Turning the resistive MHD into a stochastic field theory
NASA Astrophysics Data System (ADS)
Materassi, M.; Consolini, G.
2008-08-01
Classical systems stirred by random forces of given statistics may be described via a path integral formulation in which their degrees of freedom are stochastic variables themselves, undergoing a multiple-history probabilistic evolution. This framework seems to be easily applicable to resistive Magneto-Hydro-Dynamics (MHD). Indeed, MHD equations form a dynamic system of classical variables in which the terms representing the density, the pressure and the conductivity of the plasma are irregular functions of space and time when turbulence occurs. By treating those irregular terms as random stirring forces, it is possible to introduce a Stochastic Field Theory which should represent correctly the impulsive phenomena caused by the spece- and time-irregularity of plasma turbulence. This work is motivated by the recent observational evidences of the crucial role played by stochastic fluctuations in space plasmas.
Note on Stochastic Quantization of Field Theories with Bottomless Actions
NASA Astrophysics Data System (ADS)
Ito, M.; Morita, K.
1993-07-01
It is shown that the kerneled Langevin equation, which has recently been proposed by Tanaka et al. to quantize field theories with bottomless actions, reproduces perturbation theory results independent of the initial conditions. The effective potential is approximately determined from the kerneled Langevin equation to be bounded from below. The evolution equation for the two-point correlation function also defines the effective potential for the propagator, which is given for the zero-dimensional ``wrong-sign'' -λφ4 model under the assumption that all higher-moment cumulants than the second vanish.
Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media
Tong Zhisong; Korotkova, Olga
2010-09-15
The theory of scattering of scalar stochastic fields from deterministic and random media is generalized to the electromagnetic domain under the first-order Born approximation. The analysis allows for determining the changes in spectrum, coherence, and polarization of electromagnetic fields produced on their propagation from the source to the scattering volume, interaction with the scatterer, and propagation from the scatterer to the far field. An example of scattering of a field produced by a {delta}-correlated partially polarized source and scattered from a {delta}-correlated medium is provided.
Exact Mapping of the Stochastic Field Theory for Manna Sandpiles to Interfaces in Random Media
NASA Astrophysics Data System (ADS)
Le Doussal, Pierre; Wiese, Kay Jörg
2015-03-01
We show that the stochastic field theory for directed percolation in the presence of an additional conservation law [the conserved directed-percolation (C-DP) class] can be mapped exactly to the continuum theory for the depinning of an elastic interface in short-range correlated quenched disorder. Along one line of the parameters commonly studied, this mapping leads to the simplest overdamped dynamics. Away from this line, an additional memory term arises in the interface dynamics; we argue that this does not change the universality class. Since C-DP is believed to describe the Manna class of self-organized criticality, this shows that Manna stochastic sandpiles and disordered elastic interfaces (i.e., the quenched Edwards-Wilkinson model) share the same universal large-scale behavior.
NASA Astrophysics Data System (ADS)
Lensky, Vadim; Birse, Michael C.; Walet, Niels R.
2016-09-01
We construct a coordinate-space potential based on pionless effective field theory (EFT) with a Gaussian regulator. Charge-symmetry breaking is included through the Coulomb potential and through two- and three-body contact interactions. Starting with the effective field theory potential, we apply the stochastic variational method to determine the ground states of nuclei with mass number A ≤4 . At next-to-next-to-leading order, two out of three independent three-body parameters can be fitted to the three-body binding energies. To fix the remaining one, we look for a simultaneous description of the binding energy of 4He and the charge radii of 3He and 4He. We show that at the order considered we can find an acceptable solution, within the uncertainty of the expansion. We find that the EFT expansion shows good agreement with empirical data within the estimated uncertainty, even for a system as dense as 4He.
Stochastic geometry of critical curves, Schramm Loewner evolutions and conformal field theory
NASA Astrophysics Data System (ADS)
Gruzberg, Ilya A.
2006-10-01
Conformally invariant curves that appear at critical points in two-dimensional statistical mechanics systems and their fractal geometry have received a lot of attention in recent years. On the one hand, Schramm (2000 Israel J. Math. 118 221 (Preprint math.PR/9904022)) has invented a new rigorous as well as practical calculational approach to critical curves, based on a beautiful unification of conformal maps and stochastic processes, and by now known as Schramm-Loewner evolution (SLE). On the other hand, Duplantier (2000 Phys. Rev. Lett. 84 1363; Fractal Geometry and Applications: A Jubilee of Benot Mandelbrot: Part 2 (Proc. Symp. Pure Math. vol 72) (Providence, RI: American Mathematical Society) p 365 (Preprint math-ph/0303034)) has applied boundary quantum gravity methods to calculate exact multifractal exponents associated with critical curves. In the first part of this paper, I provide a pedagogical introduction to SLE. I present mathematical facts from the theory of conformal maps and stochastic processes related to SLE. Then I review basic properties of SLE and provide practical derivation of various interesting quantities related to critical curves, including fractal dimensions and crossing probabilities. The second part of the paper is devoted to a way of describing critical curves using boundary conformal field theory (CFT) in the so-called Coulomb gas formalism. This description provides an alternative (to quantum gravity) way of obtaining the multifractal spectrum of critical curves using only traditional methods of CFT based on free bosonic fields.
Stochastic Growth Theory of Spatially-Averaged Distributions of Langmuir Fields in Earth's Foreshock
NASA Technical Reports Server (NTRS)
Boshuizen, Christopher R.; Cairns, Iver H.; Robinson, P. A.
2001-01-01
Langmuir-like waves in the foreshock of Earth are characteristically bursty and irregular, and are the subject of a number of recent studies. Averaged over the foreshock, it is observed that the probability distribution is power-law P(bar)(log E) in the wave field E with the bar denoting this averaging over position, In this paper it is shown that stochastic growth theory (SGT) can explain a power-law spatially-averaged distributions P(bar)(log E), when the observed power-law variations of the mean and standard deviation of log E with position are combined with the log normal statistics predicted by SGT at each location.
Stochastic models: theory and simulation.
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Effective field theory during inflation. II. Stochastic dynamics and power spectrum suppression
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2016-02-01
We obtain the nonequilibrium effective action of an inflatonlike scalar field—the system—by tracing over sub-Hubble degrees of freedom of "environmental" light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflatonlike field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super-Hubble fluctuations of the inflaton field, P (k ;η )=P0(k )e-γ (k ;η ) where P0(k ) is the nearly scale invariant power spectrum in absence of coupling. γ (k ;η )>0 describes the suppression of the power spectrum; it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action for the case of a heavy scalar field of mass M ≫H ; this case yields a local "Fermi" limit with a very weak self-interaction of the inflatonlike field and dissipative terms that are suppressed by powers of H /M . We conjecture on the possibility that the large scale anomalies in the cosmic microwave background may originate in dissipative processes from inflaton coupling to sub-Hubble degrees of freedom.
Postmodern string theory: Stochastic formulation
NASA Astrophysics Data System (ADS)
Aurilia, A.; Spallucci, E.; Vanzetta, I.
1994-11-01
In this paper we study the dynamics of a statistical ensemble of strings, building on a recently proposed gauge theory of the string geodesic field. We show that this stochastic approach is equivalent to the Carathéodory formulation of the Nambu-Goto action, supplemented by an averaging procedure over the family of classical string world sheets which are solutions of the equation of motion. In this new framework, the string geodesic field is reinterpreted as the Gibbs current density associated with the string statistical ensemble. Next, we show that the classical field equations derived from the string gauge action can be obtained as the semiclassical limit of the string functional wave equation. For closed strings, the wave equation itself is completely analogous to the Wheeler-DeWitt equation used in quantum cosmology. Thus, in the string case, the wave function has support on the space of all possible spatial loop configurations. Finally, we show that the string distribution induces a multiphase, or cellular structure on the spacetime manifold characterized by domains with a purely Riemannian geometry separated by domain walls over which there exists a predominantly Weyl geometry.
Scattering theory of stochastic electromagnetic light waves.
Wang, Tao; Zhao, Daomu
2010-07-15
We generalize scattering theory to stochastic electromagnetic light waves. It is shown that when a stochastic electromagnetic light wave is scattered from a medium, the properties of the scattered field can be characterized by a 3 x 3 cross-spectral density matrix. An example of scattering of a spatially coherent electromagnetic light wave from a deterministic medium is discussed. Some interesting phenomena emerge, including the changes of the spectral degree of coherence and of the spectral degree of polarization of the scattered field.
Stochastic Microlensing: Mathematical Theory and Applications
NASA Astrophysics Data System (ADS)
Teguia, Alberto Mokak
Stochastic microlensing is a central tool in probing dark matter on galactic scales. From first principles, we initiate the development of a mathematical theory of stochastic microlensing. We first construct a natural probability space for stochastic microlensing and characterize the general behaviour of the random time delay functions' random critical sets. Next we study stochastic microlensing in two distinct random microlensing scenarios: The uniform stars' distribution with constant mass spectrum and the spatial stars' distribution with general mass spectrum. For each scenario, we determine exact and asymptotic (in the large number of point masses limit) stochastic properties of the random time delay functions and associated random lensing maps and random shear tensors, including their moments and asymptotic density functions. We use these results to study certain random observables, such as random fixed lensed images, random bending angles, and random magnifications. These results are relevant to the theory of random fields and provide a platform for further generalizations as well as analytical limits for checking astrophysical studies of stochastic microlensing. Continuing our development of a mathematical theory of stochastic microlensing, we study the stochastic version of the Image Counting Problem, first considered in the non-random setting by Einstein and generalized by Petters. In particular, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images for a general random lensing scenario. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to the uniform stars' distribution random microlensing scenario, we calculate the asymptotic global
Theory, technology, and technique of stochastic cooling
Marriner, J.
