned polarization phenomena simultaneously. Examples and numerical results are presented. When applied to classical waves, the theory correctly predicts the polarization-driven divergence of left- and right- polarized electromagnetic waves in isotropic media, such as dielectrics and nonmagnetized plasmas. In the case of particles with spin, the formalism also yields a point-particle Lagrangian model for the Dirac electron, i.e. the relativistic spin-1/2 electron, which includes both the Stern-Gerlach spin potential and the Bargmann-Michel-Telegdi spin precession. Additionally, the same theory contributes, perhaps unexpectedly, to the understanding of ponderomotive effects in both wave and particle dynamics; e.g., the formalism allows to obtain the ponderomotive Hamiltonian for a Dirac electron interacting with an arbitrarily large electromagnetic laser field with spin effects included. Supported by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948, by the U.S. DOE through Contract No. DE-AC02-09CH11466, and by the U.S. DOD NDSEG Fellowship through Contract No. 32-CFR-168a.

Relativistic quantum optics: The relativistic invariance of the light-matter interaction models

NASA Astrophysics Data System (ADS)

Martín-Martínez, Eduardo; Rodriguez-Lopez, Pablo

2018-05-01

In this article we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model atoms interacting with light. We find explicitly how the light-matter interaction Hamiltonians change under general coordinate transformations, and analyze the subtleties of the Hamiltonians commonly used to describe the light-matter interaction when relativistic motion is taken into account.

Integrable Time-Dependent Quantum Hamiltonians

NASA Astrophysics Data System (ADS)

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

2018-05-01

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Selection rule engineering of forbidden transitions of a hydrogen atom near a nanogap

NASA Astrophysics Data System (ADS)

Kim, Hyunyoung Y.; Kim, Daisik S.

2018-01-01

We perform an analytical study on the allowance of forbidden transitions for a hydrogen atom placed near line dipole sources, mimicking light emanating from a one-dimensional metallic nanogap. It is shown that the rapid variation of the electric field vector, inevitable in the near zone, completely breaks the selection rule of Δl=±1. While the forbidden transitions between spherically symmetric S states, such as 2S to 1S or 3S to 1S (Δl=0), are rather robust against selection rule breakage, Δl=±2 transitions such as between 3D and 1S or 3D and 2S states are very vulnerable to the spatial variation of the perturbing electric field. Transitions between 2S and 3D states are enhanced by many orders of magnitude, aided by the quadratic nature of both the perturbing Hamiltonian and D wavefunctions. The forbidden dipole moment, which approaches one Bohr radius times the electric charge in the vicinity of the gap, can be written in a simple closed form owing to the one-dimensional nature of our gap. With large enough effective volume together with the symmetric nature of the excited state wavefunctions, our work paves way towards atomic physics application of infinitely long nanogaps.

Application of Dirac's Generalized Hamiltonian Dynamics to Atomic and Molecular Systems

NASA Astrophysics Data System (ADS)

Uzer, Turgay

2002-10-01

Incorporating electronic degrees of freedom into classical treatments of atoms and molecules is a challenging problem from both the practical and fundamental points of view. Because it goes to the heart of classical-quantal correspondence, there are now a number of prescriptions which differ by the extent of quantal information that they include. We reach back to Dirac for inspiration, who, half a century ago, designed a so-called Generalized Hamiltonian Dynamics (GHD) with applications to field theory in mind. Physically, the GHD is a purely classical formalism for systems with constraints; it incorporates the constraints into the Hamiltonian. We apply the GHD to atomic and molecular physics by choosing integrals of motion as the constraints. We show that this purely classical formalism allows the derivation of energies of non-radiating states.

Construction of Hamiltonians by supervised learning of energy and entanglement spectra

NASA Astrophysics Data System (ADS)

Fujita, Hiroyuki; Nakagawa, Yuya O.; Sugiura, Sho; Oshikawa, Masaki

2018-02-01

Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter, nuclear, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is generically impossible to treat these problems from first principles. Thus the construction of a proper model, namely, effective Hamiltonian, is essential. Here, we propose a simple supervised learning algorithm for constructing Hamiltonians from given energy or entanglement spectra. We apply the proposed scheme to the Hubbard model at the half-filling, and compare the obtained effective low-energy spin model with several analytic results based on the high-order perturbation theory, which have been inconsistent with each other. We also show that our approach can be used to construct the entanglement Hamiltonian of a quantum many-body state from its entanglement spectrum as well. We exemplify this using the ground states of the S =1 /2 two-leg Heisenberg ladders. We observe a qualitative difference between the entanglement Hamiltonians of the two phases (the Haldane and the rung singlet phase) of the model due to the different origin of the entanglement. In the Haldane phase, we find that the entanglement Hamiltonian is nonlocal by nature, and the locality can be restored by introducing the anisotropy and turning the ground state into the large-D phase. Possible applications to the model construction from experimental data and to various problems of strongly correlated systems are discussed.

Internal phase transition induced by external forces in Finsler geometric model for membranes

NASA Astrophysics Data System (ADS)

Koibuchi, Hiroshi; Shobukhov, Andrey

2016-10-01

In this paper, we numerically study an anisotropic shape transformation of membranes under external forces for two-dimensional triangulated surfaces on the basis of Finsler geometry. The Finsler metric is defined by using a vector field, which is the tangential component of a three-dimensional unit vector σ corresponding to the tilt or some external macromolecules on the surface of disk topology. The sigma model Hamiltonian is assumed for the tangential component of σ with the interaction coefficient λ. For large (small) λ, the surface becomes oblong (collapsed) at relatively small bending rigidity. For the intermediate λ, the surface becomes planar. Conversely, fixing the surface with the boundary of area A or with the two-point boundaries of distance L, we find that the variable σ changes from random to aligned state with increasing of A or L for the intermediate region of λ. This implies that an internal phase transition for σ is triggered not only by the thermal fluctuations, but also by external mechanical forces. We also find that the frame (string) tension shows the expected scaling behavior with respect to A/N (L/N) at the intermediate region of A (L) where the σ configuration changes between the disordered and ordered phases. Moreover, we find that the string tension γ at sufficiently large λ is considerably smaller than that at small λ. This phenomenon resembles the so-called soft-elasticity in the liquid crystal elastomer, which is deformed by small external tensile forces.

Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole

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

Bellucci, Stefano; Krivonos, Sergey; Sutulin, Anton

2010-05-15

We propose Lagrangian and Hamiltonian formulations of a N=4 supersymmetric three-dimensional isospin-carrying particle moving in the non-Abelian field of a Wu-Yang monopole and in some specific scalar potential. This additional potential is completely fixed by N=4 supersymmetry, and in the simplest case of flat metrics it coincides with that which provides the existence of the Runge-Lenz vector for the bosonic subsector. The isospin degrees of freedom are described on the Lagrangian level by bosonic auxiliary variables forming N=4 supermultiplet with additional, also auxiliary, fermions. Being quite general, the constructed systems include such interesting cases as N=4 superconformally invariant systems withmore » Wu-Yang monopole, the particles living in the flat R{sup 3} and in the RxS{sup 2} spaces and interacting with the monopole, and also the particles moving on three-dimensional sphere and pseudosphere with the Wu-Yang monopole sitting in the center. The superfield Lagrangian description of these systems is so simple that one could wonder to see how all couplings and the proper coefficients arise while passing to the component action.« less

Measurement of untruncated nuclear spin interactions via zero- to ultralow-field nuclear magnetic resonance

NASA Astrophysics Data System (ADS)

Blanchard, J. W.; Sjolander, T. F.; King, J. P.; Ledbetter, M. P.; Levine, E. H.; Bajaj, V. S.; Budker, D.; Pines, A.

2015-12-01

Zero- to ultralow-field nuclear magnetic resonance (ZULF NMR) provides a new regime for the measurement of nuclear spin-spin interactions free from the effects of large magnetic fields, such as truncation of terms that do not commute with the Zeeman Hamiltonian. One such interaction, the magnetic dipole-dipole coupling, is a valuable source of spatial information in NMR, though many terms are unobservable in high-field NMR, and the coupling averages to zero under isotropic molecular tumbling. Under partial alignment, this information is retained in the form of so-called residual dipolar couplings. We report zero- to ultralow-field NMR measurements of residual dipolar couplings in acetonitrile-2-13C aligned in stretched polyvinyl acetate gels. This permits the investigation of dipolar couplings as a perturbation on the indirect spin-spin J coupling in the absence of an applied magnetic field. As a consequence of working at zero magnetic field, we observe terms of the dipole-dipole coupling Hamiltonian that are invisible in conventional high-field NMR. This technique expands the capabilities of zero- to ultralow-field NMR and has potential applications in precision measurement of subtle physical interactions, chemical analysis, and characterization of local mesoscale structure in materials.

A link between torse-forming vector fields and rotational hypersurfaces

NASA Astrophysics Data System (ADS)

Chen, Bang-Yen; Verstraelen, Leopold

Torse-forming vector fields introduced by Yano [On torse forming direction in a Riemannian space, Proc. Imp. Acad. Tokyo 20 (1944) 340-346] are natural extension of concurrent and concircular vector fields. Such vector fields have many nice applications to geometry and mathematical physics. In this paper, we establish a link between rotational hypersurfaces and torse-forming vector fields. More precisely, our main result states that, for a hypersurface M of 𝔼n+1 with n ≥ 3, the tangential component xT of the position vector field of M is a proper torse-forming vector field on M if and only if M is contained in a rotational hypersurface whose axis of rotation contains the origin.

Multi-scaling in the critical phenomena in the quenched disordered systems

NASA Astrophysics Data System (ADS)

Wu, X. T.

2018-04-01

The Landau-Ginzburg-Wilson Hamiltonian with random temperature for the phase transition in disordered systems from the Griffiths phase to ordered phase is reexamined. From the saddle point solutions, especially the excited state solutions, it is shown that the system self-organizes into blocks coupled with their neighbors like superspins, which are emergent variables. Taking the fluctuation around these saddle point solutions into account, we get an effective Hamiltonian, including the emergent superspins of the blocks, the fluctuation around the saddle point solutions, and their couplings. Applying Stratonovich-Hubbard transformation to the part of superspins, we get a Landau-Ginzburg-Wilson Hamiltonian for the blocks. From the saddle point equations for the blocks, we can get the second generation blocks, of which sizes are much larger than the first generation blocks. Repeating this procedure again and again, we get many generations of blocks to describe the asymptotic behavior. If a field is applied, the effective field on the superspins is multiplied greatly and proportional to the block size. For a very small field, the effective field on the higher generation superspins can be so strong to cause the superspins polarized radically. This can explain the extra large critical isotherm exponent discovered in the experiments. The phase space of reduced temperature vs. field is divided into many layers , in which different generation blocks dominate the critical behavior. The sizes of the different generation emergent blocks are new relevant length scales. This can explain a lot of puzzles in the experiments and the Monte Carlo simulation.

A diagram for evaluating multiple aspects of model performance in simulating vector fields

NASA Astrophysics Data System (ADS)

Xu, Zhongfeng; Hou, Zhaolu; Han, Ying; Guo, Weidong

2016-12-01

Vector quantities, e.g., vector winds, play an extremely important role in climate systems. The energy and water exchanges between different regions are strongly dominated by wind, which in turn shapes the regional climate. Thus, how well climate models can simulate vector fields directly affects model performance in reproducing the nature of a regional climate. This paper devises a new diagram, termed the vector field evaluation (VFE) diagram, which is a generalized Taylor diagram and able to provide a concise evaluation of model performance in simulating vector fields. The diagram can measure how well two vector fields match each other in terms of three statistical variables, i.e., the vector similarity coefficient, root mean square length (RMSL), and root mean square vector difference (RMSVD). Similar to the Taylor diagram, the VFE diagram is especially useful for evaluating climate models. The pattern similarity of two vector fields is measured by a vector similarity coefficient (VSC) that is defined by the arithmetic mean of the inner product of normalized vector pairs. Examples are provided, showing that VSC can identify how close one vector field resembles another. Note that VSC can only describe the pattern similarity, and it does not reflect the systematic difference in the mean vector length between two vector fields. To measure the vector length, RMSL is included in the diagram. The third variable, RMSVD, is used to identify the magnitude of the overall difference between two vector fields. Examples show that the VFE diagram can clearly illustrate the extent to which the overall RMSVD is attributed to the systematic difference in RMSL and how much is due to the poor pattern similarity.

Theory of diatomic molecules in an external electromagnetic field from first quantum mechanical principles.

PubMed

Sindelka, Milan; Moiseyev, Nimrod

2006-04-27

We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to a variety of specific applications, such as alignment or orientation of molecules by lasers, trapping of ultracold molecules in optical traps, molecular optics and interferometry, rovibrational spectroscopy of molecules in the presence of intense laser light, or generation of high order harmonics from molecules. Starting from the first quantum mechanical principles, we derive an appropriate molecular Hamiltonian suitable for description of the center of mass, rotational, vibrational, and electronic molecular motions driven by the field within the electric dipole approximation. Consequently, the concept of the Born-Oppenheimer separation between the electronic and the nuclear degrees of freedom in the presence of an electromagnetic field is introduced. Special cases of the dc/ac-field limits are then discussed separately. Finally, we consider a perturbative regime of a weak dc/ac field, and obtain simple analytic formulas for the associated Born-Oppenheimer translational/rotational/vibrational molecular Hamiltonian.

Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors.

PubMed

Xu, Danfeng; Gu, Bing; Rui, Guanghao; Zhan, Qiwen; Cui, Yiping

2016-02-22

We present an arbitrary vector field with hybrid polarization based on the combination of a pair of orthogonal elliptically polarized base vectors on the Poincaré sphere. It is shown that the created vector field is only dependent on the latitude angle 2χ but is independent on the longitude angle 2ψ on the Poincaré sphere. By adjusting the latitude angle 2χ, which is related to two identical waveplates in a common path interferometric arrangement, one could obtain arbitrary type of vector fields. Experimentally, we demonstrate the generation of such kind of vector fields and confirm the distribution of state of polarization by the measurement of Stokes parameters. Besides, we investigate the tight focusing properties of these vector fields. It is found that the additional degree of freedom 2χ provided by arbitrary vector field with hybrid polarization allows one to control the spatial structure of polarization and to engineer the focusing field.

Design of 2D time-varying vector fields.

PubMed

Chen, Guoning; Kwatra, Vivek; Wei, Li-Yi; Hansen, Charles D; Zhang, Eugene

2012-10-01

Design of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces. Our system supports the creation and modification of various time-varying vector fields with desired spatial and temporal characteristics through several design metaphors, including streamlines, pathlines, singularity paths, and bifurcations. These design metaphors are integrated into an element-based design to generate the time-varying vector fields via a sequence of basis field summations or spatial constrained optimizations at the sampled times. The key-frame design and field deformation are also introduced to support other user design scenarios. Accordingly, a spatial-temporal constrained optimization and the time-varying transformation are employed to generate the desired fields for these two design scenarios, respectively. We apply the time-varying vector fields generated using our design system to a number of important computer graphics applications that require controllable dynamic effects, such as evolving surface appearance, dynamic scene design, steerable crowd movement, and painterly animation. Many of these are difficult or impossible to achieve via prior simulation-based methods. In these applications, the time-varying vector fields have been applied as either orientation fields or advection fields to control the instantaneous appearance or evolving trajectories of the dynamic effects.

Spin manipulation and relaxation in spin-orbit qubits

NASA Astrophysics Data System (ADS)

Borhani, Massoud; Hu, Xuedong

2012-03-01

We derive a generalized form of the electric dipole spin resonance (EDSR) Hamiltonian in the presence of the spin-orbit interaction for single spins in an elliptic quantum dot (QD) subject to an arbitrary (in both direction and magnitude) applied magnetic field. We predict a nonlinear behavior of the Rabi frequency as a function of the magnetic field for sufficiently large Zeeman energies, and present a microscopic expression for the anisotropic electron g tensor. Similarly, an EDSR Hamiltonian is devised for two spins confined in a double quantum dot (DQD), where coherent Rabi oscillations between the singlet and triplet states are induced by jittering the inter-dot distance at the resonance frequency. Finally, we calculate two-electron-spin relaxation rates due to phonon emission, for both in-plane and perpendicular magnetic fields. Our results have immediate applications to current EDSR experiments on nanowire QDs, g-factor optimization of confined carriers, and spin decay measurements in DQD spin-orbit qubits.

EPR, optical and modeling of Mn(2+) doped sarcosinium oxalate monohydrate.

PubMed

Kripal, Ram; Singh, Manju

2015-01-25

Electron paramagnetic resonance (EPR) study of Mn(2+) ions doped in sarcosinium oxalate monohydrate (SOM) single crystal is done at liquid nitrogen temperature (LNT). EPR spectrum shows a bunch of five fine structure lines and further they split into six hyperfine components. Only one interstitial site was observed. With the help of EPR spectra the spin Hamiltonian parameters including zero field splitting (ZFS) parameters are evaluated. The optical absorption study at room temperature is also done in the wavelength range 195-1100 nm. From this study cubic crystal field splitting parameter, Dq=730 cm(-1) and Racah inter-electronic repulsion parameters B=792 cm(-1), C=2278 cm(-1) are determined. ZFS parameters D and E are also calculated using crystal field parameters from superposition model and microscopic spin Hamiltonian theory. The calculated ZFS parameter values are in good match with the experimental values obtained by EPR. Copyright © 2014 Elsevier B.V. All rights reserved.

Crossed-coil detection of two-photon excited nuclear quadrupole resonance

NASA Astrophysics Data System (ADS)

Eles, Philip T.; Michal, Carl A.

2005-08-01

Applying a recently developed theoretical framework for determining two-photon excitation Hamiltonians using average Hamiltonian theory, we calculate the excitation produced by half-resonant irradiation of the pure quadrupole resonance of a spin-3/2 system. This formalism provides expressions for the single-quantum and double-quantum nutation frequencies as well as the Bloch-Siegert shift. The dependence of the excitation strength on RF field orientation and the appearance of the free-induction signal along an axis perpendicular to the excitation field provide an unmistakable signature of two-photon excitation. We demonstrate single- and double-quantum excitation in an axially symmetric system using 35Cl in a single crystal of potassium chlorate ( ωQ = 28 MHz) with crossed-coil detection. A rotation plot verifies the orientation dependence of the two-photon excitation, and double-quantum coherences are observed directly with the application of a static external magnetic field.

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

DOE PAGES

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; ...

2016-09-08

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R 1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Ourmore » main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.« less

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

NASA Astrophysics Data System (ADS)

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; Wang, Huajia

2016-09-01

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on {{R}}^{1,d-1} . We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. These methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. We also discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

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

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R 1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Ourmore » main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.« less

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.

Study of the interplay between magnetic shear and resonances using Hamiltonian models for the magnetic field lines

NASA Astrophysics Data System (ADS)

Firpo, M.-C.; Constantinescu, D.

2011-03-01

The issue of magnetic confinement in magnetic fusion devices is addressed within a purely magnetic approach. Using some Hamiltonian models for the magnetic field lines, the dual impact of low magnetic shear is shown in a unified way. Away from resonances, it induces a drastic enhancement of magnetic confinement that favors robust internal transport barriers (ITBs) and stochastic transport reduction. When low shear occurs for values of the winding of the magnetic field lines close to low-order rationals, the amplitude thresholds of the resonant modes that break internal transport barriers by allowing a radial stochastic transport of the magnetic field lines may be quite low. The approach can be applied to assess the robustness versus magnetic perturbations of general (almost) integrable magnetic steady states, including nonaxisymmetric ones such as the important single-helicity steady states. This analysis puts a constraint on the tolerable mode amplitudes compatible with ITBs and may be proposed as a possible explanation of diverse experimental and numerical signatures of their collapses.

Transient regime in second harmonic generation

NASA Astrophysics Data System (ADS)

Szeftel, Jacob; Sandeau, Laure; Sandeau, Nicolas; Delezoide, Camille; Khater, Antoine

2013-09-01

The time growth of the electromagnetic field at the fundamental and double frequencies is studied from the very onset of the second harmonic generation (SHG) process for a set of dipoles lacking a symmetry centre and exhibiting a nonresonant coupling with a classical electromagnetic field. This approach consists first of solving the Schrödinger equation by applying a generalised Rabi rotation to the Hamiltonian describing the light-dipole interaction. This rotation has been devised for the resulting Hamiltonian to show up time-independent for both components of the electromagnetic field at the fundamental frequency and the second harmonic one. Then an energy conservation argument, derived from the Poynting theorem, is introduced to work out an additional relationship between the electromagnetic field and its associated electric polarisation. Finally this analysis yields the full time behaviour of all physical quantities of interest. The calculated results reproduce accurately both the observed spatial oscillations of the SHG intensity (Maker's fringes) and its power law dependence on the intensity of the incoming light at the fundamental frequency.

A Crystal Field Approach to Orbitally Degenerate SMMs: Beyond the Spin-Only Hamiltonian

NASA Astrophysics Data System (ADS)

Bhaskaran, Lakshmi; Marriott, Katie; Murrie, Mark; Hill, Stephen

Single-Molecule Magnets (SMMs) with large magnetization reversal barriers are promising candidates for high-density information storage. Recently, a large uniaxial magnetic anisotropy was observed for a mononuclear trigonal bipyramidal (TBP) [NiIICl3(Me-abco)2] SMM. High-field EPR studies analyzed on the basis of a spin-only Hamiltonian give ¦D¦>400 cm-1, which is close to the spin-orbit coupling parameter λ = 668 cm-1 for NiII, suggesting an orbitally degenerate ground state. The spin-only description is ineffective in this limit, necessitating the development of a model that includes the orbital moment. Here we describe a phenomenological approach that takes into account a full description of crystal field, electron-electron repulsion and spin-orbit coupling effects on the ground state of a NiII ion in a TBP coordination geometry. The model is in good agreement with the high-field EPR experiments, validating its use for spectroscopic studies of orbitally degenerate molecular nanomagnets. This work was supported by the NSF (DMR-1309463).

(p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation

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

Ben Geloun, Joseph; Govaerts, Jan; Hounkonnou, M. Norbert

2007-03-15

Classes of (p,q) deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q) arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translatesmore » into (p,q) deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.« less

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.

De Donder-Weyl Hamiltonian formalism of MacDowell-Mansouri gravity

NASA Astrophysics Data System (ADS)

Berra-Montiel, Jasel; Molgado, Alberto; Serrano-Blanco, David

2017-12-01

We analyse the behaviour of the MacDowell-Mansouri action with internal symmetry group SO(4, 1) under the De Donder-Weyl Hamiltonian formulation. The field equations, known in this formalism as the De Donder-Weyl equations, are obtained by means of the graded Poisson-Gerstenhaber bracket structure present within the De Donder-Weyl formulation. The decomposition of the internal algebra so(4, 1)≃so(3, 1)\\oplus{R}3, 1 allows the symmetry breaking SO(4, 1)\\toSO(3, 1) , which reduces the original action to the Palatini action without the topological term. We demonstrate that, in contrast to the Lagrangian approach, this symmetry breaking can be performed indistinctly in the polysymplectic formalism either before or after the variation of the De Donder-Weyl Hamiltonian has been done, recovering Einstein’s equations via the Poisson-Gerstenhaber bracket.

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

PubMed Central

Santagati, Raffaele; Wang, Jianwei; Gentile, Antonio A.; Paesani, Stefano; Wiebe, Nathan; McClean, Jarrod R.; Morley-Short, Sam; Shadbolt, Peter J.; Bonneau, Damien; Silverstone, Joshua W.; Tew, David P.; Zhou, Xiaoqi; O’Brien, Jeremy L.; Thompson, Mark G.

2018-01-01

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers. PMID:29387796

Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms.

PubMed

Thomas, Phillip S; Carrington, Tucker

2015-12-31

We propose a method for solving the vibrational Schrödinger equation with which one can compute hundreds of energy levels of seven-atom molecules using at most a few gigabytes of memory. It uses nested contractions in conjunction with the reduced-rank block power method (RRBPM) described in J. Chem. Phys. 2014, 140, 174111. Successive basis contractions are organized into a tree, the nodes of which are associated with eigenfunctions of reduced-dimension Hamiltonians. The RRBPM is used recursively to compute eigenfunctions of nodes in bases of products of reduced-dimension eigenfunctions of nodes with fewer coordinates. The corresponding vectors are tensors in what is called CP-format. The final wave functions are therefore represented in a hierarchical CP-format. Computational efficiency and accuracy are significantly improved by representing the Hamiltonian in the same hierarchical format as the wave function. We demonstrate that with this hierarchical RRBPM it is possible to compute energy levels of a 64-D coupled-oscillator model Hamiltonian and also of acetonitrile (CH3CN) and ethylene oxide (C2H4O), for which we use quartic potentials. The most accurate acetonitrile calculation uses 139 MB of memory and takes 3.2 h on a single processor. The most accurate ethylene oxide calculation uses 6.1 GB of memory and takes 14 d on 63 processors. The hierarchical RRBPM shatters the memory barrier that impedes the calculation of vibrational spectra.

Hyperbolic-symmetry vector fields.

PubMed

Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2015-12-14

We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.

Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

NASA Astrophysics Data System (ADS)

Evans, Denis J.; Searles, Debra J.; Mittag, Emil

2001-05-01

For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

Effect of Floquet engineering on the p-wave superconductor with second-neighbor couplings

NASA Astrophysics Data System (ADS)

Li, X. P.; Li, C. F.; Wang, L. C.; Zhou, L.

2018-06-01

The influence of the Floquet engineering on a particular one-dimensional p-wave superconductor, Kitaev model, with second-neighbor couplings is investigated in this paper. The effective Hamiltonians in the rotated reference frames have been obtained, and the convergent regions of the approximated Hamiltonian as well as the topological phase diagrams have been analyzed and discussed. We show that by modulating the external driving field amplitude, frequency as well as the second-neighbor hopping amplitude, the rich phase diagrams and transitions between different topological phases can be obtained.

Translation invariant time-dependent massive gravity: Hamiltonian analysis

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

Mourad, Jihad; Steer, Danièle A.; Noui, Karim, E-mail: mourad@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: steer@apc.univ-paris7.fr

2014-09-01

The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagating degrees of freedom are the dRGT mass terms, namely those which are linear in the lapse. We also complete the Hamiltonian analysis with the dynamical evolution of the system.

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

An EPR investigation of the dynamic Jahn-Teller effect in SrCl2:y(2 plus) and SrCl2:Sc(2 plus)

NASA Technical Reports Server (NTRS)

Herrington, J. R.; Estle, T. L.; Boatner, L. A.

1972-01-01

EPR spectra have been observed for SrCl2:Y(2+) and SrCl2:Sc(2+) at liquid helium temperatures. At 1.2 K the spectra were dominated by anisotropic hyperfine patterns whose lineshapes and angular dependences were explained using second order solutions of the effective Hamiltonian for an isolated 2Eg state split by large random internal strains. Pronounced asymmetries in some of the strin produced lineshapes for Srcl2:Sc(2+) are shown to result from second order terms in the solution of the effective Hamiltonian. Coexisting with the anisotropic hyperfine patterns are weak nearly isotropic hyperfine patterns with typical lineshapes. Variations in the apparent intensity of lines in these weak hyperfine patterns as functions of the applied magnetic field direction and temperature imply that these lines result from averaging by vibronic relaxation of a portion of the anisotropic pattern. The effective Hamiltonian parameters for SrCl2:La(2+), SrCl2:y(2+), and SrCl2:SC(2+) are analyzed in terms of crystal field theory modified to include a dynamic Jahn-Teller effect.

On the nature of the Mott transition in multiorbital systems

NASA Astrophysics Data System (ADS)

Facio, Jorge I.; Vildosola, V.; García, D. J.; Cornaglia, Pablo S.

2017-02-01

We analyze the nature of a Mott metal-insulator transition in multiorbital systems using dynamical mean-field theory. The auxiliary multiorbital quantum impurity problem is solved using continuous-time quantum Monte Carlo and the rotationally invariant slave-boson (RISB) mean-field approximation. We focus our analysis on the Kanamori Hamiltonian and find that there are two markedly different regimes determined by the nature of the lowest-energy excitations of the atomic Hamiltonian. The RISB results at T →0 suggest the following rule of thumb for the order of the transition at zero temperature: a second-order transition is to be expected if the lowest-lying excitations of the atomic Hamiltonian are charge excitations, while the transition tends to be first order if the lowest-lying excitations are in the same charge sector as the atomic ground state. At finite temperatures, the transition is first order and its strength, as measured, e.g., by the jump in the quasiparticle weight at the transition, is stronger in the parameter regime where the RISB method predicts a first-order transition at zero temperature. Interestingly, these results seem to apply to a wide variety of models and parameter regimes.

Quantum bright solitons in a quasi-one-dimensional optical lattice

NASA Astrophysics Data System (ADS)

Barbiero, Luca; Salasnich, Luca

2014-06-01

We study a quasi-one-dimensional attractive Bose gas confined in an optical lattice with a superimposed harmonic potential by analyzing the one-dimensional Bose-Hubbard Hamiltonian of the system. Starting from the three-dimensional many-body quantum Hamiltonian, we derive strong inequalities involving the transverse degrees of freedom under which the one-dimensional Bose-Hubbard Hamiltonian can be safely used. To have a reliable description of the one-dimensional ground state, which we call a quantum bright soliton, we use the density-matrix-renormalization-group (DMRG) technique. By comparing DMRG results with mean-field (MF) ones, we find that beyond-mean-field effects become relevant by increasing the attraction between bosons or by decreasing the frequency of the harmonic confinement. In particular, we find that, contrary to the MF predictions based on the discrete nonlinear Schrödinger equation, average density profiles of quantum bright solitons are not shape-invariant. We also use the time-evolving-block-decimation method to investigate the dynamical properties of bright solitons when the frequency of the harmonic potential is suddenly increased. This quantum quench induces a breathing mode whose period crucially depends on the final strength of the superimposed harmonic confinement.

Hamiltonian mean-field model: effect of temporal perturbation in coupling matrix

NASA Astrophysics Data System (ADS)

Bhadra, Nivedita; Patra, Soumen K.

2018-05-01

The Hamiltonian mean-field (HMF) model is a system of fully coupled rotators which exhibits a second-order phase transition at some critical energy in its canonical ensemble. We investigate the case where the interaction between the rotors is governed by a time-dependent coupling matrix. Our numerical study reveals a shift in the critical point due to the temporal modulation. The shift in the critical point is shown to be independent of the modulation frequency above some threshold value, whereas the impact of the amplitude of modulation is dominant. In the microcanonical ensemble, the system with constant coupling reaches a quasi-stationary state (QSS) at an energy near the critical point. Our result indicates that the QSS subsists in presence of such temporal modulation of the coupling parameter.

Nonperturbative light-front Hamiltonian methods

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2016-09-01

We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

NASA Astrophysics Data System (ADS)

Agresti, Juri; De Pietri, Roberto; Lusanna, Luca; Martucci, Luca

2004-05-01

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy {\\hat E}ADM, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) r_{\\bar a}(\\tau ,\\vec \\sigma ), \\pi_{\\bar a}(\\tau ,\\vec \\sigma ), \\bar a = 1,2. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in {\\hat E}ADM. We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's r_{\\bar a}(\\tau ,\\vec \\sigma ), which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.

Model of Anisotropic Magnetization of In(1-x)Mn(x)S: Comparison to Experiment

NASA Astrophysics Data System (ADS)

Garner, J.; Franzese, G.; Byrd, Ashlee; Pekarek, T. M.; Miotkowski, I.; Ramdas, A. K.

2004-03-01

Calculations of and experimental results for the anisotropic magnetization of the new III-VI dilute magnetic semiconductor, In(1-x)Mn(x)S, are presented. The model Hamiltonian incorporates the interaction of the incomplete shell of Mn 3d-electrons with the crystal lattice within the point-ion approximation. Other terms in the Hamiltonian include the Zeeman interaction, the spin-orbit and the spin-spin terms. It is assumed the Mn atoms do not interact with each other (this is the singlet model, which is appropriate when x is small, here 2%). The temperature- and field- dependent magnetization is found from the energy eigenvalues of the Hamiltonian matrix, which was expressed in terms of an uncoupled angular momentum basis set. Magnetization versus temperature results are found for several field values, B, pointing along various directions relative to the underlying dilute magnetic semiconductor crystal lattice. In addition, the magnetization versus field is computed for several fixed temperatures and for various B-field directions and magnitudes. Overall, the agreement of this simple model with the experimental data is very good except at low temperatures (< 20 K) and high fields (> a few Tesla). It would be useful for quantitative comparison purposes to have optical absorption data in order to better fix the crystal potential parameters that are input parameters in the theory. In addition, the model could be improved by going beyond the point-ion approximation to better model the covalent bonds in the crystal.* Supported by UNF Research Grants, Research Corporation Award, CC4845, NSF Grant Nos. DMR-03-05653, DMR-01-02699, and ECS-01-29853 and Donors of the American Chemical Society Petroleum Research Fund PRF#40209-B5M, and a Purdue Univ. Academic Reimbursement Grant.

Rotation invariants of vector fields from orthogonal moments

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

Yang, Bo; Kostková, Jitka; Flusser, Jan

Vector field images are a type of new multidimensional data that appear in many engineering areas. Although the vector fields can be visualized as images, they differ from graylevel and color images in several aspects. In order to analyze them, special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area. Here, we propose a method for the description and matching of vector field patterns under an unknown rotation of the field. Rotation of a vector field is so-called total rotation, where the action is applied not only on the spatial coordinates but alsomore » on the field values. Invariants of vector fields with respect to total rotation constructed from orthogonal Gaussian–Hermite moments and Zernike moments are introduced. Their numerical stability is shown to be better than that of the invariants published so far. We demonstrate their usefulness in a real world template matching application of rotated vector fields.« less

Huygens' optical vector wave field synthesis via in-plane electric dipole metasurface.

PubMed

Park, Hyeonsoo; Yun, Hansik; Choi, Chulsoo; Hong, Jongwoo; Kim, Hwi; Lee, Byoungho

2018-04-16

We investigate Huygens' optical vector wave field synthesis scheme for electric dipole metasurfaces with the capability of modulating in-plane polarization and complex amplitude and discuss the practical issues involved in realizing multi-modulation metasurfaces. The proposed Huygens' vector wave field synthesis scheme identifies the vector Airy disk as a synthetic unit element and creates a designed vector optical field by integrating polarization-controlled and complex-modulated Airy disks. The metasurface structure for the proposed vector field synthesis is analyzed in terms of the signal-to-noise ratio of the synthesized field distribution. The design of practical metasurface structures with true vector modulation capability is possible through the analysis of the light field modulation characteristics of various complex modulated geometric phase metasurfaces. It is shown that the regularization of meta-atoms is a key factor that needs to be considered in field synthesis, given that it is essential for a wide range of optical field synthetic applications, including holographic displays, microscopy, and optical lithography.

Rotation invariants of vector fields from orthogonal moments

DOE PAGES

Yang, Bo; Kostková, Jitka; Flusser, Jan; ...

2017-09-11

Vector field images are a type of new multidimensional data that appear in many engineering areas. Although the vector fields can be visualized as images, they differ from graylevel and color images in several aspects. In order to analyze them, special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area. Here, we propose a method for the description and matching of vector field patterns under an unknown rotation of the field. Rotation of a vector field is so-called total rotation, where the action is applied not only on the spatial coordinates but alsomore » on the field values. Invariants of vector fields with respect to total rotation constructed from orthogonal Gaussian–Hermite moments and Zernike moments are introduced. Their numerical stability is shown to be better than that of the invariants published so far. We demonstrate their usefulness in a real world template matching application of rotated vector fields.« less

Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem.

PubMed

Zhao, Zhiqiang; Chen, Jun; Zhang, Zhaojun; Zhang, Dong H; Wang, Xiao-Gang; Carrington, Tucker; Gatti, Fabien

2018-02-21

Quantum mechanical calculations of ro-vibrational energies of CH 4 , CHD 3 , CH 3 D, and CH 3 F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH 3 subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH 3 . Euler angles specifying the orientation of a frame attached to CH 3 with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH 4 , CHD 3 , and CH 3 D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH 3 F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.

Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem

NASA Astrophysics Data System (ADS)

Zhao, Zhiqiang; Chen, Jun; Zhang, Zhaojun; Zhang, Dong H.; Wang, Xiao-Gang; Carrington, Tucker; Gatti, Fabien

2018-02-01

Quantum mechanical calculations of ro-vibrational energies of CH4, CHD3, CH3D, and CH3F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH3 subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH3. Euler angles specifying the orientation of a frame attached to CH3 with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH4, CHD3, and CH3D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH3F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.

Floquet prethermalization in the resonantly driven Hubbard model

NASA Astrophysics Data System (ADS)

Herrmann, Andreas; Murakami, Yuta; Eckstein, Martin; Werner, Philipp

2017-12-01

We demonstrate the existence of long-lived prethermalized states in the Mott insulating Hubbard model driven by periodic electric fields. These states, which also exist in the resonantly driven case with a large density of photo-induced doublons and holons, are characterized by a nonzero current and an effective temperature of the doublons and holons which depends sensitively on the driving condition. Focusing on the specific case of resonantly driven models whose effective time-independent Hamiltonian in the high-frequency driving limit corresponds to noninteracting fermions, we show that the time evolution of the double occupation can be reproduced by the effective Hamiltonian, and that the prethermalization plateaus at finite driving frequency are controlled by the next-to-leading-order correction in the high-frequency expansion of the effective Hamiltonian. We propose a numerical procedure to determine an effective Hubbard interaction that mimics the correlation effects induced by these higher-order terms.

Replica Resummation of the Baker-Campbell-Hausdorff Series

NASA Astrophysics Data System (ADS)

Vajna, Szabolcs; Klobas, Katja; Prosen, Tomaž; Polkovnikov, Anatoli

2018-05-01

We developed a novel perturbative expansion based on the replica trick for the Floquet Hamiltonian governing the dynamics of periodically kicked systems where the kick strength is the small parameter. The expansion is formally equivalent to an infinite resummation of the Baker-Campbell-Hausdorff series in the undriven (nonperturbed) Hamiltonian, while considering terms up to a finite order in the kick strength. As an application of the replica expansion, we analyze an Ising spin 1 /2 chain periodically kicked with a magnetic field with a strength h , which has both longitudinal and transverse components. We demonstrate that even away from the regime of high frequency driving, if there is heating, its rate is nonperturbative in the kick strength, bounded from above by a stretched exponential: e-const h-1 /2 . This guarantees the existence of a very long prethermal regime, where the dynamics is governed by the Floquet Hamiltonian obtained from the replica expansion.

General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters

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

Skrypnyk, T., E-mail: taras.skrypnyk@unimib.it, E-mail: tskrypnyk@imath.kiev.ua

Using the technique of classical r-matrices and quantum Lax operators, we construct the most general form of the quantum integrable “n-level, many-mode” spin-boson Jaynes-Cummings-Dicke-type hamiltonians describing an interaction of a molecule of N n-level atoms with many modes of electromagnetic field and containing, in general, additional non-linear interaction terms. We explicitly obtain the corresponding quantum Lax operators and spin-boson analogs of the generalized Gaudin hamiltonians and prove their quantum commutativity. We investigate symmetries of the obtained models that are associated with the geometric symmetries of the classical r-matrices and construct the corresponding algebra of quantum integrals. We consider in detailmore » three classes of non-skew-symmetric classical r-matrices with spectral parameters and explicitly obtain the corresponding quantum Lax operators and Jaynes-Cummings-Dicke-type hamiltonians depending on the considered r-matrix.« less

Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

NASA Astrophysics Data System (ADS)

Yuzbashyan, Emil A.

2018-05-01

We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

Fractal vector optical fields.

PubMed

Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2016-07-15

We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.

Manipulation of dielectric Rayleigh particles using highly focused elliptically polarized vector fields.

PubMed

Gu, Bing; Xu, Danfeng; Rui, Guanghao; Lian, Meng; Cui, Yiping; Zhan, Qiwen

2015-09-20

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in areas where exotic optical fields are desired. In this work, we experimentally demonstrate the versatile generation of linearly polarized vector fields, elliptically polarized vector fields, and circularly polarized vortex beams through introducing attenuators in a common-path interferometer. By means of Richards-Wolf vectorial diffraction method, the characteristics of the highly focused elliptically polarized vector fields are studied. The optical force and torque on a dielectric Rayleigh particle produced by these tightly focused vector fields are calculated and exploited for the stable trapping of dielectric Rayleigh particles. It is shown that the additional degree of freedom provided by the elliptically polarized vector field allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force and torque on a dielectric Rayleigh particle.

A note on φ-analytic conformal vector fields

NASA Astrophysics Data System (ADS)

Deshmukh, Sharief; Bin Turki, Nasser

2017-09-01

Taking clue from the analytic vector fields on a complex manifold, φ-analytic conformal vector fields are defined on a Riemannian manifold (Deshmukh and Al-Solamy in Colloq. Math. 112(1):157-161, 2008). In this paper, we use φ-analytic conformal vector fields to find new characterizations of the n-sphere Sn(c) and the Euclidean space (Rn,<,> ).

Mapping the magnetic field vector in a fountain clock

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

Gertsvolf, Marina; Marmet, Louis

2011-12-15

We show how the mapping of the magnetic field vector components can be achieved in a fountain clock by measuring the Larmor transition frequency in atoms that are used as a spatial probe. We control two vector components of the magnetic field and apply audio frequency magnetic pulses to localize and measure the field vector through Zeeman spectroscopy.

Visualizing vector field topology in fluid flows

NASA Technical Reports Server (NTRS)

Helman, James L.; Hesselink, Lambertus

1991-01-01

Methods of automating the analysis and display of vector field topology in general and flow topology in particular are discussed. Two-dimensional vector field topology is reviewed as the basis for the examination of topology in three-dimensional separated flows. The use of tangent surfaces and clipping in visualizing vector field topology in fluid flows is addressed.

The Method of Unitary Clothing Transformations in the Theory of Nucleon-Nucleon Scattering

NASA Astrophysics Data System (ADS)

Dubovyk, I.; Shebeko, O.

2010-12-01

The clothing procedure, put forward in quantum field theory (QFT) by Greenberg and Schweber, is applied for the description of nucleon-nucleon ( N- N) scattering. We consider pseudoscalar ( π and η), vector ( ρ and ω) and scalar ( δ and σ) meson fields interacting with 1/2 spin ( N and {bar{N}}) fermion ones via the Yukawa-type couplings to introduce trial interactions between “bare” particles. The subsequent unitary clothing transformations are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. In this work, we are focused upon the Hermitian and energy-independent operators for the clothed nucleons, being built up in the second order in the coupling constants. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. In order to evaluate the T matrix of the N- N scattering we have used an equivalence theorem that enables us to operate in the clothed particle representation (CPR) instead of the bare particle representation with its large amount of virtual processes. We have derived the Lippmann-Schwinger type equation for the CPR elements of the T-matrix for a given collision energy in the two-nucleon sector of the Hilbert space {mathcal{H}} of hadronic states.

Poisson traces, D-modules, and symplectic resolutions

NASA Astrophysics Data System (ADS)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Poisson traces, D-modules, and symplectic resolutions.

PubMed

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Variational method for nonconservative field theories: Formulation and two PT-symmetric case examples

NASA Astrophysics Data System (ADS)

Restrepo, Juan; Ciuti, Cristiano; Favero, Ivan

2014-01-01

This Letter investigates a hybrid quantum system combining cavity quantum electrodynamics and optomechanics. The Hamiltonian problem of a photon mode coupled to a two-level atom via a Jaynes-Cummings coupling and to a mechanical mode via radiation pressure coupling is solved analytically. The atom-cavity polariton number operator commutes with the total Hamiltonian leading to an exact description in terms of tripartite atom-cavity-mechanics polarons. We demonstrate the possibility to obtain cooling of mechanical motion at the single-polariton level and describe the peculiar quantum statistics of phonons in such an unconventional regime.

Relationship Between Integro-Differential Schrodinger Equation with a Symmetric Kernel and Position-Dependent Effective Mass

NASA Astrophysics Data System (ADS)

Khosropour, B.; Moayedi, S. K.; Sabzali, R.

2018-07-01

The solution of integro-differential Schrodinger equation (IDSE) which was introduced by physicists has a great role in the fields of science. The purpose of this paper comes in two parts. First, studying the relationship between integro-differential Schrodinger equation with a symmetric non-local potential and one-dimensional Schrodinger equation with a position-dependent effective mass. Second, we show that the quantum Hamiltonian for a particle with position-dependent mass after applying Liouville-Green transformations will be converted to a quantum Hamiltonian for a particle with constant mass.