1993-10-01
The theory and technological implementation of stochastic cooling is described. Theoretical and technological limitations are discussed. Data from existing stochastic cooling systems are shown to illustrate some useful techniques.
Stochastic-field cavitation model
NASA Astrophysics Data System (ADS)
Dumond, J.; Magagnato, F.; Class, A.
2013-07-01
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Stochastic-field cavitation model
Dumond, J.; Magagnato, F.; Class, A.
2013-07-15
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
NASA Astrophysics Data System (ADS)
Gushchin, A. A.
1982-12-01
CONTENTSIntroduction § 1. Basic notation and definitions § 2. The Doléans measure and increasing fields § 3. Theorems on predictable projections. Decomposition of weak submartingales § 4. Weakly predictable random fields § 5. Theorems on weakly predictable projections § 6. Decomposition of strong martingales References
Wu, Wei; Wang, Jin
2014-09-14
We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.
NASA Astrophysics Data System (ADS)
Wu, Wei; Wang, Jin
2014-09-01
We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.
NASA Astrophysics Data System (ADS)
Skorokhod, A. V.
1982-12-01
CONTENTSIntroduction § 1. The finite-dimensional case § 2. Stochastic semigroups in the L2-strong theory § 3. Homogeneous strongly continuous semigroups with the group of the first moments § 4. Stochastic equations of diffusion type with constant coefficients § 5. Continuous homogeneous stochastic semigroups in the presence of two moments References
Stochastic kinetic mean field model
NASA Astrophysics Data System (ADS)
Erdélyi, Zoltán; Pasichnyy, Mykola; Bezpalchuk, Volodymyr; Tomán, János J.; Gajdics, Bence; Gusak, Andriy M.
2016-07-01
This paper introduces a new model for calculating the change in time of three-dimensional atomic configurations. The model is based on the kinetic mean field (KMF) approach, however we have transformed that model into a stochastic approach by introducing dynamic Langevin noise. The result is a stochastic kinetic mean field model (SKMF) which produces results similar to the lattice kinetic Monte Carlo (KMC). SKMF is, however, far more cost-effective and easier to implement the algorithm (open source program code is provided on http://skmf.eu website). We will show that the result of one SKMF run may correspond to the average of several KMC runs. The number of KMC runs is inversely proportional to the amplitude square of the noise in SKMF. This makes SKMF an ideal tool also for statistical purposes.
NASA Astrophysics Data System (ADS)
Ertaş, Mehmet; Keskin, Mustafa
2015-06-01
Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume-Emery-Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h0/J), (D/J, T/J) and (K/J, T/J) planes, where T, h0, D, K and z are the temperature, magnetic field amplitude, crystal-field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.
Transport in a stochastic magnetic field
White, R.B.; Wu, Yanlin . Plasma Physics Lab.); Rax, J.M. . Dept. de Recherches sur la Fusion Controlee)
1992-01-01
Collisional heat transport in a stochastic magnetic field configuration is investigated. Well above stochastic threshold, a numerical solution of a Chirikov-Taylor model shows a short-time nonlocal regime, but at large time the Rechester-Rosenbluth effective diffusion is confirmed. Near stochastic threshold, subdiffusive behavior is observed for short mean free paths. The nature of this subdiffusive behavior is understood in terms of the spectrum of islands in the stochastic sea.
Transport in a stochastic magnetic field
White, R.B.; Wu, Yanlin; Rax, J.M.
1992-09-01
Collisional heat transport in a stochastic magnetic field configuration is investigated. Well above stochastic threshold, a numerical solution of a Chirikov-Taylor model shows a short-time nonlocal regime, but at large time the Rechester-Rosenbluth effective diffusion is confirmed. Near stochastic threshold, subdiffusive behavior is observed for short mean free paths. The nature of this subdiffusive behavior is understood in terms of the spectrum of islands in the stochastic sea.
Stochastic processes, estimation theory and image enhancement
NASA Technical Reports Server (NTRS)
Assefi, T.
1978-01-01
An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background.
Communication: Embedded fragment stochastic density functional theory
Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2014-07-28
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.
Communication: Embedded fragment stochastic density functional theory
NASA Astrophysics Data System (ADS)
Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2014-07-01
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.
Ertaş, Mehmet; Deviren, Bayram; Keskin, Mustafa
2012-11-01
Nonequilibrium magnetic properties in a two-dimensional kinetic mixed spin-2 and spin-5/2 Ising system in the presence of a time-varying (sinusoidal) magnetic field are studied within the effective-field theory (EFT) with correlations. The time evolution of the system is described by using Glauber-type stochastic dynamics. The dynamic EFT equations are derived by employing the Glauber transition rates for two interpenetrating square lattices. We investigate the time dependence of the magnetizations for different interaction parameter values in order to find the phases in the system. We also study the thermal behavior of the dynamic magnetizations, the hysteresis loop area, and dynamic correlation. The dynamic phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane and we observe that the system exhibits dynamic tricritical and reentrant behaviors. Moreover, the system also displays a double critical end point (B), a zero-temperature critical point (Z), a critical end point (E), and a triple point (TP). We also performed a comparison with the mean-field prediction in order to point out the effects of correlations and found that some of the dynamic first-order phase lines, which are artifacts of the mean-field approach, disappeared.
Spatial Stochastic Systems Theory and Multiple Scattering of Waves.
NASA Astrophysics Data System (ADS)
Liu, Keh-Chung
In this thesis, two methods are established for deriving the expressions of the space-time correlation function of the multiply scattered fields caused by discontinuous random media, including randomly distributed discrete scatterers and irregular interfaces. These two methods are: (1) method of spatial stochastic systems, (2) method of discontinuous stochastic field. For the first method, the basic concept and theory about the spatial stochastic system and the generalized convolution estab- lished in the author's earlier papers are developed, and the problem of determining the multiply scattered field in complex media is reduced to a simple algebraic operation of generalized convolutions that is obtained from a system decomposition diagram and the corresponding operator equations (Chapter II). By means of this method, the general formulas for the mean value, mean square value and space correlation function of the multiply scattered field are established. These formulas consist of only a single summation and a single integration, and the integrands can be obtained from a recurrence formula (Chapters III -V). For the second method, a discontinuous stochastic field (beta)((')r,(omega)), which represents the properties of the random medium (randomly distributed discrete scatterers), is defined. Because of the intro- duction of (beta)((')r,(omega)) the whole process of solving the stochastic wave equation by means of the stochastic integral equation and the Neumann series expansion is greatly simplified. The result shows that the space correlation function of the multiply scattered field can be exactly expressed as the form of a series, each term of which is an integral of the statistical moment of (beta)((')r,(omega)) of corresponding order. The convergence speed of this series mainly depends on the contrast in speed between the scatterer material and the surrounding medium, i.e., the fluctuation of the random medium. Thus, the task is reduced to the calculation of
Ground movement analysis based on stochastic medium theory.
Fei, Meng; Wu, Li-chun; Zhang, Jia-sheng; Deng, Guo-dong; Ni, Zhi-hui
2014-01-01
In order to calculate the ground movement induced by displacement piles driven into horizontal layered strata, an axisymmetric model was built and then the vertical and horizontal ground movement functions were deduced using stochastic medium theory. Results show that the vertical ground movement obeys normal distribution function, while the horizontal ground movement is an exponential function. Utilizing field measured data, parameters of these functions can be obtained by back analysis, and an example was employed to verify this model. Result shows that stochastic medium theory is suitable for calculating the ground movement in pile driving, and there is no need to consider the constitutive model of soil or contact between pile and soil. This method is applicable in practice. PMID:24701184
Many body theory of stochastic gene expression
NASA Astrophysics Data System (ADS)
Walczak, Aleksandra M.
The regulation of expression states of genes in cells is a stochastic process. The relatively small numbers of protein molecules of a given type present in the cell and the nonlinear nature of chemical reactions result in behaviours, which are hard to anticipate without an appropriate mathematical development. In this dissertation, I develop theoretical approaches based on methods of statistical physics and many-body theory, in which protein and operator state dynamics are treated stochastically and on an equal footing. This development allows me to study the general principles of how noise arising on different levels of the regulatory system affects the complex collective characteristics of systems observed experimentally. I discuss simple models and approximations, which allow for, at least some, analytical progress in these problems. These have allowed us to understand how the operator state fluctuations may influence the steady state properties and lifetimes of attractors of simple gene systems. I show, that for fast binding and unbinding from the DNA, the operator state may be taken to be in equilibrium for highly cooperative binding, when predicting steady state properties as is traditionally done. Nevertheless, if proteins are produced in bursts, the DNA binding state fluctuations must be taken into account explicitly. Furthermore, even when the steady state probability distributions are weakly influenced by the operator state fluctuations, the escape rate in biologically relevant regimes strongly depends on transcription factor-DNA binding rates.
Stochastic Vorticity and Associated Filtering Theory
Amirdjanova, A.; Kallianpur, G.
2002-12-19
The focus of this work is on a two-dimensional stochastic vorticity equation for an incompressible homogeneous viscous fluid. We consider a signed measure-valued stochastic partial differential equation for a vorticity process based on the Skorohod-Ito evolution of a system of N randomly moving point vortices. A nonlinear filtering problem associated with the evolution of the vorticity is considered and a corresponding Fujisaki-Kallianpur-Kunita stochastic differential equation for the optimal filter is derived.
Crossing resonance of stochastically interacting wave fields
Ignatchenko, V. A. Polukhin, D. S.
2013-02-15
The dynamic susceptibilities (Green's functions) of the system of two interacting wave fields of different physical natures with a stochastically inhomogeneous coupling parameter between them with zero mean value have been examined. The well-known self-consistent approximation taking into account all diagrams with noncrossing correlation/interaction lines has been generalized to the case of stochastically interacting wave fields. The analysis has been performed for spin and elastic waves. The results obtained taking into account the processes of multiple scattering of waves from inhomogeneities are significantly different from those obtained for this situation earlier in the Bourret approximation [R.C. Bourret, Nuovo Cimento 26, 1 (1962)]. Instead of frequencies degeneracy removal in the wave spectrum and the splitting of resonance peaks of dynamic susceptibilities, a wide single-mode resonance peak should be observed at the crossing point of the unperturbed dispersion curves. The fine structure appears at vertices of these wide peaks in the form of a narrow resonance on the Green's-function curve of one field and a narrow antiresonance on the vertex of the Green's-function curve of the other field.
Large Deviations for Nonlocal Stochastic Neural Fields
2014-01-01
We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers’ law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multiscale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations. Mathematics Subject Classification (2000): 60F10, 60H15, 65M60, 92C20. PMID:24742297
Majorana approach to the stochastic theory of line shapes
NASA Astrophysics Data System (ADS)
Komijani, Yashar; Coleman, Piers
2016-08-01
Motivated by recent Mössbauer experiments on strongly correlated mixed-valence systems, we revisit the Kubo-Anderson stochastic theory of spectral line shapes. Using a Majorana representation for the nuclear spin we demonstrate how to recast the classic line-shape theory in a field-theoretic and diagrammatic language. We show that the leading contribution to the self-energy can reproduce most of the observed line-shape features including splitting and line-shape narrowing, while the vertex and the self-consistency corrections can be systematically included in the calculation. This approach permits us to predict the line shape produced by an arbitrary bulk charge fluctuation spectrum providing a model-independent way to extract the local charge fluctuation spectrum of the surrounding medium. We also derive an inverse formula to extract the charge fluctuation from the measured line shape.
Kheirandish, F.; Amooshahi, M.
2008-11-18
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.
Covariant Noncommutative Field Theory
Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.
2008-07-02
The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.
Existence Theory for Stochastic Power Law Fluids
NASA Astrophysics Data System (ADS)
Breit, Dominic
2015-06-01
We consider the equations of motion for an incompressible non-Newtonian fluid in a bounded Lipschitz domain during the time interval (0, T) together with a stochastic perturbation driven by a Brownian motion W. The balance of momentum reads as where v is the velocity, the pressure and f an external volume force. We assume the common power law model and show the existence of martingale weak solution provided . Our approach is based on the -truncation and a harmonic pressure decomposition which are adapted to the stochastic setting.
Records in stochastic processes—theory and applications
NASA Astrophysics Data System (ADS)
Wergen, Gregor
2013-06-01
In recent years there has been a surge of interest in the statistics of record-breaking events in stochastic processes. Along with that, many new and interesting applications of the theory of records were discovered and explored. The record statistics of uncorrelated random variables sampled from time-dependent distributions was studied extensively. The findings were applied in various areas to model and explain record-breaking events in observational data. Particularly interesting and fruitful was the study of record-breaking temperatures and their connection with global warming, but also records in sports, biology and some areas in physics were considered in the last years. Similarly, researchers have recently started to understand the record statistics of correlated processes such as random walks, which can be helpful to model record events in financial time series. This review is an attempt to summarize and evaluate the progress that has been made in the field of record statistics throughout recent years.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Towards a theory of stochastic vorticity-augmentation. [tornado model
NASA Technical Reports Server (NTRS)
Liu, V. C.
1977-01-01
A new hypothesis to account for the formation of tornadoes is presented. An elementary one-dimensional theory is formulated for vorticity transfer between an ambient sheared wind and a transverse penetrating jet. The theory points out the relevant quantities to be determined in describing the present stochastic mode of vorticity augmentation.
NASA Astrophysics Data System (ADS)
DeBock, M. F. M.; Classen, I. G. J.; Busch, C.; Jaspers, R. J. E.; Koslowski, H. R.; Unterberg, B.; TEXTOR Team
2008-01-01
For fusion reactors, based on the principle of magnetic confinement, it is important to avoid so-called magnetic islands or tearing modes. They reduce confinement and can be the cause of major disruptions. One class of magnetic islands is that of the perturbation field driven modes. This perturbation field can, for example, be the intrinsic error field. Theoretical work predicts a strong relationship between plasma rotation and the excitation of perturbation field modes. Experimentally, the theory on mode excitation and plasma rotation has been confirmed on several tokamaks. In those experiments, however, the control over the plasma rotation velocity and direction, and over the externally applied perturbation field was limited. In this paper experiments are presented that were carried out at the TEXTOR tokamak. Two tangential neutral beam injectors and a set of helical perturbation coils, called the dynamic ergodic divertor (DED), provide control over both the plasma rotation and the external perturbation field in TEXTOR. This made it possible to set up a series of experiments to test the theory on mode excitation and plasma rotation in detail. The perturbation field induced by the DED not only excites magnetic islands, it also sets up a layer near the plasma boundary where the magnetic field is stochastic. It will be shown that this stochastic field alters both the rotational response of the plasma on the perturbation field and the threshold for mode excitation. It therefore has to be included in an extended theory on mode excitation.
Evaluation of Uncertainty in Runoff Analysis Incorporating Theory of Stochastic Process
NASA Astrophysics Data System (ADS)
Yoshimi, Kazuhiro; Wang, Chao-Wen; Yamada, Tadashi
2015-04-01
The aim of this paper is to provide a theoretical framework of uncertainty estimate on rainfall-runoff analysis based on theory of stochastic process. SDE (stochastic differential equation) based on this theory has been widely used in the field of mathematical finance due to predict stock price movement. Meanwhile, some researchers in the field of civil engineering have investigated by using this knowledge about SDE (stochastic differential equation) (e.g. Kurino et.al, 1999; Higashino and Kanda, 2001). However, there have been no studies about evaluation of uncertainty in runoff phenomenon based on comparisons between SDE (stochastic differential equation) and Fokker-Planck equation. The Fokker-Planck equation is a partial differential equation that describes the temporal variation of PDF (probability density function), and there is evidence to suggest that SDEs and Fokker-Planck equations are equivalent mathematically. In this paper, therefore, the uncertainty of discharge on the uncertainty of rainfall is explained theoretically and mathematically by introduction of theory of stochastic process. The lumped rainfall-runoff model is represented by SDE (stochastic differential equation) due to describe it as difference formula, because the temporal variation of rainfall is expressed by its average plus deviation, which is approximated by Gaussian distribution. This is attributed to the observed rainfall by rain-gauge station and radar rain-gauge system. As a result, this paper has shown that it is possible to evaluate the uncertainty of discharge by using the relationship between SDE (stochastic differential equation) and Fokker-Planck equation. Moreover, the results of this study show that the uncertainty of discharge increases as rainfall intensity rises and non-linearity about resistance grows strong. These results are clarified by PDFs (probability density function) that satisfy Fokker-Planck equation about discharge. It means the reasonable discharge can be
Stochastic global modeling of the archeomagnetic field
NASA Astrophysics Data System (ADS)
Hellio, Gabrielle; Bouligand, Claire; Gillet, Nicolas; Jault, Dominique
2016-04-01
Modeling of the archeomagnetic field relies on indirect estimations of the ancient field recorded both in archeological artifacts and lake sediments. The sparse repartition of archeomagnetic data in space and time and their associated large measurement and dating uncertainties limit our ability to recover the spatio-temporal variations of the geomagnetic field over the past few millennia. The time regularization generally used to overcome the problem of non-uniqueness leads to models that are generally too smooth compared to geomagnetic time-series. The aim of this study is to perform a stochastic inversion of all available archeomagnetic data in order to build an ensemble of global models covering the past few millennia. The inverse problem is solved using a priori information on the Gauss coefficients. We rely on a time correlation function, which is compatible with present knowledge of the geomagnetic spectra and also with the rapid fluctuations observed in the geomagnetic time series. The method we developed allows us to account for dating errors in a probabilistic framework, at the expense of an inflated data space. We present here the resulting global model that offers an alternative to existing ones.
Stochastic does not equal ad hoc. [theories of lunar origin
NASA Technical Reports Server (NTRS)
Hartmann, W. K.