Reciprocity relationships in vector acoustics and their application to vector field calculations.

PubMed

Deal, Thomas J; Smith, Kevin B

2017-08-01

The reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. A similar equation that governs the orthogonal components of the particle velocity field is needed to enable this computational method to be used for acoustic vector sensors. This paper derives a general reciprocity equation that accounts for both monopole and dipole sources. This vector-scalar reciprocity equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each vector field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-dependent environment using a parabolic equation model.

Final Technical Report: Distributed Controls for High Penetrations of Renewables

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

Byrne, Raymond H.; Neely, Jason C.; Rashkin, Lee J.

2015-12-01

The goal of this effort was to apply four potential control analysis/design approaches to the design of distributed grid control systems to address the impact of latency and communications uncertainty with high penetrations of photovoltaic (PV) generation. The four techniques considered were: optimal fixed structure control; Nyquist stability criterion; vector Lyapunov analysis; and Hamiltonian design methods. A reduced order model of the Western Electricity Coordinating Council (WECC) developed for the Matlab Power Systems Toolbox (PST) was employed for the study, as well as representative smaller systems (e.g., a two-area, three-area, and four-area power system). Excellent results were obtained with themore » optimal fixed structure approach, and the methodology we developed was published in a journal article. This approach is promising because it offers a method for designing optimal control systems with the feedback signals available from Phasor Measurement Unit (PMU) data as opposed to full state feedback or the design of an observer. The Nyquist approach inherently handles time delay and incorporates performance guarantees (e.g., gain and phase margin). We developed a technique that works for moderate sized systems, but the approach does not scale well to extremely large system because of computational complexity. The vector Lyapunov approach was applied to a two area model to demonstrate the utility for modeling communications uncertainty. Application to large power systems requires a method to automatically expand/contract the state space and partition the system so that communications uncertainty can be considered. The Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) design methodology was selected to investigate grid systems for energy storage requirements to support high penetration of variable or stochastic generation (such as wind and PV) and loads. This method was applied to several small system models.« less

Different Relative Orientation of Static and Alternative Magnetic Fields and Cress Roots Direction of Growth Changes Their Gravitropic Reaction

NASA Astrophysics Data System (ADS)

Sheykina, Nadiia; Bogatina, Nina

The following variants of roots location relatively to static and alternative components of magnetic field were studied. At first variant the static magnetic field was directed parallel to the gravitation vector, the alternative magnetic field was directed perpendicular to static one; roots were directed perpendicular to both two fields’ components and gravitation vector. At the variant the negative gravitropysm for cress roots was observed. At second variant the static magnetic field was directed parallel to the gravitation vector, the alternative magnetic field was directed perpendicular to static one; roots were directed parallel to alternative magnetic field. At third variant the alternative magnetic field was directed parallel to the gravitation vector, the static magnetic field was directed perpendicular to the gravitation vector, roots were directed perpendicular to both two fields components and gravitation vector; At forth variant the alternative magnetic field was directed parallel to the gravitation vector, the static magnetic field was directed perpendicular to the gravitation vector, roots were directed parallel to static magnetic field. In all cases studied the alternative magnetic field frequency was equal to Ca ions cyclotron frequency. In 2, 3 and 4 variants gravitropism was positive. But the gravitropic reaction speeds were different. In second and forth variants the gravitropic reaction speed in error limits coincided with the gravitropic reaction speed under Earth’s conditions. At third variant the gravitropic reaction speed was slowed essentially.

PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics

NASA Astrophysics Data System (ADS)

Fring, Andreas; Jones, Hugh; Znojil, Miloslav

2008-06-01

Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong interactions at high energies via Regge models, in condensed matter physics in the context of the XXZ-spin chain, in interacting boson models in nuclear physics, in integrable quantum field theories as Toda field theories with complex coupling constants, and also very recently in a field theoretical scenario in the quantization procedure of strings on an AdS5 x S5 background. Concrete experimental realizations of these types of systems in the form of optical lattices have been proposed in 2007. In the area of mathematical physics similar non-systematic results appeared sporadically over the years. However, intensive and more systematic investigation of these types of non- Hermitian Hamiltonians with real eigenvalue spectra only began about ten years ago, when the surprising discovery was made that a large class of one-particle systems perturbed by a simple non-Hermitian potential term possesses a real energy spectrum. Since then regular international workshops devoted to this theme have taken place. This special issue is centred around the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics held in July 2007 at City University London. All the contributions contain significant new results or alternatively provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants were also invited. Meanwhile many interesting results have been obtained and consensus has been reached on various central conceptual issues in the growing community of this subject. It is, for instance, well understood that the reality of the spectrum can be attributed either to the unbroken PT-symmetry of the entire system, that is, invariance of the Hamiltonian and the corresponding wavefunctions under a simultaneous parity transformation and time reversal, or more generally to its pseudo-Hermiticity . When the spectrum is real and discrete the Hamiltonian is actually quasi-Hermitian, with a positive-definite metric operator, and can in principle be related by a similarity transformation to an isospectral Hermitian counterpart. For all approaches well-defined procedures have been developed, which allow one to construct metric operators and therefore a consistent description of the underlying quantum mechanical observables. Even though the general principles have been laid out, it remains a challenge in most concrete cases to implement the entire procedure. Solvable models in this sense, some of which may be found in this issue, remain a rare exception. Nonetheless, despite this progress some important questions are still unanswered. For instance, according to the current understanding the non-Hermitian Hamiltonian does not uniquely define the physics of the system since a meaningful metric can no longer be associated with the system in a non-trivial and unambiguous manner. A fully consistent scattering theory has also not yet been formulated. Other issues remain controversial, such as the quantum brachistochrone problem, the problem of forming a mixture between a Hermitian and non-Hermitian system, the new phenomenological possibilities of forming a kind of worm-hole effect, etc. We would like to acknowledge the financial support of the London Mathematical Society, the Institute of Physics, the Doppler Institute in Prague and the School of Engineering and Mathematical Science of City University London. We hope this special issue will be useful to the newcomer as well as to the expert in the subject. Workshop photograph Participants of the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics.

On the nature of a supposed water model

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

Heckmann, Lotta, E-mail: lotta@fkp.tu-darmstadt.de; Drossel, Barbara

2014-08-15

A cell model that has been proposed by Stanley and Franzese in 2002 for modeling water is based on Potts variables that represent the possible orientations of bonds between water molecules. We show that in the liquid phase, where all cells are occupied by a molecule, the Hamiltonian of the cell model can be rewritten as a Hamiltonian of a conventional Potts model, albeit with two types of coupling constants. We argue that such a model, while having a first-order phase transition, cannot display the critical end point that is postulated for the phase transition between a high- and low-densitymore » liquid. A closer look at the mean-field calculations that claim to find such an end point in the cell model reveals that the mean-field theory is constructed such that the symmetry constraints on the order parameter are violated. This is equivalent to introducing an external field. The introduction of such a field can be given a physical justification due to the fact that water does not have the type of long-range order occurring in the Potts model.« less

A Mössbauer spectroscopic study of the six-coordinate high-spin ferrous compound (meso-tetraphenylporphinato) bis(tetrahydrofuran) iron(II)

NASA Astrophysics Data System (ADS)

Boso, Brian; Lang, George; Reed, Christopher A.

1983-03-01

Mössbauer spectra of a polycrystalline form of the six-coordinate high-spin ferrous compound (meso-tetraphenylporphinato) bis(tetrahydrofuran) iron (II) have been recorded over a range of temperatures (4.2-195 K) and magnetic fields (0-6.0 T). Analysis of the spectra using a phenomenological model of the internal magnetic field and using an S=2 spin Hamiltonian, where applicable, yield the sign of Vzz negative, η=0.4, D=6.0 cm-1, E/D=0.1, and Ã*/g*N βN =(-7.2, -7.2, and -24.3 T). These results suggest that the iron experiences an octahedral crystal field, trigonally distorted in the (1, 1, 1) direction, producing a prolate orbital dz2 as the ground state. Crystal field calculations confirm this interpretation by reproducing the spin Hamiltonian parameters listed above. The calculation predicts an orbital doublet 1667 cm-1 above the ground state. Comparisons with deoxyheme proteins and their synthetic analogs suggest some common gross features of the orbital state and structure-related trends in the character of the ground quintet.

Transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Hiday-Johnston, L. A.; Howell, K. C.

1994-04-01

A strategy is formulated to design optimal time-fixed impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior L1 libration point of the Sun-Earth/Moon barycenter system. The adjoint equation in terms of rotating coordinates in the elliptic restricted three-body problem is shown to be of a distinctly different form from that obtained in the analysis of trajectories in the two-body problem. Also, the necessary conditions for a time-fixed two-impulse transfer to be optimal are stated in terms of the primer vector. Primer vector theory is then extended to nonoptimal impulsive trajectories in order to establish a criterion whereby the addition of an interior impulse reduces total fuel expenditure. The necessary conditions for the local optimality of a transfer containing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. Determination of location, orientation, and magnitude of each additional impulse is accomplished by the unconstrained minimization of the cost function using a multivariable search method. Results indicate that substantial savings in fuel can be achieved by the addition of interior impulsive maneuvers on transfers between libration-point orbits.

Symmetry restoration and quantumness reestablishment.

PubMed

Zeng, Guo-Mo; Wu, Lian-Ao; Xing, Hai-Jun

2014-09-18

A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.

Effective spin physics in two-dimensional cavity QED arrays

NASA Astrophysics Data System (ADS)

Minář, Jiří; Güneş Söyler, Şebnem; Rotondo, Pietro; Lesanovsky, Igor

2017-06-01

We investigate a strongly correlated system of light and matter in two-dimensional cavity arrays. We formulate a multimode Tavis-Cummings (TC) Hamiltonian for two-level atoms coupled to cavity modes and driven by an external laser field which reduces to an effective spin Hamiltonian in the dispersive regime. In one-dimension we provide an exact analytical solution. In two-dimensions, we perform mean-field study and large scale quantum Monte Carlo simulations of both the TC and the effective spin models. We discuss the phase diagram and the parameter regime which gives rise to frustrated interactions between the spins. We provide a quantitative description of the phase transitions and correlation properties featured by the system and we discuss graph-theoretical properties of the ground states in terms of graph colourings using Pólya’s enumeration theorem.

Theoretical investigations of the local distortion and spectral properties for VO2+ in SiO2 Glass

NASA Astrophysics Data System (ADS)

Li, Mu-Neng; Zhang, Zhi-Hong; Wu, Shao-Yi

2017-11-01

The local distortions and the spin Hamiltonian parameters g factors g∥, g⊥ and the hyperfine structure constants A∥ and A⊥ for isolated vanadyl ions VO2+ doped in SiO2 glass at 700°C are theoretically investigated from the perturbation formulas of these parameters for a 3d1 ion in tetragonally compressed octahedra. In these formulas, the relationships between local structure of VO2+ ions center and the tetragonal crystal field parameters are established. As a result, the distortion of the ligand octahedron is attributed to the strong axial crystal-fields associated with the short V4+-O2- bond due to the strong V=O bonding in the silica matrix. The theoretical spin Hamiltonian parameters obtained in this work show reasonable agreement with the experimental data.

Parity-time symmetry-breaking mechanism of dynamic Mott transitions in dissipative systems

DOE PAGES

Tripathi, Vikram; Galda, Alexey; Barman, Himadri; ...

2016-07-05

Here, we describe the critical behavior of the electric field-driven (dynamic) Mott insulator-to-metal transitions in dissipative Fermi and Bose systems in terms of non-Hermitian Hamiltonians invariant under simultaneous parity (P) and time-reversal (T) operations. The dynamic Mott transition is identified as a PT symmetry-breaking phase transition, with the Mott insulating state corresponding to the regime of unbroken PT symmetry with a real energy spectrum. We also established that the imaginary part of the Hamiltonian arises from the combined effects of the driving field and inherent dissipation. We derive the renormalization and collapse of the Mott gap at the dielectric breakdownmore » and describe the resulting critical behavior of transport characteristics. The critical exponent we obtained is in an excellent agreement with experimental findings.« less

Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study

NASA Astrophysics Data System (ADS)

Qin, Tao; Hofstetter, Walter

2017-08-01

We present a systematic study of the spectral functions of a time-periodically driven Falicov-Kimball Hamiltonian. In the high-frequency limit, this system can be effectively described as a Harper-Hofstadter-Falicov-Kimball model. Using real-space Floquet dynamical mean-field theory (DMFT), we take into account the interaction effects and contributions from higher Floquet bands in a nonperturbative way. Our calculations show a high degree of similarity between the interacting driven system and its effective static counterpart with respect to spectral properties. However, as also illustrated by our results, one should bear in mind that Floquet DMFT describes a nonequilibrium steady state, while an effective static Hamiltonian describes an equilibrium state. We further demonstrate the possibility of using real-space Floquet DMFT to study edge states on a cylinder geometry.

Interest rates in quantum finance: the Wilson expansion and Hamiltonian.

PubMed

Baaquie, Belal E

2009-10-01

Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field A(t,x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor phi(t,x) is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated.

Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Schwörer, Magnus; Breitenfeld, Benedikt; Tröster, Philipp; Bauer, Sebastian; Lorenzen, Konstantin; Tavan, Paul; Mathias, Gerald

2013-06-01

Hybrid molecular dynamics (MD) simulations, in which the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 103-105 molecules, pose a challenge. A corresponding computational approach should guarantee energy conservation, exclude artificial distortions of the electron density at the interface between the DFT and PMM fragments, and should treat the long-range electrostatic interactions within the hybrid simulation system in a linearly scaling fashion. Here we describe a corresponding Hamiltonian DFT/(P)MM implementation, which accounts for inducible atomic dipoles of a PMM environment in a joint DFT/PMM self-consistency iteration. The long-range parts of the electrostatics are treated by hierarchically nested fast multipole expansions up to a maximum distance dictated by the minimum image convention of toroidal boundary conditions and, beyond that distance, by a reaction field approach such that the computation scales linearly with the number of PMM atoms. Short-range over-polarization artifacts are excluded by using Gaussian inducible dipoles throughout the system and Gaussian partial charges in the PMM region close to the DFT fragment. The Hamiltonian character, the stability, and efficiency of the implementation are investigated by hybrid DFT/PMM-MD simulations treating one molecule of the water dimer and of bulk water by DFT and the respective remainder by PMM.

Weaving Knotted Vector Fields with Tunable Helicity.

PubMed

Kedia, Hridesh; Foster, David; Dennis, Mark R; Irvine, William T M

2016-12-30

We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot, and its generalizations. As finite-energy physical fields, they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knotted fields. The construction can be used to generate isolated knotted flux tubes, filled by knots encoded in the lines of the vector field. Lastly, we give examples of manifestly knotted vector fields with vanishing helicity. Our results provide building blocks for analytical models and simulations alike.

Exact solution of mean-field plus an extended T = 1 nuclear pairing Hamiltonian in the seniority-zero symmetric subspace

NASA Astrophysics Data System (ADS)

Pan, Feng; Ding, Xiaoxue; Launey, Kristina D.; Dai, Lianrong; Draayer, Jerry P.

2018-05-01

An extended pairing Hamiltonian that describes multi-pair interactions among isospin T = 1 and angular momentum J = 0 neutron-neutron, proton-proton, and neutron-proton pairs in a spherical mean field, such as the spherical shell model, is proposed based on the standard T = 1 pairing formalism. The advantage of the model lies in the fact that numerical solutions within the seniority-zero symmetric subspace can be obtained more easily and with less computational time than those calculated from the mean-field plus standard T = 1 pairing model. Thus, large-scale calculations within the seniority-zero symmetric subspace of the model is feasible. As an example of the application, the average neutron-proton interaction in even-even N ∼ Z nuclei that can be suitably described in the f5 pg9 shell is estimated in the present model, with a focus on the role of np-pairing correlations.

Phase transition and field effect topological quantum transistor made of monolayer MoS2

NASA Astrophysics Data System (ADS)

Simchi, H.; Simchi, M.; Fardmanesh, M.; Peeters, F. M.

2018-06-01

We study topological phase transitions and topological quantum field effect transistor in monolayer molybdenum disulfide (MoS2) using a two-band Hamiltonian model. Without considering the quadratic (q 2) diagonal term in the Hamiltonian, we show that the phase diagram includes quantum anomalous Hall effect, quantum spin Hall effect, and spin quantum anomalous Hall effect regions such that the topological Kirchhoff law is satisfied in the plane. By considering the q 2 diagonal term and including one valley, it is shown that MoS2 has a non-trivial topology, and the valley Chern number is non-zero for each spin. We show that the wave function is (is not) localized at the edges when the q 2 diagonal term is added (deleted) to (from) the spin-valley Dirac mass equation. We calculate the quantum conductance of zigzag MoS2 nanoribbons by using the nonequilibrium Green function method and show how this device works as a field effect topological quantum transistor.

Student difficulties regarding symbolic and graphical representations of vector fields

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; Baily, Charles; Kelly, Mossy; De Cock, Mieke

2017-12-01

The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person's understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing, and switching between representations of vector fields, using both qualitative and quantitative methods. We first identified to what extent students are fluent with the use of field vector plots, field line diagrams, and symbolic expressions of vector fields by conducting individual student interviews and analyzing in-class student activities. Based on those findings, we designed the Vector Field Representations test, a free response assessment tool that has been given to 196 second- and third-year physics, mathematics, and engineering students from four different universities. From the obtained results we gained a comprehensive overview of typical errors that students make when switching between vector field representations. In addition, the study allowed us to determine the relative prevalence of the observed difficulties. Although the results varied greatly between institutions, a general trend revealed that many students struggle with vector addition, fail to recognize the field line density as an indication of the magnitude of the field, confuse characteristics of field lines and equipotential lines, and do not choose the appropriate coordinate system when writing out mathematical expressions of vector fields.

Discovering and understanding the vector field using simulation in android app

NASA Astrophysics Data System (ADS)

Budi, A.; Muliyati, D.

2018-05-01

An understanding of vector field’s concepts are fundamental parts of the electrodynamics course. In this paper, we use a simple simulation that can be used to show qualitative imaging results as a variation of the vector field. Android application packages the simulation with consideration of the efficiency of use during the lecture. In addition, this simulation also trying to cover the divergences and curl concepts from the same conditions that students have a complete understanding and can distinguish concepts that have been described only mathematically. This simulation is designed to show the relationship between the field magnitude and its potential. This application can show vector field simulations in various conditions that help to improve students’ understanding of vector field concepts and their relation to particle existence around the field vector.

Remarks on the BRST quantized gauged WZNW models and the Toda field theories

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

Hayashi, N.

In this paper it is shown that the quantum Hamiltonian reduction proposed by Bershadsky and Ooguri enables us to connect the gauged WZNW models with fractional levels to the quantum Toda field theories, and the coupling constants of the Toda field theories with the fractional levels. The BRST framework is applied to the SL ({ital n},R)-WZNW models.

Constraint algebra in Smolin's G →0 limit of 4D Euclidean gravity

NASA Astrophysics Data System (ADS)

Varadarajan, Madhavan

2018-05-01

Smolin's generally covariant GNewton→0 limit of 4d Euclidean gravity is a useful toy model for the study of the constraint algebra in loop quantum gravity (LQG). In particular, the commutator between its Hamiltonian constraints has a metric dependent structure function. While a prior LQG-like construction of nontrivial anomaly free constraint commutators for the model exists, that work suffers from two defects. First, Smolin's remarks on the inability of the quantum dynamics to generate propagation effects apply. Second, the construction only yields the action of a single Hamiltonian constraint together with the action of its commutator through a continuum limit of corresponding discrete approximants; the continuum limit of a product of two or more constraints does not exist. Here, we incorporate changes in the quantum dynamics through structural modifications in the choice of discrete approximants to the quantum Hamiltonian constraint. The new structure is motivated by that responsible for propagation in an LQG-like quantization of paramatrized field theory and significantly alters the space of physical states. We study the off shell constraint algebra of the model in the context of these structural changes and show that the continuum limit action of multiple products of Hamiltonian constraints is (a) supported on an appropriate domain of states, (b) yields anomaly free commutators between pairs of Hamiltonian constraints, and (c) is diffeomorphism covariant. Many of our considerations seem robust enough to be applied to the setting of 4d Euclidean gravity.

Group theoretical quantization of isotropic loop cosmology

NASA Astrophysics Data System (ADS)

Livine, Etera R.; Martín-Benito, Mercedes

2012-06-01

We achieve a group theoretical quantization of the flat Friedmann-Robertson-Walker model coupled to a massless scalar field adopting the improved dynamics of loop quantum cosmology. Deparemetrizing the system using the scalar field as internal time, we first identify a complete set of phase space observables whose Poisson algebra is isomorphic to the su(1,1) Lie algebra. It is generated by the volume observable and the Hamiltonian. These observables describe faithfully the regularized phase space underlying the loop quantization: they account for the polymerization of the variable conjugate to the volume and for the existence of a kinematical nonvanishing minimum volume. Since the Hamiltonian is an element in the su(1,1) Lie algebra, the dynamics is now implemented as SU(1, 1) transformations. At the quantum level, the system is quantized as a timelike irreducible representation of the group SU(1, 1). These representations are labeled by a half-integer spin, which gives the minimal volume. They provide superselection sectors without quantization anomalies and no factor ordering ambiguity arises when representing the Hamiltonian. We then explicitly construct SU(1, 1) coherent states to study the quantum evolution. They not only provide semiclassical states but truly dynamical coherent states. Their use further clarifies the nature of the bounce that resolves the big bang singularity.

Detecting level crossings without solving the Hamiltonian. II. Applications to atoms and molecules

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

Bhattacharya, M.; Raman, C.

2007-03-15

A number of interesting phenomena occur at points where the energy levels of an atom or a molecule (anti) cross as a function of some parameter such as an external field. In a previous paper [M. Bhattacharya and C. Raman, Phys. Rev. Lett. 97, 140405 (2006)] we have outlined powerful mathematical techniques useful in identifying the parameter values at which such (avoided) crossings occur. In the accompanying article [M. Bhattacharya and C. Raman, Phys. Rev A 75, 033405 (2007)] we have developed the mathematical basis of these algebraic techniques in some detail. In this article we apply these level-crossing methodsmore » to the spectra of atoms and molecules in a magnetic field. In the case of atoms the final result is the derivation of a class of invariants of the Breit-Rabi Hamiltonian of magnetic resonance. These invariants completely describe the parametric symmetries of the Hamiltonian. In the case of molecules we present an indicator which can tell when the Born-Oppenheimer approximation breaks down without using any information about the molecular potentials other than the fact that they are real. We frame our discussion in the context of Feshbach resonances in the atom-pair {sup 23}Na-{sup 85}Rb which are of current interest.« less

Killing vector fields in three dimensions: a method to solve massive gravity field equations

NASA Astrophysics Data System (ADS)

Gürses, Metin

2010-10-01

Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.