1984-01-01
Some classes of influential events in solar system history are class-predictable but not event-predictable. Theories of lunar origin should not ignore class-predictable stochastic events. Impacts and close encounters with large objects during planet formation are class-predictable. These stochastic events, such as large impacts that triggered ejection of Earth-mantle material into a circum-Earth cloud, should not be rejected as ad hoc. A way to deal with such events scientifically is to investigate their consequences; if it can be shown that they might produce the Moon, they become viable concepts in theories of lunar origin.
Stochastic modeling of the archeomagnetic field
NASA Astrophysics Data System (ADS)
Hellio, Gabrielle; Bouligand, Claire; Gillet, Nicolas; Jault, Dominique
2014-05-01
Modeling of the archeomagnetic field relies on indirect estimations of the ancient field recorded both in archeological artifacts and lake sediments. The sparse repartition of archeomagnetic data in space and time and their associated large measurement and dating uncertainties limit our ability to recover the spatio-temporal variations of the geomagnetic field over the past few millennia. The time regularization generally used to overcome the problem of non-uniqueness leads to models that are generally too smooth compared to geomagnetic time-series. The aim of this study is to perform a stochastic inversion of archeomagnetic data in order to build an ensemble of regional models covering the past few millennia. The inverse problem is solved using a priori information on the Gauss coefficients. We rely on a time correlation function, which is compatible with present knowledge of the geomagnetic spectra and also with the rapid fluctuations observed in the geomagnetic time series. The method we developed allows us to account for dating errors in a probabilistic framework, at the expense of an inflated dataspace. We argue also the importance of covariance existing between inclination and intensity which provides additional information when few data are available. The resulting ensemble of models not only provides reliable information for processes occurring in the core but is also useful in a purpose of archeomagnetic dating. We present synthetic results to test the validity of our method and to illustrate the effect of dating errors. Furthermore, we take advantage of the large amount of data and the relatively dense temporal coverage in Western Europe to construct intensity master curves for Syria and directional and intensity curves for France. The last curves allow us to discuss the importance of covariance between inclination and intensity.
Fluid Physics Under a Stochastic Acceleration Field
NASA Technical Reports Server (NTRS)
Vinals, Jorge
2001-01-01
The research summarized in this report has involved a combined theoretical and computational study of fluid flow that results from the random acceleration environment present onboard space orbiters, also known as g-jitter. We have focused on a statistical description of the observed g-jitter, on the flows that such an acceleration field can induce in a number of experimental configurations of interest, and on extending previously developed methodology to boundary layer flows. Narrow band noise has been shown to describe many of the features of acceleration data collected during space missions. The scale of baroclinically induced flows when the driving acceleration is random is not given by the Rayleigh number. Spatially uniform g-jitter induces additional hydrodynamic forces among suspended particles in incompressible fluids. Stochastic modulation of the control parameter shifts the location of the onset of an oscillatory instability. Random vibration of solid boundaries leads to separation of boundary layers. Steady streaming ahead of a modulated solid-melt interface enhances solute transport, and modifies the stability boundaries of a planar front.
Relaxation of a three-level atom interacting with a thermostat and an external stochastic field
NASA Astrophysics Data System (ADS)
Mikhailov, Victor A.; Troshkin, Nikolay V.
2016-04-01
Relaxation of a three-level atom with non-equidistant spectrum interacting with a thermostat and an external stochastic field is studied. The master equation for the reduced density matrix and its solution in the first order of the perturbation theory are obtained. Using quantum regression theorem, explicit formulas for two-time correlation functions and shapes of radiation lines are derived for all types of three-level atoms and the following stochastic processes: a delta-correlated process and a Kubo-Anderson process. The influence of stochastic perturbations of atom's energy levels and damping constants of adjacent transitions on width of radiation lines is shown.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
Stochastic, weighted hit size theory of cellular radiobiological action
Bond, V.P.; Varma, M.N.
1982-01-01
A stochastic theory that appears to account well for the observed responses of cell populations exposed in radiation fields of different qualities and for different durations of exposure is described. The theory appears to explain well most cellular radiobiological phenomena observed in at least autonomous cell systems, argues for the use of fluence rate (phi) instead of absorbed dose for quantification of the amount of radiation involved in low level radiation exposure. With or without invoking the cell sensitivity function, the conceptual improvement would be substantial. The approach suggested also shows that the absorbed dose-cell response functions currently employed do not reflect the spectrum of cell sensitivities to increasing cell doses of a single agent, nor can RBE represent the potency ratio for different agents that can produce similar quantal responses. Thus, for accurate comparison of cell sensitivities among different cells in the same individual, or between the cells in different kinds of individuals, it is necessary to quantify cell sensitivity in terms of the hit size weighting or cell sensitivity function introduced here. Similarly, this function should be employed to evaluate the relative potency of radiation and other radiomimetic chemical or physical agents.
Integrating field production history in stochastic reservoir characterization
Vasco, D.W.; Long, J.C.S.; Datta-Gupta, A.
1996-12-31
This paper focuses on integrating field production history into reservoir characterization through stochastic inverse modeling. A key element of our approach is a three-dimensional streamline simulator which is orders of magnitude faster than traditional numerical simulators and thus, allows for rapid inversion of multiphase production data. Equiprobable permeability fields, conditioned to field production history, are then generated using simulated annealing. We also explore the spatial resolution associated with estimates of reservoir permeability variations derived using field production history. Based on techniques from geophysical inverse theory, we address such issues as data sensitivity, spatial resolution, averaging kernels and uncertainties associated with our estimates of reservoir permeability. The proposed inversion technique has been applied to synthetic as well as field cases. The synthetic example involves a sensitivity analysis of multiphase production history in heterogeneous five-spot and nine-spot patterns. The field example consists of production history from a five-spot pattern in the North Robertson Unit, a low permeability carbonate reservoir in West Texas. Water-cut history at the producers are used to estimate permeability variations in a two-layer (matrix-fracture) model of the reservoir. All computations were performed on a 125 MHz pentium with an average run time of about 4 wall-clock hours, indicating the feasibility of our approach.
A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type
Hosking, John Joseph Absalom
2012-12-15
We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.
NASA Astrophysics Data System (ADS)
Magnen, Jacques; Unterberger, Jérémie
2012-03-01
{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \\cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\\'evy area.
Multifractal vector fields and stochastic Clifford algebra
NASA Astrophysics Data System (ADS)
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Multifractal vector fields and stochastic Clifford algebra
Schertzer, Daniel Tchiguirinskaia, Ioulia
2015-12-15
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Multifractal vector fields and stochastic Clifford algebra.
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality. PMID:26723166
Multifractal vector fields and stochastic Clifford algebra.
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Pluralistic and stochastic gene regulation: examples, models and consistent theory
Salas, Elisa N.; Shu, Jiang; Cserhati, Matyas F.; Weeks, Donald P.; Ladunga, Istvan
2016-01-01
We present a theory of pluralistic and stochastic gene regulation. To bridge the gap between empirical studies and mathematical models, we integrate pre-existing observations with our meta-analyses of the ENCODE ChIP-Seq experiments. Earlier evidence includes fluctuations in levels, location, activity, and binding of transcription factors, variable DNA motifs, and bursts in gene expression. Stochastic regulation is also indicated by frequently subdued effects of knockout mutants of regulators, their evolutionary losses/gains and massive rewiring of regulatory sites. We report wide-spread pluralistic regulation in ≈800 000 tightly co-expressed pairs of diverse human genes. Typically, half of ≈50 observed regulators bind to both genes reproducibly, twice more than in independently expressed gene pairs. We also examine the largest set of co-expressed genes, which code for cytoplasmic ribosomal proteins. Numerous regulatory complexes are highly significant enriched in ribosomal genes compared to highly expressed non-ribosomal genes. We could not find any DNA-associated, strict sense master regulator. Despite major fluctuations in transcription factor binding, our machine learning model accurately predicted transcript levels using binding sites of 20+ regulators. Our pluralistic and stochastic theory is consistent with partially random binding patterns, redundancy, stochastic regulator binding, burst-like expression, degeneracy of binding motifs and massive regulatory rewiring during evolution. PMID:26823500
Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory.
Neuhauser, Daniel; Rabani, Eran; Cytter, Yael; Baer, Roi
2016-05-19
We develop a stochastic formulation of the optimally tuned range-separated hybrid density functional theory that enables significant reduction of the computational effort and scaling of the nonlocal exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham density functional theory, yet it provides a much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a self-consistent Hamiltonian that is central for additional postprocessing, for example, in the stochastic Bethe-Salpeter approach. PMID:26651840
Pluralistic and stochastic gene regulation: examples, models and consistent theory.
Salas, Elisa N; Shu, Jiang; Cserhati, Matyas F; Weeks, Donald P; Ladunga, Istvan
2016-06-01
We present a theory of pluralistic and stochastic gene regulation. To bridge the gap between empirical studies and mathematical models, we integrate pre-existing observations with our meta-analyses of the ENCODE ChIP-Seq experiments. Earlier evidence includes fluctuations in levels, location, activity, and binding of transcription factors, variable DNA motifs, and bursts in gene expression. Stochastic regulation is also indicated by frequently subdued effects of knockout mutants of regulators, their evolutionary losses/gains and massive rewiring of regulatory sites. We report wide-spread pluralistic regulation in ≈800 000 tightly co-expressed pairs of diverse human genes. Typically, half of ≈50 observed regulators bind to both genes reproducibly, twice more than in independently expressed gene pairs. We also examine the largest set of co-expressed genes, which code for cytoplasmic ribosomal proteins. Numerous regulatory complexes are highly significant enriched in ribosomal genes compared to highly expressed non-ribosomal genes. We could not find any DNA-associated, strict sense master regulator. Despite major fluctuations in transcription factor binding, our machine learning model accurately predicted transcript levels using binding sites of 20+ regulators. Our pluralistic and stochastic theory is consistent with partially random binding patterns, redundancy, stochastic regulator binding, burst-like expression, degeneracy of binding motifs and massive regulatory rewiring during evolution.
Coherent stochastic resonance in the presence of a field
NASA Astrophysics Data System (ADS)
Gitterman, Moshe; Weiss, George H.
1995-11-01
A recent paper by Bulsara, Lowen, and Rees [Phys. Rev. E 49, 4989 (1994)] presents a perturbation analysis of coherent stochastic resonance in a half-space in the presence of a field. We believe that the analysis there was flawed due to an improper use of the method of images and that a correct version of a perturbation analysis can be given by using a transformation of the underlying equations. The result still exhibits stochastic resonance.
Stochastic resonance-a nonlinear control theory interpretation
NASA Astrophysics Data System (ADS)
Repperger, D. W.; Farris, K. A.
2010-07-01
Stochastic resonance (SR) is an effect that has been known (Benzi, R., Sutera, A., and Vulpiani, A. (1981), 'The Mechanism of Stochastic Resonance', Journal of Physics, A14, L453-L457) for almost three decades and has been extensively studied in biology, statistics, signal processing and in numerous other eclectic areas (Wiesenfeld, K., and Moss, F. (1995), 'Stochastic Resonance and the Benefits of Noise: From Ice Ages to Crayfish and Squids', Nature, 373, 33-36). Herein, a nonlinear control theory analysis is conducted on how to better understand the class of systems that may exhibit the SR effect. Using nonlinear control theory methods, equilibrium points are manipulated to create the SR response (similar to shaping dynamical response in a phase plane). From this approach, a means of synthesising and designing the appropriate class of nonlinear systems is introduced. New types of nonlinear dynamics that demonstrate the SR effects are discovered, which may have utility in control theory as well as in many diverse applications. A numerical simulation illustrates some powerful attributes of these systems.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
NASA Astrophysics Data System (ADS)
You, Setthivoine
2015-11-01
A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.
Extended conformal field theories
NASA Astrophysics Data System (ADS)
Taormina, Anne
1990-08-01
Some extended conformal field theories are briefly reviewed. They illustrate how non minimal models of the Virasoro algebra (c≥1) can become minimal with respect to a larger algebra. The accent is put on N-extended superconformal algebras, which are relevant in superstring compactification.
Kinetic theory of age-structured stochastic birth-death processes.
Greenman, Chris D; Chou, Tom
2016-01-01
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.
Kinetic theory of age-structured stochastic birth-death processes
NASA Astrophysics Data System (ADS)
Greenman, Chris D.; Chou, Tom
2016-01-01
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.
Kinetic theory of age-structured stochastic birth-death processes.
Greenman, Chris D; Chou, Tom
2016-01-01
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution. PMID:26871029
Applications of queueing theory to stochastic models of gene expression
NASA Astrophysics Data System (ADS)
Kulkarni, Rahul
2012-02-01
The intrinsic stochasticity of cellular processes implies that analysis of fluctuations (`noise') is often essential for quantitative modeling of gene expression. Recent single-cell experiments have carried out such analysis to characterize moments and entire probability distributions for quantities of interest, e.g. mRNA and protein levels across a population of cells. Correspondingly, there is a need to develop general analytical tools for modeling and interpretation of data obtained from such single-cell experiments. One such approach involves the mapping between models of stochastic gene expression and systems analyzed in queueing theory. The talk will provide an overview of this approach and discuss how theorems from queueing theory (e.g. Little's Law) can be used to derive exact results for general stochastic models of gene expression. In the limit that gene expression occurs in bursts, analytical results can be obtained which provide insight into the effects of different regulatory mechanisms on the noise in protein steady-state distributions. In particular, the approach can be used to analyze the effect of post-transcriptional regulation by non-coding RNAs leading to new insights and experimentally testable predictions.
Sublinear scaling for time-dependent stochastic density functional theory
Gao, Yi; Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2015-01-21
A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (≈16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.
Electron heat transport from stochastic fields in gyrokinetic simulations
Wang, E.; Nevins, W. M.; Candy, J.; Hatch, D.; Terry, P.; Guttenfelder, W.
2011-05-15
GYRO is used to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as {beta}{sub e} is varied from 0.1% to 0.7%, as investigated by J. Candy [Phys. Plasmas 12, 072307 (2005)]. Poincare surface of section plots obtained from integrating the self-consistent magnetic field demonstrates widespread stochasticity for all nonzero values of {beta}{sub e}. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. The magnetic diffusion, d{sub m}[A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett 40, 38 (1978)], is used to quantify the degree of stochasticity and related to the electron heat transport for hundreds of time slices in each simulation.
Electron heat transport from stochastic fields in gyrokinetic simulationsa)
NASA Astrophysics Data System (ADS)
Wang, E.; Nevins, W. M.; Candy, J.; Hatch, D.; Terry, P.; Guttenfelder, W.
2011-05-01
GYRO is used to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as βe is varied from 0.1% to 0.7%, as investigated by J. Candy [Phys. Plasmas 12, 072307 (2005)]. Poincare surface of section plots obtained from integrating the self-consistent magnetic field demonstrates widespread stochasticity for all nonzero values of βe. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. The magnetic diffusion, dm [A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett 40, 38 (1978)], is used to quantify the degree of stochasticity and related to the electron heat transport for hundreds of time slices in each simulation.
Holographic effective field theories
NASA Astrophysics Data System (ADS)
Martucci, Luca; Zaffaroni, Alberto
2016-06-01
We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.
A cavitation model based on Eulerian stochastic fields
NASA Astrophysics Data System (ADS)
Magagnato, F.; Dumond, J.
2013-12-01
Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Explore Stochastic Instabilities of Periodic Points by Transition Path Theory
NASA Astrophysics Data System (ADS)
Cao, Yu; Lin, Ling; Zhou, Xiang
2016-06-01
We consider the noise-induced transitions from a linearly stable periodic orbit consisting of T periodic points in randomly perturbed discrete logistic map. Traditional large deviation theory and asymptotic analysis at small noise limit cannot distinguish the quantitative difference in noise-induced stochastic instabilities among the T periodic points. To attack this problem, we generalize the transition path theory to the discrete-time continuous-space stochastic process. In our first criterion to quantify the relative instability among T periodic points, we use the distribution of the last passage location related to the transitions from the whole periodic orbit to a prescribed disjoint set. This distribution is related to individual contributions to the transition rate from each periodic points. The second criterion is based on the competency of the transition paths associated with each periodic point. Both criteria utilize the reactive probability current in the transition path theory. Our numerical results for the logistic map reveal the transition mechanism of escaping from the stable periodic orbit and identify which periodic point is more prone to lose stability so as to make successful transitions under random perturbations.
Simulation of magnetic field line stochasticity at the magnetopause
NASA Technical Reports Server (NTRS)
Wang, Zhi; Ashour-Abdalla, Maha
1994-01-01
We have conducted a three-dimensional particle simulation to study the magnetic field line stochasticity at the magnetopause current layer. Our results show that the magnetic field lines become stochastic due to the overlap of the destabilized multiple tearing mode islands, which agrees with the percolation model suggested by Galeev et al. (1986). After the field lines become stochastic, these tearing modes grow even 2-3 times faster than in the linear stage and saturate at an amplitude level 3-4 times bigger than the single tearing mode without mode-mode coupling. The field line stochasticity also causes a strong particle diffusion across the current layer. The diffusion coefficient reaches to 10(exp 9) sq m/s for typical magnetopause parameters. Associated with the particle diffusion, the current layer becomes broader in width. As a result, the magnetic energy is dissipated into particle energy by heating parallel to the local magnetic field. The particle energy increases by 60%, while the magnetic helicity, which has always been regarded as a good invariant, changes by 20%.
Stochastical modeling for Viral Disease: Statistical Mechanics and Network Theory
NASA Astrophysics Data System (ADS)
Zhou, Hao; Deem, Michael
2007-04-01
Theoretical methods of statistical mechanics are developed and applied to study the immunological response against viral disease, such as dengue. We use this theory to show how the immune response to four different dengue serotypes may be sculpted. It is the ability of avian influenza, to change and to mix, that has given rise to the fear of a new human flu pandemic. Here we propose to utilize a scale free network based stochastic model to investigate the mitigation strategies and analyze the risk.
Beyond mean field theory: statistical field theory for neural networks
Buice, Michael A; Chow, Carson C
2014-01-01
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
NASA Astrophysics Data System (ADS)
Ginzburg, V. B.