A Mapping Model for Magnetic Fields with q-profile Variations Typical of Internal Transport Barrier Experiments

NASA Astrophysics Data System (ADS)

Rapoport, B. I.; Pavlenko, I.; Weyssow, B.; Carati, D.

2002-11-01

Recent studies of ion and electron transport indicate that the safety factor profile, q(r), affects internal transport barrier (ITB) formation in magnetic confinement devices [1, 2]. These studies are consistent with experimental observations that low shear suppresses magnetic island interaction and associated stochasticity when the ITB is formed [3]. In this sense the position and quality of the ITB depend on the stochasticity of the magnetic field, and can be controlled by q(r). This study explores effects of the q-profile on magnetic field stochasticity using two-dimensional mapping techniques. Q-profiles typical of ITB experiments are incorporated into Hamiltonian maps to investigate the relation between magnetic field stochasticity and ITB parameters predicted by other models. It is shown that the mapping technique generates results consistent with these predictions, and suggested that Hamiltonian mappings can be useful as simple and computationally inexpensive approximation methods for describing the magnetic field in ITB experiments. 1. I. Voitsekhovitch et al. 29th EPS Conference on Plasma Physics and Controlled Fusion (2002). O-4.04. 2. G.M.D. Hogeweij et al. Nucl. Fusion. 38 (1998): 1881. 3. K.A. Razumova et al. Plasma Phys. Contr. Fusion. 42 (2000): 973.

Benefits and drawbacks of low magnetic shears on the confinement in magnetic fusion toroidal devices

NASA Astrophysics Data System (ADS)

Firpo, Marie-Christine; Constantinescu, Dana

2012-10-01

The issue of confinement in magnetic fusion devices is addressed within a purely magnetic approach. As it is well known, the magnetic field being divergence-free, the equations of its field lines can be cast in Hamiltonian form. Using then some Hamiltonian models for the magnetic field lines, the dual impact of low magnetic shear is demonstrated. Away from resonances, it induces a drastic enhancement of magnetic confinement that favors robust internal transport barriers (ITBs) and turbulence reduction. However, when low-shear occurs for values of the winding of the magnetic field lines close to low-order rationals, the amplitude thresholds of the resonant modes that break internal transport barriers by allowing a radial stochastic transport of the magnetic field lines may be much lower than the ones obtained for strong shear profiles. The approach can be applied to assess the robustness versus magnetic perturbations of general almost-integrable magnetic steady states, including non-axisymmetric ones such as the important single helicity steady states. This analysis puts a constraint on the tolerable mode amplitudes compatible with ITBs and may be proposed as a possible explanation of diverse experimental and numerical signatures of their collapses.

Proper projective symmetry in LRS Bianchi type V spacetimes

NASA Astrophysics Data System (ADS)

Shabbir, Ghulam; Mahomed, K. S.; Mahomed, F. M.; Moitsheki, R. J.

2018-04-01

In this paper, we investigate proper projective vector fields of locally rotationally symmetric (LRS) Bianchi type V spacetimes using direct integration and algebraic techniques. Despite the non-degeneracy in the Riemann tensor eigenvalues, we classify proper Bianchi type V spacetimes and show that the above spacetimes do not admit proper projective vector fields. Here, in all the cases projective vector fields are Killing vector fields.

Video-rate terahertz electric-field vector imaging

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

Takai, Mayuko; Takeda, Masatoshi; Sasaki, Manabu

We present an experimental setup to dramatically reduce a measurement time for obtaining spatial distributions of terahertz electric-field (E-field) vectors. The method utilizes the electro-optic sampling, and we use a charge-coupled device to detect a spatial distribution of the probe beam polarization rotation by the E-field-induced Pockels effect in a 〈110〉-oriented ZnTe crystal. A quick rotation of the ZnTe crystal allows analyzing the terahertz E-field direction at each image position, and the terahertz E-field vector mapping at a fixed position of an optical delay line is achieved within 21 ms. Video-rate mapping of terahertz E-field vectors is likely to bemore » useful for achieving real-time sensing of terahertz vector beams, vector vortices, and surface topography. The method is also useful for a fast polarization analysis of terahertz beams.« less

Spin orbit coupling for molecular ab initio density matrix renormalization group calculations: Application to g-tensors

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

Roemelt, Michael, E-mail: michael.roemelt@theochem.rub.de

Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctionsmore » are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.« less

Orbital Selective Spin Excitations and their Impact on Superconductivity of LiFe 1 - x Co x As

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

Li, Yu; Yin, Zhiping; Wang, Xiancheng

We use neutron scattering to study spin excitations in single crystals of LiFe 0.88Co 0.12As, which is located near the boundary of the superconducting phase of LiFe 1-xCo xAs and exhibits non- Fermi-liquid behavior indicative of a quantum critical point. By comparing spin excitations of LiFe 0.88Co 0.12As with a combined density functional theory (DFT) and dynamical mean field theory (DMFT) calculation, we conclude that wave-vector correlated low energy spin excitations are mostly from the dxy orbitals, while high-energy spin excitations arise from the dyz and dxz orbitals. Unlike most iron pnictides, the strong orbital selective spin excitations in LiFeAsmore » family cannot be described by anisotropic Heisenberg Hamiltonian. While the evolution of low-energy spin excitations of LiFe 1-xCo xAs are consistent with electron-hole Fermi surface nesting condition for the dxy orbital, the reduced superconductivity in LiFe 0.88Co 0.12As suggests that Fermi surface nesting conditions for the dyz and dxz orbitals are also important for superconductivity in iron pnictides.« less

Orbital Selective Spin Excitations and their Impact on Superconductivity of LiFe 1 - x Co x As

DOE PAGES

Li, Yu; Yin, Zhiping; Wang, Xiancheng; ...

2016-06-17

We use neutron scattering to study spin excitations in single crystals of LiFe 0.88Co 0.12As, which is located near the boundary of the superconducting phase of LiFe 1-xCo xAs and exhibits non- Fermi-liquid behavior indicative of a quantum critical point. By comparing spin excitations of LiFe 0.88Co 0.12As with a combined density functional theory (DFT) and dynamical mean field theory (DMFT) calculation, we conclude that wave-vector correlated low energy spin excitations are mostly from the dxy orbitals, while high-energy spin excitations arise from the dyz and dxz orbitals. Unlike most iron pnictides, the strong orbital selective spin excitations in LiFeAsmore » family cannot be described by anisotropic Heisenberg Hamiltonian. While the evolution of low-energy spin excitations of LiFe 1-xCo xAs are consistent with electron-hole Fermi surface nesting condition for the dxy orbital, the reduced superconductivity in LiFe 0.88Co 0.12As suggests that Fermi surface nesting conditions for the dyz and dxz orbitals are also important for superconductivity in iron pnictides.« less

Sitnikov problem in the square configuration: elliptic case

NASA Astrophysics Data System (ADS)

Shahbaz Ullah, M.

2016-05-01

This paper is extension to the classical Sitnikov problem, when the four primaries of equal masses lie at the vertices of a square for all time and moving in elliptic orbits around their center of mass of the system, the distances between the primaries vary with time but always in such a way that their mutual distances remain in the same ratio. First we have established averaged equation of motion of the Sitnikov five-body problem in the light of Jalali and Pourtakdoust (Celest. Mech. Dyn. Astron. 68:151-162, 1997), by applying the Van der Pol transformation and averaging technique of Guckenheimer and Holmes (Nonlinear oscillations, dynamical system bifurcations of vector fields, Springer, Berlin, 1983). Next the Hamiltonian equation of motion has been solved with the help of action angle variables I and φ. Finally the periodicity and stability of the Sitnikov five-body problem have been examined with the help of Poincare surfaces of section (PSS). It is shown that chaotic region emerging from the destroyed islands, can easily be seen by increasing the eccentricity of the primaries to e = 0.21. It is valid for bounded small amplitude solutions z_{max} ( z_{max} = 0.65 ) and 0 ≤ e < 0.3.

Orbital Selective Spin Excitations and their Impact on Superconductivity of LiFe_{1-x}Co_{x}As.

PubMed

Li, Yu; Yin, Zhiping; Wang, Xiancheng; Tam, David W; Abernathy, D L; Podlesnyak, A; Zhang, Chenglin; Wang, Meng; Xing, Lingyi; Jin, Changqing; Haule, Kristjan; Kotliar, Gabriel; Maier, Thomas A; Dai, Pengcheng

2016-06-17

We use neutron scattering to study spin excitations in single crystals of LiFe_{0.88}Co_{0.12}As, which is located near the boundary of the superconducting phase of LiFe_{1-x}Co_{x}As and exhibits non-Fermi-liquid behavior indicative of a quantum critical point. By comparing spin excitations of LiFe_{0.88}Co_{0.12}As with a combined density functional theory and dynamical mean field theory calculation, we conclude that wave-vector correlated low energy spin excitations are mostly from the d_{xy} orbitals, while high-energy spin excitations arise from the d_{yz} and d_{xz} orbitals. Unlike most iron pnictides, the strong orbital selective spin excitations in the LiFeAs family cannot be described by an anisotropic Heisenberg Hamiltonian. While the evolution of low-energy spin excitations of LiFe_{1-x}Co_{x}As is consistent with the electron-hole Fermi surface nesting conditions for the d_{xy} orbital, the reduced superconductivity in LiFe_{0.88}Co_{0.12}As suggests that Fermi surface nesting conditions for the d_{yz} and d_{xz} orbitals are also important for superconductivity in iron pnictides.

Segmentation of discrete vector fields.

PubMed

Li, Hongyu; Chen, Wenbin; Shen, I-Fan

2006-01-01

In this paper, we propose an approach for 2D discrete vector field segmentation based on the Green function and normalized cut. The method is inspired by discrete Hodge Decomposition such that a discrete vector field can be broken down into three simpler components, namely, curl-free, divergence-free, and harmonic components. We show that the Green Function Method (GFM) can be used to approximate the curl-free and the divergence-free components to achieve our goal of the vector field segmentation. The final segmentation curves that represent the boundaries of the influence region of singularities are obtained from the optimal vector field segmentations. These curves are composed of piecewise smooth contours or streamlines. Our method is applicable to both linear and nonlinear discrete vector fields. Experiments show that the segmentations obtained using our approach essentially agree with human perceptual judgement.

Structuring Stokes correlation functions using vector-vortex beam

NASA Astrophysics Data System (ADS)

Kumar, Vijay; Anwar, Ali; Singh, R. P.

2018-01-01

Higher order statistical correlations of the optical vector speckle field, formed due to scattering of a vector-vortex beam, are explored. Here, we report on the experimental construction of the Stokes parameters covariance matrix, consisting of all possible spatial Stokes parameters correlation functions. We also propose and experimentally realize a new Stokes correlation functions called Stokes field auto correlation functions. It is observed that the Stokes correlation functions of the vector-vortex beam will be reflected in the respective Stokes correlation functions of the corresponding vector speckle field. The major advantage of proposing Stokes correlation functions is that the Stokes correlation function can be easily tuned by manipulating the polarization of vector-vortex beam used to generate vector speckle field and to get the phase information directly from the intensity measurements. Moreover, this approach leads to a complete experimental Stokes characterization of a broad range of random fields.

Vector optical fields with bipolar symmetry of linear polarization.

PubMed

Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Si, Yu; Tu, Chenghou; Wang, Hui-Tian

2013-09-15

We focus on a new kind of vector optical field with bipolar symmetry of linear polarization instead of cylindrical and elliptical symmetries, enriching members of family of vector optical fields. We design theoretically and generate experimentally the demanded vector optical fields and then explore some novel tightly focusing properties. The geometric configurations of states of polarization provide additional degrees of freedom assisting in engineering the field distribution at the focus to the specific applications such as lithography, optical trapping, and material processing.

Novel Approach on the Optimisation of Mid-Course Corrections Along Interplanetary Trajectories

NASA Astrophysics Data System (ADS)

Iorfida, Elisabetta; Palmer, Phil; Roberts, Mark

The primer vector theory, firstly proposed by Lawden, defines a set of necessary conditions to characterise whether an impulsive thrust trajectory is optimal with respect to propellant usage, within a two-body problem context. If the conditions are not satisfied, one or more potential intermediate impulses are performed along the transfer arc, in order to lower the overall cost. The method is based on the propagation of the state transition matrix and on the solution of a boundary value problem, which leads to a mathematical and computational complexity.In this paper, a different approach is introduced. It is based on a polar coordinates transformation of the primer vector which allows the decoupling between its in-plane and out-of-plane components. The out-of-plane component is solved analytically while for the in-plane ones a Hamiltonian approximation is made.The novel procedure reduces the mathematical complexity and the computational cost of Lawden's problem and gives also a different perspective about the optimisation of a transfer trajectory.

On the Milankovitch orbital elements for perturbed Keplerian motion

NASA Astrophysics Data System (ADS)

Rosengren, Aaron J.; Scheeres, Daniel J.

2014-03-01

We consider sets of natural vectorial orbital elements of the Milankovitch type for perturbed Keplerian motion. These elements are closely related to the two vectorial first integrals of the unperturbed two-body problem; namely, the angular momentum vector and the Laplace-Runge-Lenz vector. After a detailed historical discussion of the origin and development of such elements, nonsingular equations for the time variations of these sets of elements under perturbations are established, both in Lagrangian and Gaussian form. After averaging, a compact, elegant, and symmetrical form of secular Milankovitch-like equations is obtained, which reminds of the structure of canonical systems of equations in Hamiltonian mechanics. As an application of this vectorial formulation, we analyze the motion of an object orbiting about a planet (idealized as a point mass moving in a heliocentric elliptical orbit) and subject to solar radiation pressure acceleration (obeying an inverse-square law). We show that the corresponding secular problem is integrable and we give an explicit closed-form solution.

Dynamical Causal Modeling from a Quantum Dynamical Perspective

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

Demiralp, Emre; Demiralp, Metin

Recent research suggests that any set of first order linear vector ODEs can be converted to a set of specific vector ODEs adhering to what we have called ''Quantum Harmonical Form (QHF)''. QHF has been developed using a virtual quantum multi harmonic oscillator system where mass and force constants are considered to be time variant and the Hamiltonian is defined as a conic structure over positions and momenta to conserve the Hermiticity. As described in previous works, the conversion to QHF requires the matrix coefficient of the first set of ODEs to be a normal matrix. In this paper, thismore » limitation is circumvented using a space extension approach expanding the potential applicability of this method. Overall, conversion to QHF allows the investigation of a set of ODEs using mathematical tools available to the investigation of the physical concepts underlying quantum harmonic oscillators. The utility of QHF in the context of dynamical systems and dynamical causal modeling in behavioral and cognitive neuroscience is briefly discussed.« less

Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory

NASA Astrophysics Data System (ADS)

Benioff, Paul

2015-05-01

The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value are combined in the usual representations of number structures. This is valid as long as just one structure of each number type is being considered. It is not valid when different structures of each number type are being considered. Elements of base sets of number structures, considered by themselves, have no meaning. They acquire meaning or value as elements of a number structure. Fiber bundles over a space or space time manifold, M, are described. The fiber consists of a collection of many real or complex number structures and vector space structures. The structures are parameterized by a real or complex scaling factor, s. A vector space at a fiber level, s, has, as scalars, real or complex number structures at the same level. Connections are described that relate scalar and vector space structures at both neighbor M locations and at neighbor scaling levels. Scalar and vector structure valued fields are described and covariant derivatives of these fields are obtained. Two complex vector fields, each with one real and one imaginary field, appear, with one complex field associated with positions in M and the other with position dependent scaling factors. A derivation of the covariant derivative for scalar and vector valued fields gives the same vector fields. The derivation shows that the complex vector field associated with scaling fiber levels is the gradient of a complex scalar field. Use of these results in gauge theory shows that the imaginary part of the vector field associated with M positions acts like the electromagnetic field. The physical relevance of the other three fields, if any, is not known.

Semiclassical theory of the self-consistent vibration-rotation fields and its application to the bending-rotation interaction in the H{sub 2}O molecule

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

Skalozub, A.S.; Tsaune, A.Ya.

1994-12-01

A new approach for analyzing the highly excited vibration-rotation (VR) states of nonrigid molecules is suggested. It is based on the separation of the vibrational and rotational terms in the molecular VR Hamiltonian by introducing periodic auxiliary fields. These fields transfer different interactions within a molecule and are treated in terms of the mean-field approximation. As a result, the solution of the stationary Schroedinger equation with the VR Hamiltonian amounts to a quantization of the Berry phase in a problem of the molecular angular-momentum motion in a certain periodic VR field (rotational problem). The quantization procedure takes into account themore » motion of the collective vibrational variables in the appropriate VR potentials (vibrational problem). The quantization rules, the mean-field configurations of auxiliary interactions, and the solutions to the Schrodinger equations for the vibrational and rotational problems are self-consistently connected with one another. The potentialities of the theory are demonstrated by the bending-rotation interaction modeled by the Bunker-Landsberg potential function in the H{sub 2} molecule. The calculations are compared with both the results of the exact computations and those of other approximate methods. 32 refs., 4 tabs.« less

The effect of band Jahn-Teller distortion on the magnetoresistivity of manganites: a model study.

PubMed

Rout, G C; Panda, Saswati; Behera, S N

2011-10-05

We present a model study of magnetoresistance through the interplay of magnetisation, structural distortion and external magnetic field for the manganite systems. The manganite system is described by the Hamiltonian which consists of the s-d type double exchange interaction, Heisenberg spin-spin interaction among the core electrons, and the static and dynamic band Jahn-Teller (JT) interaction in the e(g) band. The relaxation time of the e(g) electron is found from the imaginary part of the Green's function using the total Hamiltonian consisting of the interactions due to the electron and phonon. The calculated resistivity exhibits a peak in the pure JT distorted insulating phase separating the low temperature metallic ferromagnetic phase and the high temperature paramagnetic phase. The resistivity is suppressed with the increase of the external magnetic field. The e(g) electron band splitting and its effect on magnetoresistivity is reported here. © 2011 IOP Publishing Ltd

Evaluation of Spin Hamiltonian Parameters and Local Structure of Cu2+-doped Ion in xK2SO4-(50 - x)Na2SO4-50ZnSO4 Glasses with Various K2SO4 Concentrations

NASA Astrophysics Data System (ADS)

Ding, Ch.-Ch.; Wu, Sh.-Y.; Xu, Y.-Q.; Zhang, L.-J.; He, J.-J.

2018-03-01

The spin Hamiltonian parameters (SHPs), i.e., g factors and hyperfine structure constants, and local structures are theoretically studied by analyzing tetragonally elongated 3d9 clusters for Cu2+ in xK2SO4-(50 - x)Na2SO4-50ZnSO4 glasses with various K2SO4 concentrations x. The concentration dependences of the SHPs are attributed to the parabolic decreases of the cubic field parameter Dq, orbital reduction factor k, relative tetragonal elongation ratio τ, and core polarization constant κ with x. The [CuO6]10- clusters are found to undergo significant elongations of about 17% due to the Jahn-Teller effect. The calculated cubic field splittings and the SHPs at various concentrations agree well with the experimental data.

Theory of Stochastic Laplacian Growth

NASA Astrophysics Data System (ADS)

Alekseev, Oleg; Mineev-Weinstein, Mark

2017-07-01

We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple combinatorial arguments we determine probabilities of different growth scenarios and prove that the most probable evolution is governed by the deterministic Laplacian growth equation. A potential-theoretical analysis of the growth probabilities reveals connections with the tau-function of the integrable dispersionless limit of the two-dimensional Toda hierarchy, normal matrix ensembles, and the two-dimensional Dyson gas confined in a non-uniform magnetic field. We introduce the time-dependent Hamiltonian, which generates transitions between different classes of equivalence of closed curves, and prove the Hamiltonian structure of the interface dynamics. Finally, we propose a relation between probabilities of growth scenarios and the semi-classical limit of certain correlation functions of "light" exponential operators in the Liouville conformal field theory on a pseudosphere.

Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial field

NASA Astrophysics Data System (ADS)

Gros, J.-B.; Kuhl, U.; Legrand, O.; Mortessagne, F.

2016-03-01

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response.

Lorentz symmetry breaking in a cosmological context

NASA Astrophysics Data System (ADS)

Gresham, Moira I.

This thesis is comprised primarily of work from three independent papers, written in collaboration with Sean Carroll, Tim Dulaney, and Heywood Tam. The original motivation for the projects undertaken came from revisiting the standard assumption of spatial isotropy during inflation. Each project relates to the spontaneous breaking of Lorentz symmetry---in early Universe cosmology or in the context of effective field theory, in general. Chapter 1 is an introductory chapter that provides context for the thesis. Chapter 2 is an investigation of the stability of theories in which Lorentz invariance is spontaneously broken by fixed-norm vector "aether" fields. It is shown that models with generic kinetic terms are plagued either by ghosts or by tachyons, and are therefore physically unacceptable. Chapter 3 is an investigation of the phenomenological properties of the one low-energy effective theory of spontaneous Lorentz symmetry breaking found in the previous chapter to have a globally bounded Hamiltonian and a perturbatively stable vacuum---the theory in which the Lagrangian takes the form of a sigma model. In chapter 4 cosmological perturbations in a dynamical theory of inflation in which an Abelian gauge field couples directly to the inflaton are examined. The dominant effects of a small, persistent anisotropy on the primordial gravitational wave and curvature perturbation power spectra are found using the "in-in" formalism of perturbation theory. It is found that the primordial power spectra of cosmological perturbations gain significant direction dependence and that the fractional direction dependence of the tensor power spectrum is suppressed in comparison to that of the scalar power spectrum.

Light scattering of rectangular slot antennas: parallel magnetic vector vs perpendicular electric vector

NASA Astrophysics Data System (ADS)

Lee, Dukhyung; Kim, Dai-Sik

2016-01-01

We study light scattering off rectangular slot nano antennas on a metal film varying incident polarization and incident angle, to examine which field vector of light is more important: electric vector perpendicular to, versus magnetic vector parallel to the long axis of the rectangle. While vector Babinet’s principle would prefer magnetic field along the long axis for optimizing slot antenna function, convention and intuition most often refer to the electric field perpendicular to it. Here, we demonstrate experimentally that in accordance with vector Babinet’s principle, the incident magnetic vector parallel to the long axis is the dominant component, with the perpendicular incident electric field making a small contribution of the factor of 1/|ε|, the reciprocal of the absolute value of the dielectric constant of the metal, owing to the non-perfectness of metals at optical frequencies.