1996-09-01
A toroidal spiral field is introduced that propagates around all the objects in the universe. The nature of this field can be either gravitational or electrostatic or magnetic, and it governs the motion of the objects as well as the forces that act upon them. The topology of the toroidal spiral field is obtained when the Bertrami vortex comprised of two helical fluxes of opposite vorticity is curved into a circle. The main parameter that defines the geometry of the toroidal spiral field is the inversion radius of a sphere at which the toroidal fluxes of opposite vorticity meet. The inversion sphere is the border surface at which the matter converts into anti-matter, and at which the law of physics are inverted. The theory covers the problem of two objects orbiting each other with possible sizes ranging from an elementary particle to a black hole and to a galaxy. The equations obtained define the radii of the stationary quantum orbits which can be applied to a structure of the hydrogen atom, including its nucleus, as well as to a structure of a planetary system and a black hole. They also establish the relativistic relationships for the gravitational and inertial masses as well as for the electrical charge which are quite different than those proposed by Lorentz.
Effect of stochasticity in mean field dynamo models
Newton, Andrew P. L.; Kim, Eun-Jin
2012-07-15
We present a comprehensive investigation into the effect of choosing the stochastic control parameters in a simplified-Parker dynamo model. Through considering the manifold of marginal stability, i.e., the region of parameter space where the mean growth rate is zero, we show that stochastic fluctuations are not prohibitive to dynamo. Furthermore, by directly comparing results obtained by periodic and Gaussian coloured noise alpha with identical characteristic time-scales and fluctuating amplitudes, we find that the transition to dynamo is significantly eased for stochastically fluctuating alpha. The effect of stochasticity in magnetic diffusion is also investigated, highlighting the importance of resonance between poloidal and toroidal magnetic fields on the growth rate. Furthermore, we show that probability density functions of the growth-rate, magnetic field, and magnetic energy can provide a wealth of useful information regarding the dynamo behaviour/intermittency. Finally, the statistical properties of the dynamo such as temporal correlation and fluctuating amplitude are found to be dependent on the distribution of the fluctuations in stocastic parameters.
A stochastic perturbation theory for non-autonomous systems
Moon, W.; Wettlaufer, J. S.
2013-12-15
We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF{sub 0}. The deterministic model, developed by Eisenman and Wettlaufer [“Nonlinear threshold behavior during the loss of Arctic sea ice,” Proc. Natl. Acad. Sci. U.S.A. 106(1), 28–32 (2009)] exhibits several transitions as ΔF{sub 0} increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
Full particle orbit effects in regular and stochastic magnetic fields
NASA Astrophysics Data System (ADS)
Ogawa, Shun; Cambon, Benjamin; Leoncini, Xavier; Vittot, Michel; del Castillo-Negrete, Diego; Dif-Pradalier, Guilhem; Garbet, Xavier
2016-07-01
We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the
Stochastic queueing-theory approach to human dynamics
NASA Astrophysics Data System (ADS)
Walraevens, Joris; Demoor, Thomas; Maertens, Tom; Bruneel, Herwig
2012-02-01
Recently, numerous studies have shown that human dynamics cannot be described accurately by exponential laws. For instance, Barabási [Nature (London)NATUAS0028-083610.1038/nature03459 435, 207 (2005)] demonstrates that waiting times of tasks to be performed by a human are more suitably modeled by power laws. He presumes that these power laws are caused by a priority selection mechanism among the tasks. Priority models are well-developed in queueing theory (e.g., for telecommunication applications), and this paper demonstrates the (quasi-)immediate applicability of such a stochastic priority model to human dynamics. By calculating generating functions and by studying them in their dominant singularity, we prove that nonexponential tails result naturally. Contrary to popular belief, however, these are not necessarily triggered by the priority selection mechanism.
Optomechanically induced stochastic resonance and chaos transfer between optical fields
NASA Astrophysics Data System (ADS)
Monifi, Faraz; Zhang, Jing; Özdemir, Şahin Kaya; Peng, Bo; Liu, Yu-Xi; Bo, Fang; Nori, Franco; Yang, Lan
2016-06-01
Chaotic dynamics has been reported in many physical systems and has affected almost every field of science. Chaos involves hypersensitivity to the initial conditions of a system and introduces unpredictability into its output. Thus, it is often unwanted. Interestingly, the very same features make chaos a powerful tool to suppress decoherence, achieve secure communication and replace background noise in stochastic resonance—a counterintuitive concept that a system's ability to transfer information can be coherently amplified by adding noise. Here, we report the first demonstration of chaos-induced stochastic resonance in an optomechanical system, as well as the optomechanically mediated chaos transfer between two optical fields such that they follow the same route to chaos. These results will contribute to the understanding of nonlinear phenomena and chaos in optomechanical systems, and may find applications in the chaotic transfer of information and for improving the detection of otherwise undetectable signals in optomechanical systems.
Flow damping due to stochastization of the magnetic field
Ida, K.; Yoshinuma, M.; Tsuchiya, H.; Kobayashi, T.; Suzuki, C.; Yokoyama, M.; Shimizu, A.; Nagaoka, K.; Inagaki, S.; Itoh, K.; Akiyama, T.; Emoto, M.; Evans, T.; Dinklage, A.; Du, X.; Fujii, K.; Goto, M.; Goto, T.; Hasuo, M.; Hidalgo, C.; Ichiguchi, K.; Ishizawa, A.; Jakubowski, M.; Kamiya, K.; Kasahara, H.; Kawamura, G.; Kato, D.; Kobayashi, M.; Morita, S.; Mukai, K.; Murakami, I.; Murakami, S.; Narushima, Y.; Nunami, M.; Ohdach, S.; Ohno, N.; Osakabe, M.; Pablant, N.; Sakakibara, S.; Seki, T.; Shimozuma, T.; Shoji, M.; Sudo, S.; Tanaka, K.; Tokuzawa, T.; Todo, Y.; Wang, H.; Yamada, H.; Takeiri, Y.; Mutoh, T.; Imagawa, S.; Mito, T.; Nagayama, Y.; Watanabe, K. Y.; Ashikawa, N.; Chikaraishi, H.; Ejiri, A.; Furukawa, M.; Fujita, T.; Hamaguchi, S.; Igami, H.; Isobe, M.; Masuzaki, S.; Morisaki, T.; Motojima, G.; Nagasaki, K.; Nakano, H.; Oya, Y.; Suzuki, Y.; Sakamoto, R.; Sakamoto, M.; Sanpei, A.; Takahashi, H.; Tokitani, M.; Ueda, Y.; Yoshimura, Y.; Yamamoto, S.; Nishimura, K.; Sugama, H.; Yamamoto, T.; Idei, H.; Isayama, A.; Kitajima, S.; Masamune, S.; Shinohara, K.; Bawankar, P. S.; Bernard, E.; von Berkel, M.; Funaba, H.; Huang, X. L.; Ii, T.; Ido, T.; Ikeda, K.; Kamio, S.; Kumazawa, R.; Moon, C.; Muto, S.; Miyazawa, J.; Ming, T.; Nakamura, Y.; Nishimura, S.; Ogawa, K.; Ozaki, T.; Oishi, T.; Ohno, M.; Pandya, S.; Seki, R.; Sano, R.; Saito, K.; Sakaue, H.; Takemura, Y.; Tsumori, K.; Tamura, N.; Tanaka, H.; Toi, K.; Wieland, B.; Yamada, I.; Yasuhara, R.; Zhang, H.; Kaneko, O.; Komori, A.
2015-01-01
The driving and damping mechanism of plasma flow is an important issue because flow shear has a significant impact on turbulence in a plasma, which determines the transport in the magnetized plasma. Here we report clear evidence of the flow damping due to stochastization of the magnetic field. Abrupt damping of the toroidal flow associated with a transition from a nested magnetic flux surface to a stochastic magnetic field is observed when the magnetic shear at the rational surface decreases to 0.5 in the large helical device. This flow damping and resulting profile flattening are much stronger than expected from the Rechester–Rosenbluth model. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. This observation suggests that the flow damping is due to the change in the non-diffusive term of momentum transport. PMID:25569268
A study of full particle orbit effects in stochastic magnetic fields
NASA Astrophysics Data System (ADS)
Ogawa, Shun; Cambon, Benjamin; Leoncini, Xavier; Del-Castillo Negrete, Diego; Vittot, Michel; Dif-Pradalier, Guilhem; Garbet, Xavier
2015-11-01
Full orbit effects of charged particle motion in a stochastic magnetic field are investigated. Particles move following the Lorentz force in a prescribed static magnetic field with no electric field in a cylinder with periodic boundary condition. The magnetic field model consists of the perturbation of equilibrium fields with monotonic and reversed shear q-profiles. Unlike the gyrokinetic theory, the adiabatic invariance of the magnetic momentum is not assumed, and the full Hamiltonian equations of motion are numerically integrated by using a symplectic method. Contrary to the simpler case of magnetic field line tracing, the dynamical properties of full orbit is not easily straightforward. To address this issue, we propose a method to construct reduced Poincaré plots from the full particle trajectory in three-dimensional space. This diagnostic is used to clarify the nontrivial relationship between the integrability and stochasticity of field lines and particle orbits. A problem of particular interest is the study of finite Larmor radius effects on the stochasticity and the topology of orbits.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
NASA Astrophysics Data System (ADS)
Hermes, Matthew R.; Hirata, So
2014-08-01
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm-1 and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
Hermes, Matthew R.; Hirata, So
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Stochastic Mean-Field Dynamics For Nuclear Collisions
Ayik, Sakir
2008-11-11
We discuss a stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. For small amplitude fluctuations, this approach gives a result for the dispersion of a one-body observable that is identical to the result obtained previously through a variational approach. Furthermore, it incorporates one-body dissipation and fluctuation mechanisms in accordance with quantal fluctuation-dissipation relation.
Unification Theory of Optimal Life Histories and Linear Demographic Models in Internal Stochasticity
Oizumi, Ryo
2014-01-01
Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of “Stochastic Control Theory” in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path–integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models. PMID:24945258
Matrix models and stochastic growth in Donaldson-Thomas theory
NASA Astrophysics Data System (ADS)
Szabo, Richard J.; Tierz, Miguel
2012-10-01
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
NASA Technical Reports Server (NTRS)
Huang, Dong; Knyazikhin, Yuri; Wang, Weile; Deering, Donald W,; Stenberg, Pauline; Shabanov, Nikolay; Tan, Bin; Myneni, Ranga B.
2008-01-01
Radiation reflected from vegetation canopies exhibits high spatial variation. Satellite-borne sensors measure the mean intensities emanating from heterogeneous vegetated pixels. The theory of radiative transfer in stochastic media provides the most logical linkage between satellite observations and the three-dimensional canopy structure through a closed system of simple equations which contains the mean intensity and higher statistical moments directly as its unknowns. Although this theory has been a highly active research field in recent years, its potential for satellite remote sensing of vegetated surfaces has not been fully realized because of the lack of models of a canopy pair-correlation function that the stochastic radiative transfer equations require. The pair correlation function is defined as the probability of finding simultaneously phytoelements at two points. This paper presents analytical and Monte Carlo generated pair correlation functions. Theoretical and numerical analyses show that the spatial correlation between phytoelements is primarily responsible for the effects of the three-dimensional canopy structure on canopy reflective and absorptive properties. The pair correlation function, therefore, is the most natural and physically meaningful measure of the canopy structure over a wide range of scales. The stochastic radiative transfer equations naturally admit this measure and thus provide a powerful means to investigate the three-dimensional canopy structure from space. Canopy reflectances predicted by the stochastic equations are assessed by comparisons with the PARABOLA measurements from coniferous and broadleaf forest stands in the BOREAS Southern Study Areas. The pair correlation functions are derived from data on tree structural parameters collected during field campaigns conducted at these sites. The simulated canopy reflectances compare well with the PARABOLA data.
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Simulation of underground gravity gradients from stochastic seismic fields
Harms, Jan; Dorsher, Steven; Mandic, Vuk; DeSalvo, Riccardo
2009-12-15
We present results obtained from a finite-element simulation of seismic displacement fields and of gravity gradients generated by those fields. The displacement field is constructed by a plane-wave model with a 3D isotropic stochastic field and a 2D fundamental Rayleigh field. The plane-wave model provides an accurate representation of stationary fields from distant sources. Underground gravity gradients are calculated as the acceleration of a free test mass inside a cavity. The results are discussed in the context of gravity-gradient noise subtraction in third generation gravitational-wave detectors. Error analysis with respect to the density of the simulated grid leads to a derivation of an improved seismometer placement inside a 3D array which would be used in practice to monitor the seismic field.
Stochastic Definitions of Planck and Boltzmann Constants and Quantum Theory of Gravitation
NASA Astrophysics Data System (ADS)
Sohrab, S. H.
2001-04-01
Physical space is identified as a tachyonic fluid that is Dirac's "stochastic ether" or de Broglie's "hidden thermostat", and is described in terms of stochastic definitions of Planck h=m_k<λ_k>c and Boltzmann k=m_k<ν_k>c constants leading to photon gravitational mass m_k=(hk/c^3)^1/2 and Avogadro number N^o = 1/(hkc)^1/2. The finite pressure of vacuum is P_kV=N^okT_k=1 where T_k=<λ_k>= 0.11935 K, and pressures of matter Pm and anti-matter Pa fields lie in the range from black-hole P=∞ to white-hole P=0 singularities 0
A field test of a simple stochastic radiative transfer model
Byrne, N.
1995-09-01
The problem of determining the effect of clouds on the radiative energy balance of the globe is of well-recognized importance. One can in principle solve the problem for any given configuration of clouds using numerical techniques. This knowledge is not useful however, because of the amount of input data and computer resources required. Besides, we need only the average of the resulting solution over the grid scale of a general circulation model (GCM). Therefore, we are interested in estimating the average of the solutions of such fine-grained problems using only coarse grained data, a science or art called stochastic radiation transfer. Results of the described field test indicate that the stochastic description is a somewhat better fit to the data than is a fractional cloud cover model, but more data are needed. 1 ref., 3 figs.
Two stochastic mean-field polycrystal plasticity methods
Tonks, Michael
2008-01-01
In this work, we develop two mean-field polycrystal plasticity models in which the L{sup c} are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the L{sup c} tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the STM and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates D{sup c} are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the FCM, and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.
Stochastic cooling of bunched beams from fluctuation and kinetic theory
Chattopadhyay, S.
1982-09-01
A theoretical formalism for stochastic phase-space cooling of bunched beams in storage rings is developed on the dual basis of classical fluctuation theory and kinetic theory of many-body systems in phase-space. The physics is that of a collection of three-dimensional oscillators coupled via retarded nonconservative interactions determined by an electronic feedback loop. At the heart of the formulation is the existence of several disparate time-scales characterizing the cooling process. Both theoretical approaches describe the cooling process in the form of a Fokker-Planck transport equation in phase-space valid up to second order in the strength and first order in the auto-correlation of the cooling signal. With neglect of the collective correlations induced by the feedback loop, identical expressions are obtained in both cases for the coherent damping and Schottky noise diffusion coefficients. These are expressed in terms of Fourier coefficients in a harmonic decomposition in angle of the generalized nonconservative cooling force written in canonical action-angle variables of the particles in six-dimensional phase-space. Comparison of analytic results to a numerical simulation study with 90 pseudo-particles in a model cooling system is presented.
Stochastic theory of quantum vortex on a sphere.
Kuratsuji, Hiroshi
2012-03-01
A stochastic theory is presented for a quantum vortex in superfluid films coated on a two-dimensional sphere S^{2}. The starting point is the canonical equation of motion (Kirchhoff equation) for a point vortex, which is derived using the time-dependent Landau-Ginzburg theory. The vortex equation, which is equivalent to the spin equation, turns out to be the Langevin equation in presence of random forces. This is converted to the Fokker-Planck (FP) equation for the distribution function of a point vortex by using a functional integral technique. The FP equation is analyzed with special emphasis on the role of the pinning potential. By considering a typical form of the pinning potential, we address two problems: (i) The one is concerning an interplay between strength of the pinning potential and effective temperature, which discriminates the weak and strong coupling scheme to determine the solutions of the FP equation. (ii) The other is concerning a small diffusion limit, for which an asymptotic analysis is given using the functional integral to lead a compact expression of the distribution function. An extension to the vortex in nonspherical geometry is briefly discussed for the case of vortex on a plane and a pseudosphere.
On collisional diffusion in a stochastic magnetic field
Abdullaev, S. S.
2013-08-15
The effect of particle collisions on the transport in a stochastic magnetic field in tokamaks is investigated. The model of resonant magnetic perturbations generated by external coils at the plasma edge is used for the stochastic magnetic field. The particle collisions are simulated by a random walk process along the magnetic field lines and the jumps across the field lines at the collision instants. The dependencies of the local diffusion coefficients on the mean free path λ{sub mfp}, the diffusion coefficients of field lines D{sub FL}, and the collisional diffusion coefficients, χ{sub ⊥} are studied. Based on these numerical data and the heuristic arguments, the empirical formula, D{sub r}=χ{sub ⊥}+v{sub ||}D{sub FL}/(1+L{sub c}/λ{sub mfp}), for the local diffusion coefficient is proposed, where L{sub c} is the characteristic length of order of the connection length l{sub c}=πqR{sub 0}, q is the safety factor, R{sub 0} is the major radius. The formula quite well describes the results of numerical simulations. In the limiting cases, the formula describes the Rechester-Rosenbluth and Laval scalings.
Dyons in topological field theories
NASA Astrophysics Data System (ADS)
Temple-Raston, M.
1991-10-01
We examine a class of topological field theories defined by Lagrangians that under certain conditions can be written as the sum of two characteristic numbers or winding numbers. Therefore, the action or the energy is a topological invariant and stable under perturbations. The sufficient conditions required for stability take the form of first-order field equations, analogous to the self-duality and Bogomol'nyi equations in Yang-Mills(-Higgs) theory. Solutions to the first-order equations automatically satisfy the full field equations. We show the existence of nontrivial, nonsingular, minimum energy spherically symmetric dyon solutions and that they are stable. We also discuss evidence for a dual field theory to Yang-Mills-Higgs in topological field theory. The existence of dual field theories and electric monopoles is predicted by Montonen and Olive.