Frame-dragging effect in the field of non rotating body due to unit gravimagnetic moment

NASA Astrophysics Data System (ADS)

Deriglazov, Alexei A.; Ramírez, Walberto Guzmán

2018-04-01

Nonminimal spin-gravity interaction through unit gravimagnetic moment leads to modified Mathisson-Papapetrou-Tulczyjew-Dixon equations with improved behavior in the ultrarelativistic limit. We present exact Hamiltonian of the resulting theory and compute an effective 1/c2-Hamiltonian and leading post-Newtonian corrections to the trajectory and spin. Gravimagnetic moment causes the same precession of spin S as a fictitious rotation of the central body with angular momentum J = M/m S. So the modified equations imply a number of qualitatively new effects, that could be used to test experimentally, whether a rotating body in general relativity has null or unit gravimagnetic moment.

Collective coordinates and constrained hamiltonian systems

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

Dayi, O.F.

1992-07-01

A general method of incorporating collective coordinates (transformation of fields into an overcomplete basis) with constrained hamiltonian systems is given where the original phase space variables and collective coordinates can be bosonic or/and fermionic. This method is illustrated by applying it to the SU(2) Yang-Mills-Higgs theory and its BFV-BRST quantization is discussed. Moreover, this formalism is used to give a systematic way of converting second class constraints into effectively first class ones, by considering second class constraints as first class constraints and gauge fixing conditions. This approach is applied to the massive superparticle. Proca lagrangian, and some topological quantum fieldmore » theories.« less

Competing bosonic condensates in optical lattice with a mixture of single and pair hoppings

NASA Astrophysics Data System (ADS)

Travin, V. M.; Kopeć, T. K.

2017-01-01

A system of ultra-cold atoms with single boson and pair tunneling of bosonic atoms is considered in an optical lattice at arbitrary temperature. A mean-field theory was applied to the extended Bose-Hubbard Hamiltonian describing the system in order to investigate the competition between superfluid and pair superfluid as a function of the chemical potential and the temperature. To this end we have applied a method based on the Laplace transform method for the efficient calculation of the statistical sum for the quantum Hamiltonian. These results may be of interest for experiments on cold atom systems in optical lattices.

The nonrelativistic limit of (central-extended) Poincaré group and some consequences for quantum actualization

NASA Astrophysics Data System (ADS)

Ardenghi, Juan S.; Castagnino, M.; Campoamor-Stursberg, R.

2009-10-01

The nonrelativistic limit of the centrally extended Poincaré group is considered and their consequences in the modal Hamiltonian interpretation of quantum mechanics are discussed [O. Lombardi and M. Castagnino, Stud. Hist. Philos. Mod. Phys 39, 380 (2008); J. Phys, Conf. Ser. 128, 012014 (2008)]. Through the assumption that in quantum field theory the Casimir operators of the Poincaré group actualize, the nonrelativistic limit of the latter group yields to the actualization of the Casimir operators of the Galilei group, which is in agreement with the actualization rule of previous versions of modal Hamiltonian interpretation [Ardenghi et al., Found. Phys. (submitted)].

Theoretical explanation of spin-Hamiltonian parameters and local structure for the orthorhombic MnO2 -4 clusters in K2CrO4 : Mn6 + crystal

NASA Astrophysics Data System (ADS)

Wang, Ning; Xie, Linhua

2017-12-01

In this paper, the spin-Hamiltonian parameters (g factors gx, gy, gz and hyperfine structure constants A Ax, Ay, Az) and the absorption spectrum of K2CrO4 : Mn6 + crystal are theoretically explained by using the high-order perturbation theory, the double-spin-orbit-coupling model theory and the double-mechanism theory (the crystal field mechanism and the charge-transfer (CT) mechanism). The calculation results show that the contribution of the CT mechanism cannot be neglected for Mn6 + ions in orthorhombic clusters with the ground state ?.

Time dependence of correlation functions following a quantum quench.

PubMed

Calabrese, Pasquale; Cardy, John

2006-04-07

We show that the time dependence of correlation functions in an extended quantum system in d dimensions, which is prepared in the ground state of some Hamiltonian and then evolves without dissipation according to some other Hamiltonian, may be extracted using methods of boundary critical phenomena in d + 1 dimensions. For d = 1 particularly powerful results are available using conformal field theory. These are checked against those available from solvable models. They may be explained in terms of a picture, valid more generally, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate classically through the system.

Two-body problem in scalar-tensor theories as a deformation of general relativity: An effective-one-body approach

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis; Deruelle, Nathalie

2017-06-01

In this paper we address the two-body problem in massless scalar-tensor (ST) theories within an effective-one-body (EOB) framework. We focus on the first building block of the EOB approach, that is, mapping the conservative part of the two-body dynamics onto the geodesic motion of a test particle in an effective external metric. To this end, we first deduce the second post-Keplerian (2PK) Hamiltonian of the two-body problem from the known 2PK Lagrangian. We then build, by means of a canonical transformation, a ST deformation of the general relativistic EOB Hamiltonian that allows us to incorporate the scalar-tensor (2PK) corrections to the currently best available general relativity EOB results. This EOB-ST Hamiltonian defines a resummation of the dynamics that may provide information on the strong-field regime, in particular, the ISCO location and associated orbital frequency, and can be compared to, other, e.g., tidal, corrections.

Spin-curvature interaction from curved Dirac equation: Application to single-wall carbon nanotubes

NASA Astrophysics Data System (ADS)

Zhang, Kai; Zhang, Erhu; Chen, Huawei; Zhang, Shengli

2017-06-01

The spin-curvature interaction (SCI) and its effects are investigated based on curved Dirac equation. Through the low-energy approximation of curved Dirac equation, the Hamiltonian of SCI is obtained and depends on the geometry and spinor structure of manifold. We find that the curvature can be considered as field strength and couples with spin through Zeeman-like term. Then, we use dimension reduction to derive the local Hamiltonian of SCI for cylinder surface, which implies that the effective Hamiltonian of single-wall carbon nanotubes results from the geometry and spinor structure of lattice and includes two types of interactions: one does not break any symmetries of the lattice and only shifts the Dirac points for all nanotubes, while the other one does and opens the gaps except for armchair nanotubes. At last, analytical expressions of the band gaps and the shifts of their positions induced by curvature are given for metallic nanotubes. These results agree well with experiments and can be verified experimentally.

Canonical formalism for modelling and control of rigid body dynamics.

PubMed

Gurfil, P

2005-12-01

This paper develops a new paradigm for stabilization of rigid-body dynamics. The state-space model is formulated using canonical elements, known as the Serret-Andoyer (SA) variables, thus far scarcely used for engineering applications. The main feature of the SA formalism is the reduction of the dynamics via the underlying symmetry stemming from conservation of angular momentum and rotational kinetic energy. The controllability of the system model is examined using the notion of accessibility, and is shown to be accessible from all points. Based on the accessibility proof, two nonlinear asymptotic feedback stabilizers are developed: a damping feedback is designed based on the Jurdjevic-Quinn method, and a Hamiltonian controller is derived by using the Hamiltonian as a natural Lyapunov function for the closed-loop dynamics. It is shown that the Hamiltonian control is both passive and inverse optimal with respect to a meaningful performance index. The performance of the new controllers is examined and compared using simulations of realistic scenarios from the satellite attitude dynamics field.

Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time

NASA Astrophysics Data System (ADS)

Noble, J. H.; Jentschura, U. D.

2016-03-01

We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.

Vector curvaton with varying kinetic function

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

Dimopoulos, Konstantinos; Karciauskas, Mindaugas; Wagstaff, Jacques M.

2010-01-15

A new model realization of the vector curvaton paradigm is presented and analyzed. The model consists of a single massive Abelian vector field, with a Maxwell-type kinetic term. By assuming that the kinetic function and the mass of the vector field are appropriately varying during inflation, it is shown that a scale-invariant spectrum of superhorizon perturbations can be generated. These perturbations can contribute to the curvature perturbation of the Universe. If the vector field remains light at the end of inflation it is found that it can generate substantial statistical anisotropy in the spectrum and bispectrum of the curvature perturbation.more » In this case the non-Gaussianity in the curvature perturbation is predominantly anisotropic, which will be a testable prediction in the near future. If, on the other hand, the vector field is heavy at the end of inflation then it is demonstrated that particle production is approximately isotropic and the vector field alone can give rise to the curvature perturbation, without directly involving any fundamental scalar field. The parameter space for both possibilities is shown to be substantial. Finally, toy models are presented which show that the desired variation of the mass and kinetic function of the vector field can be realistically obtained, without unnatural tunings, in the context of supergravity or superstrings.« less

Killing spinors are Killing vector fields in Riemannian supergeometry

NASA Astrophysics Data System (ADS)

Alekseevsky, D. V.; Cortés, V.; Devchand, C.; Semmelmann, U.

1998-06-01

A supermanifold M is canonically associated to any pseudo-Riemannian spin manifold ( M0, g0). Extending the metric g0 to a field g of bilinear forms g( p) on TpM, pɛM0, the pseudo-Riemannian supergeometry of ( M, g) is formulated as G-structure on M, where G is a supergroup with even part G 0 ≊ Spin(k, l); (k, l) the signature of ( M0, go). Killing vector fields on ( M, g) are, by definition, infinitesimal automorphisms of this G-structure. For every spinor field s there exists a corresponding odd vector field Xs on M. Our main result is that Xs is a Killing vector field on ( M, g) if and only if s is a twistor spinor. In particular, any Killing spinor s defines a Killing vector field Xs.

Classification of three-state Hamiltonians solvable by the coordinate Bethe ansatz

NASA Astrophysics Data System (ADS)

Crampé, N.; Frappat, L.; Ragoucy, E.

2013-10-01

We classify ‘all’ Hamiltonians with rank 1 symmetry and nearest-neighbour interactions, acting on a periodic three-state spin chain, and solvable through (generalization of) the coordinate Bethe ansatz (CBA). In this way we obtain four multi-parametric extensions of the known 19-vertex Hamiltonians (such as Zamolodchikov-Fateev, Izergin-Korepin and Bariev Hamiltonians). Apart from the 19-vertex Hamiltonians, there exist 17-vertex and 14-vertex Hamiltonians that cannot be viewed as subcases of the 19-vertex ones. In the case of 17-vertex Hamiltonians, we get a generalization of the genus 5 special branch found by Martins, plus three new ones. We also get two 14-vertex Hamiltonians. We solve all these Hamiltonians using CBA, and provide their spectrum, eigenfunctions and Bethe equations. Special attention is given to provide the specifications of our multi-parametric Hamiltonians that give back known Hamiltonians.

Pseudo Landau levels and quantum oscillations in strained Weyl semimetals

NASA Astrophysics Data System (ADS)

Alisultanov, Z. Z.

2018-05-01

The crystal lattice deformation in Weyl materials where the two chiralities are separated in momentum space leads to the appearance of gauge pseudo-fields. We investigated the pseudo-magnetic field induced quantum oscillations in strained Weyl semimetal (WSM). In contrast to all previous works on this problem, we use here a more general tilted Hamiltonian. Such Hamiltonian, seems to be is more suitable for a strained WSMs. We have shown that a pseudo-magnetic field induced magnetization of strained WSM is nonzero due to the fact that electric field (gradient of the deformation potential) is induced simultaneously with the pseudo-magnetic field. This related with fact that the pseudo Landau levels (LLs) in strained WSM are differ in vicinities of different WPs due to the presence of tilt in spectrum. Such violation of the equivalence between Weyl points (WPs) leads to modulation of quantum oscillations. We also showed that magnetization magnitude can be changed by application of an external electric field. In particular, it can be reduced to zero. The possibility of controlling of the magnetization by an electric field is interesting both from a fundamental point of view (a new type of magneto-electric effect) and application point of view (additional possibility to control diamagnetism of deformed WSMs). Finally, a coexistence of type-I and type-II Weyl fermions is possible in the system under investigation. Such phase is absolutely new for physics of topological systems.

Anyons in an electromagnetic field and the Bargmann-Michel-Telegdi equation

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

Ghosh, S.

1995-05-15

The Lagrangian model for anyons, presented earlier, is extended to include interactions with an external, homogeneous electromagnetic field. Explicit electric and magnetic moment terms for the anyon are introduced in the Lagrangian. The (2+1)-dimensional Bargmann-Michel-Telegdi equation as well as the correct value (2) of the gyromagnetic ratio is rederived, in the Hamiltonian framework.

Identifying different mechanisms in the control of a nitrogen-vacancy center system

NASA Astrophysics Data System (ADS)

Li, Shouzhi; Yang, Ling; Cao, Dewen; Wang, Yaoxiong; Shuang, Feng; Gao, Fang

2017-10-01

The nitrogen-vacancy (NV) center system has shown great potential in quantum computing due to its long decoherence time at room temperature by encoding the qubit in dressed states [28]. The corresponding control mechanisms, which is expressed by the pathways linking the initial and target states, can be naturally investigated with the Hamiltonian-encoding and observable-decoding (HE-OD) method in the interaction adiabatic representation. This is proved by the fact that the mechanisms change slightly with different detunings, magnetic and driving field intensities, and the dominant pathway is always | g 〉 → | d 〉 → | g 〉 , with | g 〉 and | d 〉 as the first two lowest dressed states. Cases are different in the diabatic representation. The orders of dominant pathways increase the driving field intensities. Tendencies of quantum pathway amplitudes with driving fields, magnetic fields and detunings change at different conditions, which can be analyzed from the Dyson series. HE-OD analysis show that the two states | g 〉 and | d 〉 in the interaction adiabatic representation are preferable to be employed as a qubit than the state pair |0〉 and | - 1 〉 in the diabatic representation under the current Hamiltonian and parameters.

Estimation of Discontinuous Displacement Vector Fields with the Minimum Description Length Criterion.

DTIC Science & Technology

1990-10-01

type of approach for finding a dense displacement vector field has a time complexity that allows a real - time implementation when an appropriate control...hardly vector fields as they appear in Stereo or motion. The reason for this is the fact that local displacement vector field ( DVF ) esti- mates bave...2 objects’ motion, but that the quantitative optical flow is not a reliable measure of the real motion [VP87, SU87]. This applies even more to the

Microwave Magnetic Materials for Radar and Signal Processing Devices - Thin Film and Bulk Oxides and Metals

DTIC Science & Technology

2007-11-29

films, (3) low field effective linewidth in polycrystalline ferrites, (4) Fermi-Pasta-Ulam recurrence for spin wave solitons in yttrium iron garnet...Fermi- Pasta-Ulam recurrence for spin wave solitons in yttrium iron garnet (YIG) film strips in a feedback ring system, (5) the Hamiltonian...XRD data. point in field was so small that field modulation and lock -in The FMR field is taken at the peak loss point in the (b) detection methods

Product-State Approximations to Quantum States

NASA Astrophysics Data System (ADS)

Brandão, Fernando G. S. L.; Harrow, Aram W.

2016-02-01

We show that for any many-body quantum state there exists an unentangled quantum state such that most of the two-body reduced density matrices are close to those of the original state. This is a statement about the monogamy of entanglement, which cannot be shared without limit in the same way as classical correlation. Our main application is to Hamiltonians that are sums of two-body terms. For such Hamiltonians we show that there exist product states with energy that is close to the ground-state energy whenever the interaction graph of the Hamiltonian has high degree. This proves the validity of mean-field theory and gives an explicitly bounded approximation error. If we allow states that are entangled within small clusters of systems but product across clusters then good approximations exist when the Hamiltonian satisfies one or more of the following properties: (1) high degree, (2) small expansion, or (3) a ground state where the blocks in the partition have sublinear entanglement. Previously this was known only in the case of small expansion or in the regime where the entanglement was close to zero. Our approximations allow an extensive error in energy, which is the scale considered by the quantum PCP (probabilistically checkable proof) and NLTS (no low-energy trivial-state) conjectures. Thus our results put restrictions on the possible Hamiltonians that could be used for a possible proof of the qPCP or NLTS conjectures. By contrast the classical PCP constructions are often based on constraint graphs with high degree. Likewise we show that the parallel repetition that is possible with classical constraint satisfaction problems cannot also be possible for quantum Hamiltonians, unless qPCP is false. The main technical tool behind our results is a collection of new classical and quantum de Finetti theorems which do not make any symmetry assumptions on the underlying states.

Vector optical fields with polarization distributions similar to electric and magnetic field lines.

PubMed

Pan, Yue; Li, Si-Min; Mao, Lei; Kong, Ling-Jun; Li, Yongnan; Tu, Chenghou; Wang, Pei; Wang, Hui-Tian

2013-07-01

We present, design and generate a new kind of vector optical fields with linear polarization distributions modeling to electric and magnetic field lines. The geometric configurations of "electric charges" and "magnetic charges" can engineer the spatial structure and symmetry of polarizations of vector optical field, providing additional degrees of freedom assisting in controlling the field symmetry at the focus and allowing engineering of the field distribution at the focus to the specific applications.

Optimization of Protein Backbone Dihedral Angles by Means of Hamiltonian Reweighting

PubMed Central

2016-01-01

Molecular dynamics simulations depend critically on the accuracy of the underlying force fields in properly representing biomolecules. Hence, it is crucial to validate the force-field parameter sets in this respect. In the context of the GROMOS force field, this is usually achieved by comparing simulation data to experimental observables for small molecules. In this study, we develop new amino acid backbone dihedral angle potential energy parameters based on the widely used 54A7 parameter set by matching to experimental J values and secondary structure propensity scales. In order to find the most appropriate backbone parameters, close to 100 000 different combinations of parameters have been screened. However, since the sheer number of combinations considered prohibits actual molecular dynamics simulations for each of them, we instead predicted the values for every combination using Hamiltonian reweighting. While the original 54A7 parameter set fails to reproduce the experimental data, we are able to provide parameters that match significantly better. However, to ensure applicability in the context of larger peptides and full proteins, further studies have to be undertaken. PMID:27559757

A four-field model for collisionless reconnection: Hamiltonian structure and numerical simulations

NASA Astrophysics Data System (ADS)

Tassi, Emanuele; Grasso, Daniela; Pegoraro, Francesco

2008-11-01

A 4-field model for magnetic reconnection in collisionless plasmas is investigated both analytically and numerically. The model equations are shown to admit a non-canonical Hamiltonian formulation with four infinite families of Casimir invariants [1]. Numerical simulations show that, consistently with previously investigated models [2,3], in the absence of significant fluctuations along the toroidal direction, reconnection can lead to a macroscopic saturated state exhibiting filamentation on microsocopic scales, or to a secondary Kelvin-Helmholtz-like instability, depending on the value of a parameter measuring the compressibility of the electron fluid. The novel feature exhibited by the four-field model is the coexistence of significant filamentation with a secondary instability when magnetic and velocity perturbations along the toroidal direction are no longer negligible. An interpretation of this phenomenon in terms of Casimir invariants is given.[0pt] [1] E. Tassi et al., Plasma Phys. Contr. Fus., 50, 085014 (2008)[0pt] [2] D. Grasso et al., Phys. Rev. Lett. 86, 5051 (2001)[0pt] [3] D. Del Sarto, F. Califano and F. Pegoraro, Phys. Plasmas 12, 012317 (2005)

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.

Electron spectra in forbidden β decays and the quenching of the weak axial-vector coupling constant gA

NASA Astrophysics Data System (ADS)

Kostensalo, Joel; Haaranen, Mikko; Suhonen, Jouni

2017-04-01

Evolution of the electron spectra with the effective value of the weak axial-vector coupling constant gA was followed for 26 first-, second-, third-, fourth- and fifth-forbidden β- decays of odd-A nuclei by calculating the involved nuclear matrix elements (NMEs) in the framework of the microscopic quasiparticle-phonon model (MQPM). The next-to-leading-order terms were included in the β -decay shape factor of the electron spectra. The spectrum shapes of third- and fourth-forbidden nonunique decays were found to depend strongly on the value of gA, while first- and second-forbidden decays were mostly unaffected by the tuning of gA. The gA-driven evolution of the normalized β spectra was found to be quite universal, largely insensitive to the small changes in the nuclear mean field and the adopted residual many-body Hamiltonian producing the excitation spectra of the MQPM. This makes the comparison of experimental and theoretical electron spectra, coined "the spectrum-shape method" (SSM), a robust tool for extracting information on the effective values of the weak coupling constants. In this exploratory work two new experimentally interesting decays for the SSM treatment were discovered: the ground-state-to-ground-state decays of 99Tc and 87Rb. Comparing the experimental and theoretical spectra of these decays could shed light on the effective values of gA and gV for second- and third-forbidden nonunique decays. The measurable decay transitions of 135Cs and 137Cs, in turn, can be used to test the SSM in different many-body formalisms. The present work can also be considered as a (modest) step towards solving the gA problem of the neutrinoless double beta decay.

Gyro-gauge-independent formulation of the guiding-center reduction to arbitrary order in the Larmor radius

NASA Astrophysics Data System (ADS)

de Guillebon, L.; Vittot, M.

2013-10-01

Guiding-center reduction is studied using gyro-gauge-independent coordinates. The Lagrangian 1-form of charged particle dynamics is Lie transformed without introducing a gyro-gauge, but using directly the unit vector of the component of the velocity perpendicular to the magnetic field as the coordinate corresponding to Larmor gyration. The reduction is shown to provide a maximal reduction for the Lagrangian and to work for all orders in the Larmor radius, following exactly the same procedure as when working with the standard gauge-dependent coordinate. The gauge-dependence is removed from the coordinate system by using a constrained variable for the gyro-angle. The closed 1-form dθ is replaced by a more general non-closed 1-form, which is equal to dθ in the gauge-dependent case. The gauge vector is replaced by a more general connection in the definition of the gradient, which behaves as a covariant derivative, in perfect agreement with the circle-bundle picture. This explains some results of previous works, whose gauge-independent expressions did not correspond to gauge fixing but did indeed correspond to connection fixing. In addition, some general results are obtained for the guiding-center reduction. The expansion is polynomial in the cotangent of the pitch-angle as an effect of the structure of the Lagrangian, preserved by Lie derivatives. The induction for the reduction is shown to rely on the inversion of a matrix, which is the same for all orders higher than three. It is inverted and explicit induction relations are obtained to go to an arbitrary order in the perturbation expansion. The Hamiltonian and symplectic representations of the guiding-center reduction are recovered, but conditions for the symplectic representation at each order are emphasized.

Giant electrocaloric response in the prototypical Pb(Mg,Nb)O3 relaxor ferroelectric from atomistic simulations

NASA Astrophysics Data System (ADS)

Jiang, Zhijun; Nahas, Y.; Prokhorenko, S.; Prosandeev, S.; Wang, D.; Íñiguez, Jorge; Bellaiche, L.

2018-03-01

An atomistic effective Hamiltonian is used to investigate electrocaloric (EC) effects of Pb (Mg1 /3Nb2 /3) O3 relaxor ferroelectrics in its ergodic regime, and subject to electric fields applied along the pseudocubic [111] direction. Such a Hamiltonian qualitatively reproduces (i) the electric field-versus-temperature phase diagram, including the existence of a critical point where first-order and second-order transitions meet each other; and (ii) a giant EC response near such a critical point. It also reveals that such giant response around this critical point is microscopically induced by field-induced percolation of polar nanoregions. Moreover, it is also found that, for any temperature above the critical point, the EC coefficient-versus-electric-field curve adopts a maximum (and thus larger electrocaloric response too), that can be well described by the general Landau-like model proposed by Jiang et al., [Phys. Rev. B 96, 014114 (2017)], 10.1103/PhysRevB.96.014114, and that is further correlated with specific microscopic features related to dipoles lying along different rhombohedral directions. Furthermore, for temperatures being at least 40 K higher than the critical temperature, the (electric field, temperature) line associated with this maximal EC coefficient is below both the Widom line and the line representing percolation of polar nanoregions.

Some Correlation Functions in Matrix Product Ground States of One-Dimensional Two-State Chains

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Aghamohammadi, Amir; Fatollahi, Amir H.; Khorrami, Mohammad

2014-04-01

Consider one-dimensional chains with nearest neighbour interactions, for which to each site correspond two independent states (say up and down), and the ground state is a matrix product state. It has been shown [23] that for such systems, the ground states are linear combinations of specific vectors which are essentially direct products of specific numbers of ups and downs, symmetrized in a generalized manner. By a generalized manner, it is meant that the coefficient corresponding to the interchange of states of two sites, in not necessarily plus one or minus one, but a phase which depends on the Hamiltonian and the position of the two sites. Such vectors are characterized by a phase χ, the N-th power of which is one (where N is the number of sites), and an integer. Corresponding to χ, there is another integer M which is the smallest positive integer that χM is one. Two classes of correlation functions for such systems (basically correlation functions for such vectors) are calculated. The first class consists of correlation functions of tensor products of one-site diagonal observables; the second class consists of correlation functions of tensor products of less than M one-site observables (but not necessarily diagonal).

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.

Analytical and experimental comparisons of electromechanical vibration response of a piezoelectric bimorph beam for power harvesting

NASA Astrophysics Data System (ADS)

Lumentut, M. F.; Howard, I. M.

2013-03-01

Power harvesters that extract energy from vibrating systems via piezoelectric transduction show strong potential for powering smart wireless sensor devices in applications of health condition monitoring of rotating machinery and structures. This paper presents an analytical method for modelling an electromechanical piezoelectric bimorph beam with tip mass under two input base transverse and longitudinal excitations. The Euler-Bernoulli beam equations were used to model the piezoelectric bimorph beam. The polarity-electric field of the piezoelectric element is excited by the strain field caused by base input excitation, resulting in electrical charge. The governing electromechanical dynamic equations were derived analytically using the weak form of the Hamiltonian principle to obtain the constitutive equations. Three constitutive electromechanical dynamic equations based on independent coefficients of virtual displacement vectors were formulated and then further modelled using the normalised Ritz eigenfunction series. The electromechanical formulations include both the series and parallel connections of the piezoelectric bimorph. The multi-mode frequency response functions (FRFs) under varying electrical load resistance were formulated using Laplace transformation for the multi-input mechanical vibrations to provide the multi-output dynamic displacement, velocity, voltage, current and power. The experimental and theoretical validations reduced for the single mode system were shown to provide reasonable predictions. The model results from polar base excitation for off-axis input motions were validated with experimental results showing the change to the electrical power frequency response amplitude as a function of excitation angle, with relevance for practical implementation.

The method of unitary clothing transformations in the theory of nucleon-nucleon scattering

NASA Astrophysics Data System (ADS)

Dubovyk, I.; Shebeko, A.

2010-04-01

The clothing procedure, put forward in quantum field theory (QFT) by Greenberg and Schweber, is applied for the description of nucleon-nucleon (N -N) scattering. We consider pseudoscalar (π and η), vector (ρ and ω) and scalar (δ and σ) meson fields interacting with 1/2 spin (N and N) fermion ones via the Yukawa-type couplings to introduce trial interactions between “bare” particles. The subsequent unitary clothing transformations (UCTs) are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. In this work, we are focused upon the Hermitian and energy-independent operators for the clothed nucleons, being built up in the second order in the coupling constants. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. In order to evaluate the T matrix of the N-N scattering we have used an equivalence theorem that enables us to operate in the clothed particle representation (CPR) instead of the bare particle representation (BPR) with its huge amount of virtual processes. We have derived the Lippmann-Schwinger(LS)-type equation for the CPR elements of the T-matrix for a given collision energy in the two-nucleon sector of the Hilbert space H of hadronic states and elaborated a code for its numerical solution in momentum space.

The average motion of a charged particle in a dipole field

NASA Technical Reports Server (NTRS)

Chen, A. J.; Stern, D. P.

1974-01-01

The numerical representation of the average motion of a charged particle trapped in a geomagnetic field is developed. An assumption is made of the conservation of the first two adiabatic invariants where integration is along a field line between mirror points. The averaged motion also involved the parameters defining the magnetic field line to which the particle is attached. Methods involved in obtaining the motion in the equatorial plane of model magnetospheres are based on Hamiltonian functions. The restrictions imposed by the special nature of the dipole field are defined.

Ghost circles in lattice Aubry-Mather theory

NASA Astrophysics Data System (ADS)

Mramor, Blaz; Rink, Bob

Monotone lattice recurrence relations such as the Frenkel-Kontorova lattice, arise in Hamiltonian lattice mechanics, as models for ferromagnetism and as discretization of elliptic PDEs. Mathematically, they are a multi-dimensional counterpart of monotone twist maps. Such recurrence relations often admit a variational structure, so that the solutions x:Z→R are the stationary points of a formal action function W(x). Given any rotation vector ω∈R, classical Aubry-Mather theory establishes the existence of a large collection of solutions of ∇W(x)=0 of rotation vector ω. For irrational ω, this is the well-known Aubry-Mather set. It consists of global minimizers and it may have gaps. In this paper, we study the parabolic gradient flow {dx}/{dt}=-∇W(x) and we will prove that every Aubry-Mather set can be interpolated by a continuous gradient-flow invariant family, the so-called 'ghost circle'. The existence of these ghost circles is known in dimension d=1, for rational rotation vectors and Morse action functions. The main technical result of this paper is therefore a compactness theorem for lattice ghost circles, based on a parabolic Harnack inequality for the gradient flow. This implies the existence of lattice ghost circles of arbitrary rotation vectors and for arbitrary actions. As a consequence, we can give a simple proof of the fact that when an Aubry-Mather set has a gap, then this gap must be filled with minimizers, or contain a non-minimizing solution.

Study of Equatorial Ionospheric irregularities and Mapping of Electron Density Profiles and Ionograms

DTIC Science & Technology

2012-03-09

equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the...wave function arguments from complex scalars to complex vectors . This conversion allows us to separate the electric field vector and the imaginary...magnetic field vector , because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while ex- ponentials of imaginary

Reconstruction of Vectorial Acoustic Sources in Time-Domain Tomography

PubMed Central

Xia, Rongmin; Li, Xu; He, Bin

2009-01-01

A new theory is proposed for the reconstruction of curl-free vector field, whose divergence serves as acoustic source. The theory is applied to reconstruct vector acoustic sources from the scalar acoustic signals measured on a surface enclosing the source area. It is shown that, under certain conditions, the scalar acoustic measurements can be vectorized according to the known measurement geometry and subsequently be used to reconstruct the original vector field. Theoretically, this method extends the application domain of the existing acoustic reciprocity principle from a scalar field to a vector field, indicating that the stimulating vectorial source and the transmitted acoustic pressure vector (acoustic pressure vectorized according to certain measurement geometry) are interchangeable. Computer simulation studies were conducted to evaluate the proposed theory, and the numerical results suggest that reconstruction of a vector field using the proposed theory is not sensitive to variation in the detecting distance. The present theory may be applied to magnetoacoustic tomography with magnetic induction (MAT-MI) for reconstructing current distribution from acoustic measurements. A simulation on MAT-MI shows that, compared to existing methods, the present method can give an accurate estimation on the source current distribution and a better conductivity reconstruction. PMID:19211344

Scaling laws of Rydberg excitons

NASA Astrophysics Data System (ADS)

Heckötter, J.; Freitag, M.; Fröhlich, D.; Aßmann, M.; Bayer, M.; Semina, M. A.; Glazov, M. M.

2017-09-01

Rydberg atoms have attracted considerable interest due to their huge interaction among each other and with external fields. They demonstrate characteristic scaling laws in dependence on the principal quantum number n for features such as the magnetic field for level crossing or the electric field of dissociation. Recently, the observation of excitons in highly excited states has allowed studying Rydberg physics in cuprous oxide crystals. Fundamentally different insights may be expected for Rydberg excitons, as the crystal environment and associated symmetry reduction compared to vacuum give not only optical access to many more states within an exciton multiplet but also extend the Hamiltonian for describing the exciton beyond the hydrogen model. Here we study experimentally and theoretically the scaling of several parameters of Rydberg excitons with n , for some of which we indeed find laws different from those of atoms. For others we find identical scaling laws with n , even though their origin may be distinctly different from the atomic case. At zero field the energy splitting of a particular multiplet n scales as n-3 due to crystal-specific terms in the Hamiltonian, e.g., from the valence band structure. From absorption spectra in magnetic field we find for the first crossing of levels with adjacent principal quantum numbers a Br∝n-4 dependence of the resonance field strength, Br, due to the dominant paramagnetic term unlike for atoms for which the diamagnetic contribution is decisive, resulting in a Br∝n-6 dependence. By contrast, the resonance electric field strength shows a scaling as Er∝n-5 as for Rydberg atoms. Also similar to atoms with the exception of hydrogen we observe anticrossings between states belonging to multiplets with different principal quantum numbers at these resonances. The energy splittings at the avoided crossings scale roughly as n-4, again due to crystal specific features in the exciton Hamiltonian. The data also allow us to assess the susceptibility of Rydberg excitons to the external fields: The crossover field strength in magnetic field from a hydrogenlike exciton to a magnetoexciton dominated by electron and hole Landau level quantization scales as n-3. In electric field, on the other hand, we observe the exciton polarizability to scale as n7. At higher fields, the exciton ionization can be studied with ionization voltages that demonstrate an n-4 scaling law. Particularly interesting is the field dependence of the width of the absorption lines which remains constant before dissociation for high enough n , while for small n ≲12 an exponential increase is found. These results are in excellent agreement with theoretical predictions.

Measuring magnetic field vector by stimulated Raman transitions

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

Wang, Wenli; Wei, Rong, E-mail: weirong@siom.ac.cn; Lin, Jinda

2016-03-21

We present a method for measuring the magnetic field vector in an atomic fountain by probing the line strength of stimulated Raman transitions. The relative line strength for a Λ-type level system with an existing magnetic field is theoretically analyzed. The magnetic field vector measured by our proposed method is consistent well with that by the traditional bias magnetic field method with an axial resolution of 6.1 mrad and a radial resolution of 0.16 rad. Dependences of the Raman transitions on laser polarization schemes are also analyzed. Our method offers the potential advantages for magnetic field measurement without requiring additional bias fields,more » beyond the limitation of magnetic field intensity, and extending the spatial measurement range. The proposed method can be widely used for measuring magnetic field vector in other precision measurement fields.« less

Transformation of vector magnetograms and the problems associated with the effects of perspective and the azimuthal ambiguity

NASA Technical Reports Server (NTRS)

Gary, G. Allen; Hagyard, M. J.

1990-01-01

Off-center vector magnetograms which use all three components of the measured field provide the maximum information content from the photospheric field and can provide the most consistent potential field independent of the viewing angle by defining the normal component of the field. The required transformations of the magnetic field vector and the geometric mapping of the observed field in the image plane into the heliographic plane have been described. Here we discuss the total transformation of specific vector magnetograms to detail the problems and procedures that one should be aware of in analyzing observational magnetograms. The effect of the 180-deg ambiguity of the observed transverse field is considered as well as the effect of curvature of the photosphere. Specific results for active regions AR 2684 (September 23, 1980) and AR 4474 (April 26, 1984) from the Marshall Space Flight Center Vector magnetograph are described which point to the need for the heliographic projection in determining the field structure of an active region.

Quantum phase transition between cluster and antiferromagnetic states

NASA Astrophysics Data System (ADS)

Son, W.; Amico, L.; Fazio, R.; Hamma, A.; Pascazio, S.; Vedral, V.

2011-09-01

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like exchange. We show that the ground state in the cluster phase possesses symmetry protected topological order. A continuous quantum phase transition occurs as result of the competition between the cluster and Ising terms. At the critical point the Hamiltonian is self-dual. The geometric entanglement is also studied and used to investigate the quantum phase transition. Our findings in one dimension corroborate the analysis of the two-dimensional generalization of the system, indicating, at a mean-field level, the presence of a direct transition between an antiferromagnetic and a valence bond solid ground state.

A Thin Lens Model for Charged-Particle RF Accelerating Gaps

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

Allen, Christopher K.

Presented is a thin-lens model for an RF accelerating gap that considers general axial fields without energy dependence or other a priori assumptions. Both the cosine and sine transit time factors (i.e., Fourier transforms) are required plus two additional functions; the Hilbert transforms the transit-time factors. The combination yields a complex-valued Hamiltonian rotating in the complex plane with synchronous phase. Using Hamiltonians the phase and energy gains are computed independently in the pre-gap and post-gap regions then aligned using the asymptotic values of wave number. Derivations of these results are outlined, examples are shown, and simulations with the model aremore » presented.« less

Time-dependent mean-field theory for x-ray near-edge spectroscopy

NASA Astrophysics Data System (ADS)

Bertsch, G. F.; Lee, A. J.

2014-02-01

We derive equations of motion for calculating the near-edge x-ray absorption spectrum in molecules and condensed matter, based on a two-determinant approximation and Dirac's variational principle. The theory provides an exact solution for the linear response when the Hamiltonian or energy functional has only diagonal interactions in some basis. We numerically solve the equations to compare with the Mahan-Nozières-De Dominicis theory of the edge singularity in metallic conductors. Our extracted power-law exponents are similar to those of the analytic theory, but are not in quantitative agreement. The calculational method can be readily generalized to treat Kohn-Sham Hamiltonians with electron-electron interactions derived from correlation-exchange potentials.

Ensemble of single quadrupolar nuclei in rotating solids: sidebands in NMR spectrum.

PubMed

Kundla, Enn

2006-07-01

A novel way is proposed to describe the evolution of nuclear magnetic polarization and the induced NMR spectrum. In this method, the effect of a high-intensity external static magnetic field and the effects of proper Hamiltonian left over interaction components, which commute with the first, are taken into account simultaneously and equivalently. The method suits any concrete NMR problem. This brings forth the really existing details in the registered spectra, evoked by Hamiltonian secular terms, which may be otherwise smoothed due to approximate treatment of the effects of the secular terms. Complete analytical expressions are obtained describing the NMR spectra including the rotational sideband sets of single quadrupolar nuclei in rotating solids.

On the Hamiltonian formalism of the tetrad-gravity with fermions

NASA Astrophysics Data System (ADS)

Lagraa, M. H.; Lagraa, M.

2018-06-01

We extend the analysis of the Hamiltonian formalism of the d-dimensional tetrad-connection gravity to the fermionic field by fixing the non-dynamic part of the spatial connection to zero (Lagraa et al. in Class Quantum Gravity 34:115010, 2017). Although the reduced phase space is equipped with complicated Dirac brackets, the first-class constraints which generate the diffeomorphisms and the Lorentz transformations satisfy a closed algebra with structural constants analogous to that of the pure gravity. We also show the existence of a canonical transformation leading to a new reduced phase space equipped with Dirac brackets having a canonical form leading to the same algebra of the first-class constraints.

Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator

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

Szalay, Viktor, E-mail: szalay.viktor@wigner.mta.hu

A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, T-hat, is presented. It is in the Eckart frame and it is of the same form as Watson’s normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact T-hat given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.

Vector-beam solutions of Maxwell's wave equation.

PubMed

Hall, D G

1996-01-01

The Hermite-Gauss and Laguerre-Gauss modes are well-known beam solutions of the scalar Helmholtz equation in the paraxial limit. As such, they describe linearly polarized fields or single Cartesian components of vector fields. The vector wave equation admits, in the paraxial limit, of a family of localized Bessel-Gauss beam solutions that can describe the entire transverse electric field. Two recently reported solutions are members of this family of vector Bessel-Gauss beam modes.

Asymmetric Invisibility Cloaking Theory Based on the Concept of Effective Electromagnetic Fields for Photons

NASA Astrophysics Data System (ADS)

Amemiya, Tomo; Taki, Masato; Kanazawa, Toru; Arai, Shigehisa

2014-03-01

The asymmetric invisibility cloak is a special cloak with unidirectional transparency; that is, a person in the cloak should not be seen from the outside but should be able to see the outside. Existing theories of designing invisibility cloaks cannot be used for asymmetric cloaking because they are based on the transformation optics that uses Riemannian metric tensor independent of direction. To overcome this problem, we propose introducing directionality into invisibility cloaking. Our theory is based on ``the theory of effective magnetic field for photons'' proposed by Stanford University.[2] To realize asymmetric cloaking, we have extended the Stanford's theory to add the concept of ``effective electric field for photons.'' The effective electric and the magnetic field can be generated using a photonc resonator lattice, which is a kind of metamaterial. The Hamiltonian for photons in these fields has a similar form to that of the Hamiltonian for a charged particle in an electromagnetic field. An incident photon therefore experiences a ``Lorentz-like'' and a ``Coulomb-like'' force and shows asymmetric movement depending of its travelling direction.We show the procedure of designing actual invisibility cloaks using the photonc resonator lattice and confirm their operation with the aid of computer simulation. This work was supported in part by the MEXT; JSPS KAKENHI Grant Numbers #24246061, #24656046, #25420321, #25420322.

Quantum theory of structured monochromatic light

NASA Astrophysics Data System (ADS)

Punnoose, Alexander; Tu, J. J.

2017-08-01

Applications that envisage utilizing the orbital angular momentum (OAM) at the single photon level assume that the OAM degrees of freedom of the photons are orthogonal. To test this critical assumption, we quantize the beam-like solutions of the vector Helmholtz equation from first principles. We show that although the photon operators of a diffracting monochromatic beam do not in general satisfy the canonical commutation relations, implying that the photon states in Fock space are not orthogonal, the states are bona fide eigenstates of the number and Hamiltonian operators. As a result, the representation for the photon operators presented in this work form a natural basis to study structured monochromatic light at the single photon level.

On a new class of completely integrable nonlinear wave equations. II. Multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.

1987-11-01

The multi-Hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed. Infinitely many conservation laws had earlier been obtained for these equations. Starting from a (primary) Hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi-Hamiltonian structure are obtained and it is shown that the second Hamiltonian operator can be constructed solely through a knowledge of the first Hamiltonian function. The recursion operator which first appears at the level of bi-Hamiltonian structure gives rise to an infinite sequence of conserved Hamiltonians. It is found that in general there exist two different infinite sequences of conserved quantities for these equations. The recursion relation defining higher Hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the (k+1)st Hamiltonian operator which depends on the kth Hamiltonian function. The infinite sequence of conserved Hamiltonians are common to all the higher Hamiltonian structures. The equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri-Hamiltonian structure with two distinct infinite sets of conserved quantities. The isothermal case of γ=1 is an exceptional one that requires separate treatment. This corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to Poisson's equation in nonlinear acoustics.

Correlation between topological structure and its properties in dynamic singular vector fields.

PubMed

Vasilev, Vasyl; Soskin, Marat

2016-04-20

A new technique for establishment of topology measurements for static and dynamic singular vector fields is elaborated. It is based on precise measurement of the 3D landscape of ellipticity distribution for a checked singular optical field with C points on the tops of ellipticity hills. Vector fields possess three-component topology: areas with right-hand (RH) and left-hand (LH) ellipses, and delimiting those L lines as the singularities of handedness. The azimuth map of polarization ellipses is common for both RH and LH ellipses of vector fields and do not feel L lines. The strict rules were confirmed experimentally, which define the connection between the sign of underlying optical vortices and morphological parameters of upper-lying C points. Percolation phenomena explain their realization in-between singular vector fields and long duration of their chains of 10³  s order.

Nonparaxial propagation and focusing properties of azimuthal-variant vector fields diffracted by an annular aperture.

PubMed

Gu, Bing; Xu, Danfeng; Pan, Yang; Cui, Yiping

2014-07-01

Based on the vectorial Rayleigh-Sommerfeld integrals, the analytical expressions for azimuthal-variant vector fields diffracted by an annular aperture are presented. This helps us to investigate the propagation behaviors and the focusing properties of apertured azimuthal-variant vector fields under nonparaxial and paraxial approximations. The diffraction by a circular aperture, a circular disk, or propagation in free space can be treated as special cases of this general result. Simulation results show that the transverse intensity, longitudinal intensity, and far-field divergence angle of nonparaxially apertured azimuthal-variant vector fields depend strongly on the azimuthal index, the outer truncation parameter and the inner truncation parameter of the annular aperture, as well as the ratio of the waist width to the wavelength. Moreover, the multiple-ring-structured intensity pattern of the focused azimuthal-variant vector field, which originates from the diffraction effect caused by an annular aperture, is experimentally demonstrated.

The Application of Some Hartree-Fock Model Calculation to the Analysis of Atomic and Free-Ion Optical Spectra

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

Hayhurst, Thomas Laine

1980-08-06

Techniques for applying ab-initio calculations to the is of atomic spectra are investigated, along with the relationship between the semi-empirical and ab-initio forms of Slater-Condon theory. Slater-Condon theory is reviewed with a focus on the essential features that lead to the effective Hamiltonians associated with the semi-empirical form of the theory. Ab-initio spectroscopic parameters are calculated from wavefunctions obtained via self-consistent field methods, while multi-configuration Hamiltonian matrices are constructed and diagonalized with computer codes written by Robert Cowan of Los Alamos Scientific Laboratory. Group theoretical analysis demonstrates that wavefunctions more general than Slater determinants (i.e. wavefunctions with radial correlations betweenmore » electrons) lead to essentially the same parameterization of effective Hamiltonians. In the spirit of this analysis, a strategy is developed for adjusting ab-initio values of the spectroscopic parameters, reproducing parameters obtained by fitting the corresponding effective Hamiltonian. Secondary parameters are used to "screen" the calculated (primary) spectroscopic parameters, their values determined by least squares. Extrapolations of the secondary parameters determined from analyzed spectra are attempted to correct calculations of atoms and ions without experimental levels. The adjustment strategy and extrapolations are tested on the K I sequence from K 0+ through Fe 7+, fitting to experimental levels for V 4+, and Cr 5+; unobserved levels and spectra are predicted for several members of the sequence. A related problem is also discussed: Energy levels of the Uranium hexahalide complexes, (UX 6) 2- for X= F, Cl, Br, and I, are fit to an effective Hamiltonian (the f 2 configuration in O h symmetry) with corrections proposed by Brian Judd.« less

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

Berres, Anne Sabine

This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.

Origin and structures of solar eruptions II: Magnetic modeling

NASA Astrophysics Data System (ADS)

Guo, Yang; Cheng, Xin; Ding, MingDe

2017-07-01

The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We have to observe and model the vector magnetic field to understand the structures and physical mechanisms of these solar activities. Vector magnetic fields on the photosphere are routinely observed via the polarized light, and inferred with the inversion of Stokes profiles. To analyze these vector magnetic fields, we need first to remove the 180° ambiguity of the transverse components and correct the projection effect. Then, the vector magnetic field can be served as the boundary conditions for a force-free field modeling after a proper preprocessing. The photospheric velocity field can also be derived from a time sequence of vector magnetic fields. Three-dimensional magnetic field could be derived and studied with theoretical force-free field models, numerical nonlinear force-free field models, magnetohydrostatic models, and magnetohydrodynamic models. Magnetic energy can be computed with three-dimensional magnetic field models or a time series of vector magnetic field. The magnetic topology is analyzed by pinpointing the positions of magnetic null points, bald patches, and quasi-separatrix layers. As a well conserved physical quantity, magnetic helicity can be computed with various methods, such as the finite volume method, discrete flux tube method, and helicity flux integration method. This quantity serves as a promising parameter characterizing the activity level of solar active regions.

Gaugeon formalism for the second-rank antisymmetric tensor gauge fields

NASA Astrophysics Data System (ADS)

Aochi, Masataka; Endo, Ryusuke; Miura, Hikaru

2018-02-01

We present a BRST symmetric gaugeon formalism for the second-rank antisymmetric tensor gauge fields. A set of vector gaugeon fields is introduced as a quantum gauge freedom. One of the gaugeon fields satisfies a higher-derivative field equation; this property is necessary to change the gauge-fixing parameter of the antisymmetric tensor gauge field. A naive Lagrangian for the vector gaugeon fields is itself invariant under a gauge transformation for the vector gaugeon field. The Lagrangian of our theory includes the gauge-fixing terms for the gaugeon fields and corresponding Faddeev-Popov ghost terms.

Microchip solid-state cylindrical vector lasers with orthogonally polarized dual laser-diode end pumping.

PubMed

Otsuka, Kenju; Chu, Shu-Chun

2013-05-01

We report a simple method for generating cylindrical vector beams directly from laser-diode (LD)-pumped microchip solid-state lasers by using dual end-pumping beams. Radially as well as azimuthally polarized vector field emissions have been generated from the common c-cut Nd:GdVO4 laser cavity merely by controlling the focus positions of orthogonally polarized LD off-axis pump beams. Hyperbolically polarized vector fields have also been observed, in which the cylindrical symmetry of vector fields is broken. Experimental results have been well reproduced by numerical simulations.

Inflation with a massive vector field nonminimally coupled to gravity

NASA Astrophysics Data System (ADS)

Páramos, J.

2018-01-01

The possibility that inflation is driven by a massive vector field with SO(3) global symmetry nonminimally coupled to gravity is presented. Through an appropriate Ansatz for the vector field, the behaviour of the equations of motion is studied through the ensuing dynamical system, focusing on the characterisation of the ensuing fixed points.

Spin Chirality of Cu3 and V3 Nanomagnets. 1. Rotation Behavior of Vector Chirality, Scalar Chirality, and Magnetization in the Rotating Magnetic Field, Magnetochiral Correlations.

PubMed

Belinsky, Moisey I

2016-05-02

The rotation behavior of the vector chirality κ, scalar chirality χ, and magnetization M in the rotating magnetic field H1 is considered for the V3 and Cu3 nanomagnets, in which the Dzialoshinsky-Moriya coupling is active. The polar rotation of the field H1 of the given strength H1 results in the energy spectrum characterized by different vector and scalar chiralities in the ground and excited states. The magnetochiral correlations between the vector and scalar chiralities, energy, and magnetization in the rotating field were considered. Under the uniform polar rotation of the field H1, the ground-state chirality vector κI performs sawtooth oscillations and the magnetization vector MI performs the sawtooth oscillating rotation that is accompanied by the correlated transformation of the scalar chirality χI. This demonstrates the magnetochiral effect of the joint rotation behavior and simultaneous frustrations of the spin chiralities and magnetization in the rotating field, which are governed by the correlation between the chiralities and magnetization.

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.

Magnetic vector field tag and seal

DOEpatents

Johnston, Roger G.; Garcia, Anthony R.

2004-08-31

One or more magnets are placed in a container (preferably on objects inside the container) and the magnetic field strength and vector direction are measured with a magnetometer from at least one location near the container to provide the container with a magnetic vector field tag and seal. The location(s) of the magnetometer relative to the container are also noted. If the position of any magnet inside the container changes, then the measured vector fields at the these locations also change, indicating that the tag has been removed, the seal has broken, and therefore that the container and objects inside may have been tampered with. A hollow wheel with magnets inside may also provide a similar magnetic vector field tag and seal. As the wheel turns, the magnets tumble randomly inside, removing the tag and breaking the seal.

Accelerating 4D flow MRI by exploiting vector field divergence regularization.

PubMed

Santelli, Claudio; Loecher, Michael; Busch, Julia; Wieben, Oliver; Schaeffter, Tobias; Kozerke, Sebastian

2016-01-01

To improve velocity vector field reconstruction from undersampled four-dimensional (4D) flow MRI by penalizing divergence of the measured flow field. Iterative image reconstruction in which magnitude and phase are regularized separately in alternating iterations was implemented. The approach allows incorporating prior knowledge of the flow field being imaged. In the present work, velocity data were regularized to reduce divergence, using either divergence-free wavelets (DFW) or a finite difference (FD) method using the ℓ1-norm of divergence and curl. The reconstruction methods were tested on a numerical phantom and in vivo data. Results of the DFW and FD approaches were compared with data obtained with standard compressed sensing (CS) reconstruction. Relative to standard CS, directional errors of vector fields and divergence were reduced by 55-60% and 38-48% for three- and six-fold undersampled data with the DFW and FD methods. Velocity vector displays of the numerical phantom and in vivo data were found to be improved upon DFW or FD reconstruction. Regularization of vector field divergence in image reconstruction from undersampled 4D flow data is a valuable approach to improve reconstruction accuracy of velocity vector fields. © 2014 Wiley Periodicals, Inc.

Dynamico-FE: A Structure-Preserving Hydrostatic Dynamical Core

NASA Astrophysics Data System (ADS)

Eldred, Christopher; Dubos, Thomas; Kritsikis, Evaggelos

2017-04-01

It is well known that the inviscid, adiabatic equations of atmospheric motion constitute a non-canonical Hamiltonian system, and therefore posses many important conserved quantities such as as mass, potential vorticity and total energy. In addition, there are also key mimetic properties (such as curl grad = 0) of the underlying continuous vector calculus. Ideally, a dynamical core should have similar properties. A general approach to deriving such structure-preserving numerical schemes has been developed under the frameworks of Hamiltonian methods and mimetic discretizations, and over the past decade, there has been a great deal of work on the development of atmospheric dynamical cores using these techniques. An important example is Dynamico, which conserves mass, potential vorticity and total energy; and possesses additional mimetic properties such as a curl-free pressure gradient. Unfortunately, the underlying finite-difference discretization scheme used in Dynamico has been shown to be inconsistent on general grids. To resolve these accuracy issues, a scheme based on mimetic Galerkin discretizations has been developed that achieves higher-order accuracy while retaining the structure-preserving properties of the existing discretization. This presentation will discuss the new dynamical core, termed Dynamico-FE, and show results from a standard set of test cases on both the plane and the sphere.

The classical Taub-Nut system: factorization, spectrum generating algebra and solution to the equations of motion

NASA Astrophysics Data System (ADS)

Latini, Danilo; Ragnisco, Orlando

2015-05-01

The formalism of SUperSYmmetric quantum mechanics (SUSYQM) is properly modified in such a way to be suitable for the description and the solution of a classical maximally superintegrable Hamiltonian system, the so-called Taub-Nut system, associated with the Hamiltonian: In full agreement with the results recently derived by Ballesteros et al for the quantum case, we show that the classical Taub-Nut system shares a number of essential features with the Kepler system, that is just its Euclidean version arising in the limit η \\to 0, and for which a ‘SUSYQM’ approach has been recently introduced by Kuru and Negro. In particular, for positive η and negative energy the motion is always periodic; it turns out that the period depends upon η and goes to the Euclidean value as η \\to 0. Moreover, the maximal superintegrability is preserved by the η-deformation, due to the existence of a larger symmetry group related to an η-deformed Runge-Lenz vector, which ensures that in {{{R}}3} closed orbits are again ellipses. In this context, a deformed version of the third Kepler’s law is also recovered. The closing section is devoted to a discussion of the η \\lt 0 case, where new and partly unexpected features arise.

Equivalent theories redefine Hamiltonian observables to exhibit change in general relativity

NASA Astrophysics Data System (ADS)

Pitts, J. Brian

2017-03-01

Change and local spatial variation are missing in canonical General Relativity’s observables as usually defined, an aspect of the problem of time. Definitions can be tested using equivalent formulations of a theory, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, thus constraining definitions. For massive photons, the de Broglie-Proca non-gauge formulation observable {{A}μ} is equivalent to the Stueckelberg-Utiyama gauge formulation quantity {{A}μ}+{{\\partial}μ}φ, which must therefore be an observable. To achieve that result, observables must have 0 Poisson bracket not with each first-class constraint, but with the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables. The definition for external gauge symmetries can be tested using massive gravity, where one can install gauge freedom by parametrization with clock fields X A . The non-gauge observable {{g}μ ν} has the gauge equivalent {{X}A}{{,}μ}{{g}μ ν}{{X}B}{{,}ν}. The Poisson bracket of {{X}A}{{,}μ}{{g}μ ν}{{X}B}{{,}ν} with G turns out to be not 0 but a Lie derivative. This non-zero Poisson bracket refines and systematizes Kuchař’s proposal to relax the 0 Poisson bracket condition with the Hamiltonian constraint. Thus observables need covariance, not invariance, in relation to external gauge symmetries. The Lagrangian and Hamiltonian for massive gravity are those of General Relativity  +   Λ   +  4 scalars, so the same definition of observables applies to General Relativity. Local fields such as {{g}μ ν} are observables. Thus observables change. Requiring equivalent observables for equivalent theories also recovers Hamiltonian-Lagrangian equivalence.

Hamiltonian formalism for f (T ) gravity

NASA Astrophysics Data System (ADS)

Ferraro, Rafael; Guzmán, María José

2018-05-01

We present the Hamiltonian formalism for f (T ) gravity, and prove that the theory has n/(n -3 ) 2 +1 degrees of freedom (d.o.f.) in n dimensions. We start from a scalar-tensor action for the theory, which represents a scalar field minimally coupled with the torsion scalar T that defines the teleparallel equivalent of general relativity (TEGR) Lagrangian. T is written as a quadratic form of the coefficients of anholonomy of the vierbein. We obtain the primary constraints through the analysis of the structure of the eigenvalues of the multi-index matrix involved in the definition of the canonical momenta. The auxiliary scalar field generates one extra primary constraint when compared with the TEGR case. The secondary constraints are the super-Hamiltonian and supermomenta constraints, that are preserved from the Arnowitt-Deser-Misner formulation of GR. There is a set of n/(n -1 ) 2 primary constraints that represent the local Lorentz transformations of the theory, which can be combined to form a set of n/(n -1 ) 2 -1 first-class constraints, while one of them becomes second class. This result is irrespective of the dimension, due to the structure of the matrix of the brackets between the constraints. The first-class canonical Hamiltonian is modified due to this local Lorentz violation, and the only one local Lorentz transformation that becomes second-class pairs up with the second-class constraint π ≈0 to remove one d.o.f. from the n2+1 pairs of canonical variables. The remaining n/(n -1 ) 2 +2 n -1 primary constraints remove the same number of d.o.f., leaving the theory with n/(n -3 ) 2 +1 d.o.f. This means that f (T ) gravity has only one extra d.o.f., which could be interpreted as a scalar d.o.f.

Theoretical research on the spin-Hamiltonian parameters of the rhombic W5+ centers in CaWO4:Y3+ crystal

NASA Astrophysics Data System (ADS)

Mei, Yang; Wei, Cheng-Fu; Zheng, Wen-Chen

2016-02-01

Detailed theoretical calculations for the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, where i=x, y, z) of the rhombic W5+ center in CaWO4:Y3+ crystal are performed by using the high-order perturbation formulas for d1 ions in rhombic tetrahedral clusters with the ground state |dz2>. These formulas consist of the contributions from two mechanisms, the crystal-field (CF) mechanism connected with CF excited states in the vastly-used CF theory and the frequently-neglected charge-transfer (CT) mechanism related to CT excited states. The calculated results agree well with the experimental values. The calculations indicate that for W5+ ion (or other high valence state dn ions) in crystals, the model calculations of spin-Hamiltonian parameters should take both the CF and CT mechanisms into account. The signs of hyperfine structure constants Ai are suggested and the forming (or defect model) of rhombic W5+ center in CaWO4:Y3+ crystal is confirmed from the calculations.

Theoretical research of the spin-Hamiltonian parameters for two rhombic W5+ centers in KTiOPO4 (KTP) crystal through a two-mechanism model

NASA Astrophysics Data System (ADS)

Mei, Yang; Chen, Bo-Wei; Wei, Chen-Fu; Zheng, Wen-Chen

2016-09-01

The high-order perturbation formulas based on the two-mechanism model are employed to calculate the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, where i=x, y, z) for two approximately rhombic W5+ centers in KTiOPO4 (KTP) crystal. In the model, both the widely-applied crystal-field (CF) mechanism concerning the interactions of CF excited states with the ground state and the generally-neglected charge-transfer (CT) mechanism concerning the interactions of CT excited states with the ground state are included. The calculated results agree with the experimental values, and the signs of constants Ai are suggested. The calculations indicate that (i) for the high valence state dn ions in crystals, the contributions to spin-Hamiltonian parameters should take into account both the CF and CT mechanisms and (ii) the large g-shifts |Δgi | (=|gi-ge |, where ge≈ 2.0023) for W5+ centers in crystals are due to the large spin-orbit parameter of free W5+ ion.

Visualizing Vector Fields Using Line Integral Convolution and Dye Advection

NASA Technical Reports Server (NTRS)

Shen, Han-Wei; Johnson, Christopher R.; Ma, Kwan-Liu

1996-01-01

We present local and global techniques to visualize three-dimensional vector field data. Using the Line Integral Convolution (LIC) method to image the global vector field, our new algorithm allows the user to introduce colored 'dye' into the vector field to highlight local flow features. A fast algorithm is proposed that quickly recomputes the dyed LIC images. In addition, we introduce volume rendering methods that can map the LIC texture on any contour surface and/or translucent region defined by additional scalar quantities, and can follow the advection of colored dye throughout the volume.

Definitive determination of the transverse Hamiltonian parameters in the single molecule magnet Mn_12-Ac

NASA Astrophysics Data System (ADS)

Edwards, Rachel S.; Hill, Stephen; North, J. Micah; Dalal, Naresh; Jones, Shaela; Maccagnano, Sara

2003-03-01

We present high frequency high field electron paramagnetic resonance (EPR) measurements on the single molecule magnet Mn_12-Ac. Using a split coil magnet and highly sensitive resonant cavity techniques we are able to perform an angle dependent study of the single crystal EPR with the field applied in the hard plane, and hence unambiguously determine the transverse Hamiltonian parameters to fourth order. A variation in the line-shape of the resonances with angle supports the recent proposal of a ligand disorder in this material causing local quadratic anisotropy, and is used to determine the magnitude of the second order transverse term. This could have important implications for describing magnetic quantum tunneling in Mn_12-Ac. S. Hill, J.A.A.J. Perenboom, N.S. Dalal, T. Hathaway, T. Stalcup and J.S. Brooks, Phys. Rev. Lett. 80, 2453 (1998). A. Cornia, R. Sessoli, L. Sorace, D. Gatteschi, A.L. Barra and C. Daiguebonne, cond-mat/0112112.

A Symbolic and Graphical Computer Representation of Dynamical Systems

NASA Astrophysics Data System (ADS)

Gould, Laurence I.

2005-04-01

AUTONO is a Macsyma/Maxima program, designed at the University of Hartford, for solving autonomous systems of differential equations as well as for relating Lagrangians and Hamiltonians to their associated dynamical equations. AUTONO can be used in a number of fields to decipher a variety of complex dynamical systems with ease, producing their Lagrangian and Hamiltonian equations in seconds. These equations can then be incorporated into VisSim, a modeling and simulation program, which yields graphical representations of motion in a given system through easily chosen input parameters. The program, along with the VisSim differential-equations graphical package, allows for resolution and easy understanding of complex problems in a relatively short time; thus enabling quicker and more advanced computing of dynamical systems on any number of platforms---from a network of sensors on a space probe, to the behavior of neural networks, to the effects of an electromagnetic field on components in a dynamical system. A flowchart of AUTONO, along with some simple applications and VisSim output, will be shown.

Polarization ellipse and Stokes parameters in geometric algebra.

PubMed

Santos, Adler G; Sugon, Quirino M; McNamara, Daniel J

2012-01-01

In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

Dependence of nuclear quadrupole resonance transitions on the electric field gradient asymmetry parameter for nuclides with half-integer spins

DOE PAGES

Cho, Herman

2016-02-28

Allowed transition energies and eigenstate expansions have been calculated and tabulated in numerical form as functions of the electric field gradient asymmetry parameter for the zero field Hamiltonian of quadrupolar nuclides with I = 3/2,5/2,7/2, and 9/2. These results are essential to interpret nuclear quadrupole resonance (NQR) spectra and extract accurate values of the electric field gradient tensors. Furthermore, applications of NQR methods to studies of electronic structure in heavy element systems are proposed.

Synthetic magnetism for photon fluids

NASA Astrophysics Data System (ADS)

Westerberg, N.; Maitland, C.; Faccio, D.; Wilson, K.; Öhberg, P.; Wright, E. M.

2016-08-01

We develop a theory of artificial gauge fields in photon fluids for the cases of both second-order and third-order optical nonlinearities. This applies to weak excitations in the presence of pump fields carrying orbital angular momentum and is thus a type of Bogoliubov theory. The resulting artificial gauge fields experienced by the weak excitations are an interesting generalization of previous cases and reflect the PT-symmetry properties of the underlying non-Hermitian Hamiltonian. We illustrate the observable consequences of the resulting synthetic magnetic fields for examples involving both second-order and third-order nonlinearities.

Gravitation: Foundations and Frontiers

NASA Astrophysics Data System (ADS)

Padmanabhan, T.

2010-01-01

1. Special relativity; 2. Scalar and electromagnetic fields in special relativity; 3. Gravity and spacetime geometry: the inescapable connection; 4. Metric tensor, geodesics and covariant derivative; 5. Curvature of spacetime; 6. Einstein's field equations and gravitational dynamics; 7. Spherically symmetric geometry; 8. Black holes; 9. Gravitational waves; 10. Relativistic cosmology; 11. Differential forms and exterior calculus; 12. Hamiltonian structure of general relativity; 13. Evolution of cosmological perturbations; 14. Quantum field theory in curved spacetime; 15. Gravity in higher and lower dimensions; 16. Gravity as an emergent phenomenon; Notes; Index.

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.

Ground state transitions in vertically coupled N-layer single electron quantum dots

NASA Astrophysics Data System (ADS)

Xie, Wenfang; Wang, Anmei

2003-12-01

A method is proposed to exactly diagonalize the Hamiltonian of a N-layer quantum dot containing a single electron in each dot in arbitrary magnetic fields. For N=4, the energy spectra of the dot are calculated as a function of the applied magnetic field. We find discontinuous ground-state energy transitions induced by an external magnetic field in the case of strong coupling. However, in the case of weak coupling, such a transition does not occur and the angular momentum remains zero.

Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation.

PubMed

Chen, Rui-Pin; Chen, Zhaozhong; Chew, Khian-Hooi; Li, Pei-Gang; Yu, Zhongliang; Ding, Jianping; He, Sailing

2015-05-29

A caustic vector vortex optical field is experimentally generated and demonstrated by a caustic-based approach. The desired caustic with arbitrary acceleration trajectories, as well as the structured states of polarization (SoP) and vortex orders located in different positions in the field cross-section, is generated by imposing the corresponding spatial phase function in a vector vortex optical field. Our study reveals that different spin and orbital angular momentum flux distributions (including opposite directions) in different positions in the cross-section of a caustic vector vortex optical field can be dynamically managed during propagation by intentionally choosing the initial polarization and vortex topological charges, as a result of the modulation of the caustic phase. We find that the SoP in the field cross-section rotates during propagation due to the existence of the vortex. The unique structured feature of the caustic vector vortex optical field opens the possibility of multi-manipulation of optical angular momentum fluxes and SoP, leading to more complex manipulation of the optical field scenarios. Thus this approach further expands the functionality of an optical system.

Creating orbiting vorticity vectors in magnetic particle suspensions through field symmetry transitions–a route to multi-axis mixing

DOE PAGES

Martin, James E.; Solis, Kyle Jameson

2015-11-09

It has recently been reported that two types of triaxial electric or magnetic fields can drive vorticity in dielectric or magnetic particle suspensions, respectively. The first type-symmetry -- breaking rational fields -- consists of three mutually orthogonal fields, two alternating and one dc, and the second type -- rational triads -- consists of three mutually orthogonal alternating fields. In each case it can be shown through experiment and theory that the fluid vorticity vector is parallel to one of the three field components. For any given set of field frequencies this axis is invariant, but the sign and magnitude ofmore » the vorticity (at constant field strength) can be controlled by the phase angles of the alternating components and, at least for some symmetry-breaking rational fields, the direction of the dc field. In short, the locus of possible vorticity vectors is a 1-d set that is symmetric about zero and is along a field direction. In this paper we show that continuous, 3-d control of the vorticity vector is possible by progressively transitioning the field symmetry by applying a dc bias along one of the principal axes. Such biased rational triads are a combination of symmetry-breaking rational fields and rational triads. A surprising aspect of these transitions is that the locus of possible vorticity vectors for any given field bias is extremely complex, encompassing all three spatial dimensions. As a result, the evolution of a vorticity vector as the dc bias is increased is complex, with large components occurring along unexpected directions. More remarkable are the elaborate vorticity vector orbits that occur when one or more of the field frequencies are detuned. As a result, these orbits provide the basis for highly effective mixing strategies wherein the vorticity axis periodically explores a range of orientations and magnitudes.« less

The Curl of a Vector Field: Beyond the Formula

ERIC Educational Resources Information Center

Burch, Kimberly Jordan; Choi, Youngna

2006-01-01

It has been widely acknowledged that there is some discrepancy in the teaching of vector calculus in mathematics courses and other applied fields. The curl of a vector field is one topic many students can calculate without understanding its significance. In this paper, we explain the origin of the curl after presenting the standard mathematical…

Structural aspects of Hamilton-Jacobi theory

NASA Astrophysics Data System (ADS)

Cariñena, J. F.; Gràcia, X.; Marmo, G.; Martínez, E.; Muñoz-Lecanda, M. C.; Román-Roy, N.

2016-12-01

In our previous papers [J. F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M. C. Muñoz-Lecanda and N. Román-Roy, Geometric Hamilton-Jacobi theory, Int. J. Geom. Meth. Mod. Phys. 3 (2006) 1417-1458; Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems, Int. J. Geom. Meth. Mod. Phys. 7 (2010) 431-454] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton-Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (slicing vector fields) on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton-Jacobi theory, by considering special cases like fibered manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion.

Sachs' free data in real connection variables

NASA Astrophysics Data System (ADS)

De Paoli, Elena; Speziale, Simone

2017-11-01

We discuss the Hamiltonian dynamics of general relativity with real connection variables on a null foliation, and use the Newman-Penrose formalism to shed light on the geometric meaning of the various constraints. We identify the equivalent of Sachs' constraint-free initial data as projections of connection components related to null rotations, i.e. the translational part of the ISO(2) group stabilising the internal null direction soldered to the hypersurface. A pair of second-class constraints reduces these connection components to the shear of a null geodesic congruence, thus establishing equivalence with the second-order formalism, which we show in details at the level of symplectic potentials. A special feature of the first-order formulation is that Sachs' propagating equations for the shear, away from the initial hypersurface, are turned into tertiary constraints; their role is to preserve the relation between connection and shear under retarded time evolution. The conversion of wave-like propagating equations into constraints is possible thanks to an algebraic Bianchi identity; the same one that allows one to describe the radiative data at future null infinity in terms of a shear of a (non-geodesic) asymptotic null vector field in the physical spacetime. Finally, we compute the modification to the spin coefficients and the null congruence in the presence of torsion.

The Existence of Topological Edge States in Honeycomb Plasmonic Lattices

NASA Astrophysics Data System (ADS)

Wang, Li

In this paper, we investigate the band properties of 2D honeycomb plasmonic lattices consisting of metallic nanoparticles. By means of the coupled dipole method and quasi-static approximation, we theoretically analyze the band structures stemming from near-field interaction of localized surface plasmon polaritons for both the infinite lattice and ribbons. Naturally, the interaction of point dipoles decouples into independent out-of-plane and in-plane polarizations. For the out-of-plane modes, both the bulk spectrum and the range of the momentum k∥ where edge states exist in ribbons are similar to the electronic bands in graphene. Nevertheless, the in-plane polarized modes show significant differences, which do not only possess additional non-flat edge states in ribbons, but also have different distributions of the flat edge states in reciprocal space. For in-plane polarized modes, we derived the bulk-edge correspondence, namely, the relation between the number of flat edge states at a fixed k∥, Zak phases of the bulk bands and the winding number associated with the bulk hamiltonian, and verified it through four typical ribbon boundaries, i.e. zigzag, bearded zigzag, armchair, and bearded armchair. Our approach gives a new topological understanding of edge states in such plasmonic systems, and may also apply to other 2D vector wave systems.

The existence of topological edge states in honeycomb plasmonic lattices

NASA Astrophysics Data System (ADS)

Wang, Li; Zhang, Ruo-Yang; Xiao, Meng; Han, Dezhuan; Chan, C. T.; Wen, Weijia

2016-10-01

In this paper, we investigate the band properties of 2D honeycomb plasmonic lattices consisting of metallic nanoparticles. By means of the coupled dipole method and quasi-static approximation, we theoretically analyze the band structures stemming from near-field interaction of localized surface plasmon polaritons for both the infinite lattice and ribbons. Naturally, the interaction of point dipoles decouples into independent out-of-plane and in-plane polarizations. For the out-of-plane modes, both the bulk spectrum and the range of the momentum k ∥ where edge states exist in ribbons are similar to the electronic bands in graphene. Nevertheless, the in-plane polarized modes show significant differences, which do not only possess additional non-flat edge states in ribbons, but also have different distributions of the flat edge states in reciprocal space. For in-plane polarized modes, we derived the bulk-edge correspondence, namely, the relation between the number of flat edge states at a fixed {k}\\parallel , Zak phases of the bulk bands and the winding number associated with the bulk Hamiltonian, and verified it through four typical ribbon boundaries, i.e. zigzag, bearded zigzag, armchair, and bearded armchair. Our approach gives a new topological understanding of edge states in such plasmonic systems, and may also apply to other 2D ‘vector wave’ systems.

Kepler orbits in the Stokesian sedimentation of discs

NASA Astrophysics Data System (ADS)

Chajwa, Rahul; Menon, Narayanan; Ramaswamy, Sriram

We study experimentally the settling dynamics of a pair of falling discs in a viscous fluid (Re 10-4), in a quasi-two-dimensional geometry with the vector normal to the discs, and the trajectory of the centres of the discs, lying in a plane. For initial conditions that are symmetric about the settling direction, we find periodic or scattering orbits of the settling pair [S. Jung et al., PRE 74, 035302 (2006)], and account for these in a purely far-field analysis [S. Kim, Int J Multiphase Flow 11, 699 (1985)]. In particular, we show that the problem of a symmetrically settling pair of spheroids can be mapped to the Kepler two-body problem. The solution to this problem gives a sharp transition between bound and scattering trajectories which is consistent with experimental observations. For initial conditions where the motions of the particles are not symmetric about the settling direction, we obtain yet another separatrix between full rotations and periodic oscillations which we study within an effective Hamiltonian description of this inertialess and entirely dissipative dynamical system. Present addresses - RC: ICTS-TIFR, Hessarghatta, Bengaluru 560 089; NM: Physics Department, UMass Amherst MA 01003; SR: Dept of Physics, IISc, Bengaluru 560 012 SR was supported in part by a J C Bose Fellowship of the SERB, India.

A comparison of in situ measurements of vector-E and - vector-V x vector-B from Dynamics Explorer 2

NASA Technical Reports Server (NTRS)

Hanson, W. B.; Coley, W. R.; Heelis, R. A.; Maynard, N. C.; Aggson, T. L.

1993-01-01

Dynamics Explorer-2 provided the first opportunity to make a direct comparison of in situ measurements of the high-latitude convection electric field by two distinctly different techniques. The vector electric field instrument (VEFI) used antennae to measure the intrinsic electric fields and the ion drift meter (IDM) and retarding potential analyzer (RPA) measured the ion drift velocity vector, from which the convection electric field can be deduced. The data from three orbits having large electric fields at high latitude are presented, one at high, one at medium, and one at low altitudes. The general agreement between the two measurements of electric field is very good, with typical differences at high latitudes of the order of a few millivolts per meter, but there are some regions where the particle fluxes are extremely large (e.g., the cusp) and the disagreement is worse, probably because of IDM difficulties. The auroral zone potential patterns derived from the two devices are in excellent agreement for two of the cases, but not in the third, where bad attitude data may be the problem. At low latitudes there are persistent differences in the measurements of a few millivolts per meter, though these differences are quite constant from orbit to orbit. This problem seems to arise from some shortcoming in the VEFI measurments. Overall, however, these measurements confirm the concept of `frozen-in' plasma that drifts with velocity vector-E x vector-B/B(exp 2) within the measurement errors of the two techniques.

Standing electromagnetic solitons in hot ultra-relativistic electron-positron plasmas

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

Heidari, E., E-mail: ehphys75@iaubushehr.ac.ir; Aslaninejad, M.; Eshraghi, H.

2014-03-15

Using a one-dimensional self-consistent fluid model, we investigate standing relativistic bright solitons in hot electron-positron plasmas. The positron dynamics is taken into account. A set of nonlinear coupled differential equations describing the evolution of electromagnetic waves in fully relativistic two-fluid plasma is derived analytically and solved numerically. As a necessary condition for the existence of standing solitons the system should be relativistic. For the case of ultra-relativistic plasma, we investigate non-drifting bright solitary waves. Detailed discussions of the acceptable solutions are presented. New single hump non-trivial symmetric solutions for the scalar potential were found, and single and multi-nodal symmetric andmore » anti-symmetric solutions for the vector potential are presented. It is shown that for a fixed value of the fluid velocity excited modes with more zeros in the profile of the vector potential show a higher magnitude for the scalar potential. An increase in the plasma fluid velocity also increases the magnitude of the scalar potential. Furthermore, the Hamiltonian and the first integral of the system are given.« less

Extending geometrical optics: A Lagrangian theory for vector waves

DOE PAGES

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

2017-03-16

Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wavemore » spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.« less

Extending geometrical optics: A Lagrangian theory for vector waves

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

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

Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wavemore » spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.« less

An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling

NASA Astrophysics Data System (ADS)

Liu, Junzi; Cheng, Lan

2018-04-01

An atomic mean-field (AMF) spin-orbit (SO) approach within exact two-component theory (X2C) is reported, thereby exploiting the exact decoupling scheme of X2C, the one-electron approximation for the scalar-relativistic contributions, the mean-field approximation for the treatment of the two-electron SO contribution, and the local nature of the SO interactions. The Hamiltonian of the proposed SOX2CAMF scheme comprises the one-electron X2C Hamiltonian, the instantaneous two-electron Coulomb interaction, and an AMF SO term derived from spherically averaged Dirac-Coulomb Hartree-Fock calculations of atoms; no molecular relativistic two-electron integrals are required. Benchmark calculations for bond lengths, harmonic frequencies, dipole moments, and electric-field gradients for a set of diatomic molecules containing elements across the periodic table show that the SOX2CAMF scheme offers a balanced treatment for SO and scalar-relativistic effects and appears to be a promising candidate for applications to heavy-element containing systems. SOX2CAMF coupled-cluster calculations of molecular properties for bismuth compounds (BiN, BiP, BiF, BiCl, and BiI) are also presented and compared with experimental results to further demonstrate the accuracy and applicability of the SOX2CAMF scheme.

Physical subspace in a model of the quantized electromagnetic field coupled to an external field with an indefinite metric

NASA Astrophysics Data System (ADS)

Suzuki, Akito

2008-04-01

We study a model of the quantized electromagnetic field interacting with an external static source ρ in the Feynman (Lorentz) gauge and construct the quantized radiation field Aμ (μ=0,1,2,3) as an operator-valued distribution acting on the Fock space F with an indefinite metric. By using the Gupta subsidiary condition ∂μAμ(x)(+)Ψ=0, one can select the physical subspace Vphys. According to the Gupta-Bleuler formalism, Vphys is a non-negative subspace so that elements of Vphys, called physical states, can be probabilistically interpretable. Indeed, assuming that the external source ρ is infrared regular, i.e., ρ̂/∣k∣3/2ɛL2(R3), we can characterize the physical subspace Vphys and show that Vphys is non-negative. In addition, we find that the Hamiltonian of the model is reduced to the Hamiltonian of the transverse photons with the Coulomb interaction. We, however, prove that the physical subspace is trivial, i.e., Vphys={0}, if and only if the external source ρ is infrared singular, i.e., ρ̂/∣k∣3/2∉L2(R3). We also discuss a representation different from the above representation such that the physical subspace is not trivial under the infrared singular condition.

Quantum model of a hysteresis in a single-domain magnetically soft ferromagnetic

NASA Astrophysics Data System (ADS)

Ignatiev, V. K.; Lebedev, N. G.; Orlov, A. A.

2018-01-01

A quantum model of a single-domain magnetically soft ferromagnetic is proposed. The α-Fe crystal in a state of the saturation magnetization and a variable magnetic field is considered as a sample. The method of an effective Hamiltonian, including the operators of the Zeeman energy, the spin-orbit interaction and the interaction with the crystal field, is used in the model. An expansion of trial single-electron wave function in a series in small parameter of the spin-orbit interaction is suggested to account for the magnetic anisotropy. Within the framework of the Heisenberg representation, the nonlinear equations of motion for the magnetization and the orbital moment of single domain are obtained. Parameters of the modelling Hamiltonian are found from a comparison with experimental data on the magnetic anisotropy of iron. A phenomenological term of the magnetic friction is introduced into equation of the magnetization motion. Nonlinear equations are solved numerically by the Runge-Kutta method. A dependence of the single domain magnetization on magnetic field intensity has a characteristic form of a hysteresis loop which parameters are quantitatively coordinated with experimental data of researches of magnetic properties of nanoparticles of iron and iron oxide. The method is extended for modelling the magnetization dynamics of multi-domain ferromagnetic in the approximation of a strong crystal field.

Tailored optical vector fields for ultrashort-pulse laser induced complex surface plasmon structuring.

PubMed

Ouyang, J; Perrie, W; Allegre, O J; Heil, T; Jin, Y; Fearon, E; Eckford, D; Edwardson, S P; Dearden, G

2015-05-18

Precise tailoring of optical vector beams is demonstrated, shaping their focal electric fields and used to create complex laser micro-patterning on a metal surface. A Spatial Light Modulator (SLM) and a micro-structured S-waveplate were integrated with a picosecond laser system and employed to structure the vector fields into radial and azimuthal polarizations with and without a vortex phase wavefront as well as superposition states. Imprinting Laser Induced Periodic Surface Structures (LIPSS) elucidates the detailed vector fields around the focal region. In addition to clear azimuthal and radial plasmon surface structures, unique, variable logarithmic spiral micro-structures with a pitch Λ ∼1μm, not observed previously, were imprinted on the surface, confirming unambiguously the complex 2D focal electric fields. We show clearly also how the Orbital Angular Momentum(OAM) associated with a helical wavefront induces rotation of vector fields along the optic axis of a focusing lens and confirmed by the observed surface micro-structures.

From Majorana fermions to topological order.

PubMed

Terhal, Barbara M; Hassler, Fabian; DiVincenzo, David P

2012-06-29

We consider a system consisting of a 2D network of links between Majorana fermions on superconducting islands. We show that the fermionic Hamiltonian modeling this system is topologically ordered in a region of parameter space: we show that Kitaev's toric code emerges in fourth-order perturbation theory. By using a Jordan-Wigner transformation we can map the model onto a family of signed 2D Ising models in a transverse field where the signs, ferromagnetic or antiferromagnetic, are determined by additional gauge bits. Our mapping allows an understanding of the nonperturbative regime and the phase transition to a nontopological phase. We discuss the physics behind a possible implementation of this model and argue how it can be used for topological quantum computation by adiabatic changes in the Hamiltonian.

Integrable cosmological potentials

NASA Astrophysics Data System (ADS)

Sokolov, V. V.; Sorin, A. S.

2017-09-01

The problem of classification of the Einstein-Friedman cosmological Hamiltonians H with a single scalar inflaton field φ, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint H=0, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential V(φ). In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed.

Superradiant phase transition with graphene embedded in one dimensional optical cavity

NASA Astrophysics Data System (ADS)

Li, Benliang; Liu, Tao; Hewak, Daniel W.; Wang, Qi Jie

2018-01-01

We theoretically investigate the cavity QED of graphene embedded in an optical cavity under perpendicular magnetic field. We consider the coupling of cyclotron transition and a multimode cavity described by a multimode Dicke model. This model exhibits a superradiant quantum phase transition, which we describe exactly in an effective Hamiltonian approach. The complete excitation spectrum in both the normal phase and superradiant phase regimes is given. In contrast to the single mode case, multimode coupling of cavity photon and cyclotron transition can greatly reduce the critical vacuum Rabi frequency required for quantum phase transition, and dramatically enhance the superradiant emission by fast modulating the Hamiltonian. Our work paves a way to experimental explorations of quantum phase transitions in solid state systems.

Interest Rates and Coupon Bonds in Quantum Finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2009-09-01

1. Synopsis; 2. Interest rates and coupon bonds; 3. Options and option theory; 4. Interest rate and coupon bond options; 5. Quantum field theory of bond forward interest rates; 6. Libor Market Model of interest rates; 7. Empirical analysis of forward interest rates; 8. Libor Market Model of interest rate options; 9. Numeraires for bond forward interest rates; 10. Empirical analysis of interest rate caps; 11. Coupon bond European and Asian options; 12. Empirical analysis of interest rate swaptions; 13. Correlation of coupon bond options; 14. Hedging interest rate options; 15. Interest rate Hamiltonian and option theory; 16. American options for coupon bonds and interest rates; 17. Hamiltonian derivation of coupon bond options; Appendixes; Glossaries; List of symbols; Reference; Index.

Spatial Dynamics Methods for Solitary Waves on a Ferrofluid Jet

NASA Astrophysics Data System (ADS)

Groves, M. D.; Nilsson, D. V.

2018-04-01

This paper presents existence theories for several families of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet surrounding a stationary metal rod. The ferrofluid, which is governed by a general (nonlinear) magnetisation law, is subject to an azimuthal magnetic field generated by an electric current flowing along the rod. The ferrohydrodynamic problem for axisymmetric travelling waves is formulated as an infinite-dimensional Hamiltonian system in which the axial direction is the time-like variable. A centre-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite number of degrees of freedom, and homoclinic solutions to the reduced system, which correspond to solitary waves, are detected by dynamical-systems methods.

A first class constraint generates not a gauge transformation, but a bad physical change: The case of electromagnetism

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

Pitts, J. Brian, E-mail: jbp25@cam.ac.uk

In Dirac–Bergmann constrained dynamics, a first-class constraint typically does not alone generate a gauge transformation. By direct calculation it is found that each first-class constraint in Maxwell’s theory generates a change in the electric field E{sup →} by an arbitrary gradient, spoiling Gauss’s law. The secondary first-class constraint p{sup i},{sub i}=0 still holds, but being a function of derivatives of momenta (mere auxiliary fields), it is not directly about the observable electric field (a function of derivatives of A{sub μ}), which couples to charge. Only a special combination of the two first-class constraints, the Anderson–Bergmann–Castellani gauge generator G, leaves E{supmore » →} unchanged. Likewise only that combination leaves the canonical action invariant—an argument independent of observables. If one uses a first-class constraint to generate instead a canonical transformation, one partly strips the canonical coordinates of physical meaning as electromagnetic potentials, vindicating the Anderson–Bergmann Lagrangian orientation of interesting canonical transformations. The need to keep gauge-invariant the relation q-dot −(δH)/(δp) =−E{sub i}−p{sup i}=0 supports using the gauge generator and primary Hamiltonian rather than the separate first-class constraints and the extended Hamiltonian. Partly paralleling Pons’s criticism, it is shown that Dirac’s proof that a first-class primary constraint generates a gauge transformation, by comparing evolutions from identical initial data, cancels out and hence fails to detect the alterations made to the initial state. It also neglects the arbitrary coordinates multiplying the secondary constraints inside the canonical Hamiltonian. Thus the gauge-generating property has been ascribed to the primaries alone, not the primary–secondary team G. Hence the Dirac conjecture about secondary first-class constraints as generating gauge transformations rests upon a false presupposition about primary first-class constraints. Clarity about Hamiltonian electromagnetism will be useful for an analogous treatment of GR. - Highlights: • A first-class constraint changes the electric field E, spoiling Gauss’s law. • A first-class constraint does not leave the action invariant or preserve q,0−dH/dp. • The gauge generator preserves E,q,0−dH/dp, and the canonical action. • The error in proofs that first-class primaries generating gauge is shown. • Dirac’s conjecture about secondary first-class constraints is blocked.« less

Understanding Vector Fields.

ERIC Educational Resources Information Center

Curjel, C. R.

1990-01-01

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

The hopf algebra of vector fields on complex quantum groups

NASA Astrophysics Data System (ADS)

Drabant, Bernhard; Jurčo, Branislav; Schlieker, Michael; Weich, Wolfgang; Zumino, Bruno

1992-10-01

We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A n , B n , C n , and D n by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals.

On Finsler spacetimes with a timelike Killing vector field

NASA Astrophysics Data System (ADS)

Caponio, Erasmo; Stancarone, Giuseppe

2018-04-01

We study Finsler spacetimes and Killing vector fields taking care of the fact that the generalised metric tensor associated to the Lorentz–Finsler function L is in general well defined only on a subset of the slit tangent bundle. We then introduce a new class of Finsler spacetimes endowed with a timelike Killing vector field that we call stationary splitting Finsler spacetimes. We characterize when a Finsler spacetime with a timelike Killing vector field is locally a stationary splitting. Finally, we show that the causal structure of a stationary splitting is the same of one of two Finslerian static spacetimes naturally associated to the stationary splitting.