NASA Astrophysics Data System (ADS)
Kwak, Seung Ki
The existence of momentum and winding modes of closed string on a torus leads to a natural idea that the field theoretical approach of string theory should involve winding type coordinates as well as the usual space-time coordinates. Recently developed double field theory is motivated from this idea and it implements T-duality manifestly by doubling the coordinates. In this thesis we will mainly focus on the double field theory formulation of different string theories in its low energy limit: bosonic, heterotic, type II and its massive extensions, and N = 1 supergravity theory. In chapter 2 of the thesis we study the equivalence of different formulations of double field theory. There are three different formulations of double field theory: background field E formulation, generalized metric H formulation, and frame field EAM formulation. Starting from the frame field formalism and choosing an appropriate gauge, the equivalence of the three formulations of bosonic theory are explicitly verified. In chapter 3 we construct the double field theory formulation of heterotic strings. The global symmetry enlarges to O( D, D + n) for heterotic strings and the enlarged generalized metric features this symmetry. The structural form of bosonic theory can directly be applied to the heterotic theory with the enlarged generalized metric. In chapter 4 we develop a unified framework of double field theory for type II theories. The Ramond-Ramond potentials fit into spinor representations of the duality group O( D, D) and the theory displays Spin+( D, D) symmetry with its self-duality relation. For a specific form of RR 1-form the theory reduces to the massive deformation of type IIA theory due to Romans. In chapter 5 we formulate the N = 1 supersymmetric extension of double field theory including the coupling to n abelian vector multiplets. This theory features a local O(1, 9 + n) x O(1, 9) tangent space symmetry under which the fermions transform. (Copies available exclusively from
Incorporation of generalized uncertainty principle into Lifshitz field theories
Faizal, Mir; Majumder, Barun
2015-06-15
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
Energy-Conservation Constraint in Stochastic Structural Stability Theory
NASA Astrophysics Data System (ADS)
Parker, J. B.; Krommes, J. A.
2011-10-01
The stochastic structural stability theory (SSST) is a technique, originally developed in the neutral-fluids community, that can be used for understanding the statistical behavior of drift-wave-zonal-flow (DW-ZF) systems. The technique involves parameterizing the nonlinear DW-DW interactions as white noise while keeping the correct behavior of the DW-ZF interactions. The SSST equations describe the dynamics of the zonal flow and the quadratic statistics of the drift waves, which are then simulated numerically. The SSST has been applied to the Modified Hasegawa-Wakatani system recently, and it has been demonstrated that the SSST equations exhibit ZF emergence. However, that work did not perform the DW-DW parameterization in a manner consistent with energy conservation. Here we apply the SSST to the Modified Hasegawa-Wakatani system while demanding that conservation of energy be satisfied. Preliminary results on how the energy-conservation constraint affects the dynamics of the SSST system will be reported. Work supported by U.S. DOE Contract No. DE-AC02-09CH11466 and by a U.S. DOE FES Fellowship.
Stochastic resonance in ion channels characterized by information theory.
Goychuk, I; Hänggi, P
2000-04-01
We identify a unifying measure for stochastic resonance (SR) in voltage dependent ion channels which comprises periodic (conventional), aperiodic, and nonstationary SR. Within a simplest setting, the gating dynamics is governed by two-state conductance fluctuations, which switch at random time points between two values. The corresponding continuous time point process is analyzed by virtue of information theory. In pursuing this goal we evaluate for our dynamics the tau information, the mutual information, and the rate of information gain. As a main result we find an analytical formula for the rate of information gain that solely involves the probability of the two channel states and their noise averaged rates. For small voltage signals it simplifies to a handy expression. Our findings are applied to study SR in a potassium channel. We find that SR occurs only when the closed state is predominantly dwelled upon. Upon increasing the probability for the open channel state the application of an extra dose of noise monotonically deteriorates the rate of information gain, i.e., no SR behavior occurs.
NASA Technical Reports Server (NTRS)
Robinson, P. A.; Cairns, I. H.; Gurnett, D. A.
1993-01-01
Detailed comparisons are made between the Langmuir-wave properties predicted by the recently developed stochastic-growth theory of type III sources and those observed by the plasma wave experiment on ISEE 3, after correcting for the main instrumental and selection effects. Analysis of the observed field-strength distribution confirms the theoretically predicted form and implies that wave growth fluctuates both spatially and temporally in sign and magnitude, leading to an extremely clumpy distribution of fields. A cutoff in the field-strength distribution is seen at a few mV/m, corresponding to saturation via nonlinear effects. Analysis of the size distribution of Langmuir clumps yields results in accord with those obtained in earlier work and with the size distribution of ambient density fluctuations in the solar wind. This confirms that the inhomogeneities in the Langmuir growth rate are determined by the density fluctuations and that these fluctuations persist during type III events.
Stochastic acceleration of charged particle in nonlinear wave field
NASA Astrophysics Data System (ADS)
He, Kaifen
2003-04-01
Possibility of stochastic acceleration of charged particle by nonlinear waves is investigated. Spatially regular (SR) and spatiotemporal chaotic (STC) wave solutions evolving from saddle steady wave are tested as the fields. In the non-steady SR field the particle is finally trapped by the wave and averagely gains its group velocity, while in the STC field the particle motion displays trapped-free phases with its averaged velocity larger or smaller than the group velocity depending on the charge sign. A simplified model is established to investigate the acceleration mechanism. By analogy with motor protein, it is found that the virtual pattern of saddle steady wave plays a role of asymmetric potential, which and the nonlinear varying perturbation wave are the two sufficient ingredients for the acceleration in our case.
Stochastic inflation in a simple two-field model
Mollerach, S. ); Matarrese, S. ); Ortolan, A. ); Lucchin, F. )
1991-09-15
The dynamics of a nondominating scalar field during inflation is considered in the framework of the stochastic approach where its motion and that of the inflaton are described by two coupled Langevin equations. Curvature perturbations induced by the inflaton make the problem that of a Brownian motion in a random medium. The associated Fokker-Planck equation is solved for a free massless field in a power-law inflation driven by an inflaton with an exponential potential: this simple model could describe the dynamics of the axion, or any other pseudoGoldstone boson, during inflation. In spite of being free, the field shows a highly non-Gaussian behavior on scales much larger than the present horizon; on observable scales it gives rise to isocurvature perturbations which are both essentially Gaussian and scale-free.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
Introduction to Statistical Field Theory
NASA Astrophysics Data System (ADS)
Brézin, Edouard
2010-07-01
1. A few well-known basic results; 2. Introduction: order parameters, broken symmetries; 3. Examples of physical situations modelled by the Ising model; 4. A few results about the Ising model; 5. High temperature and low temperature expansions; 6. Some geometric problems related to phase transitions; 7. Phenomenological description of the critical behaviour; 8. Mean field theory; 9. Beyond mean field theory; 10. Introduction to the renormalization group; 11. Renormalization group for the φ4 theory; 12. Renormalized theory; 13. Goldstone modes; 14. Large n; Index.
First Test of Stochastic Growth Theory for Langmuir Waves in Earth's Foreshock
NASA Technical Reports Server (NTRS)
Cairns, Iver H.; Robinson, P. A.
1997-01-01
This paper presents the first test of whether stochastic growth theory (SGT) can explain the detailed characteristics of Langmuir-like waves in Earth's foreshock. A period with unusually constant solar wind magnetic field is analyzed. The observed distributions P(logE) of wave fields E for two intervals with relatively constant spacecraft location (DIFF) are shown to agree well with the fundamental prediction of SGT, that P(logE) is Gaussian in log E. This stochastic growth can be accounted for semi-quantitatively in terms of standard foreshock beam parameters and a model developed for interplanetary type III bursts. Averaged over the entire period with large variations in DIFF, the P(logE) distribution is a power-law with index approximately -1; this is interpreted in terms of convolution of intrinsic, spatially varying P(logE) distributions with a probability function describing ISEE's residence time at a given DIFF. Wave data from this interval thus provide good observational evidence that SGT can sometimes explain the clumping, burstiness, persistence, and highly variable fields of the foreshock Langmuir-like waves.
Status of dual control theory. [stochastic decision making
NASA Technical Reports Server (NTRS)
Tse, E.
1975-01-01
Theoretical studies of decision making and stochastic processes are discussed. Several approaches are described for an improved performing control method. It is shown that control performance is highly dependent on the knowledge of the unknown parameters in the system.
The Theory of Conceptual Fields
ERIC Educational Resources Information Center
Vergnaud, Gerard
2009-01-01
The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…
Double field theory inspired cosmology
Wu, Houwen; Yang, Haitang E-mail: hyanga@scu.edu.cn
2014-07-01
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that double field theory provides a more consistent way to construct cosmological solutions than the standard string cosmology. We construct solutions for vanishing and non-vanishing symmetry preserving dilaton potentials. The solutions assemble the pre- and post-big bang evolutions in one single line element. Our results show a smooth evolution from an anisotropic early stage to an isotropic phase without any special initial conditions in contrast to previous models. In addition, we demonstrate that the contraction of the dual space automatically leads to both an inflation phase and a decelerated expansion of the ordinary space during different evolution stages.
String theory in electromagnetic fields
NASA Astrophysics Data System (ADS)
Ambjørn, Jan; Makeenko, Yuri M.; Semenoff, Gordon W.; Szabo, Richard J.
2003-02-01
A review of various aspects of superstrings in background electromagnetic fields is presented. Topics covered include the Born-Infeld action, spectrum of open strings in background gauge fields, the Schwinger mechanism, finite-temperature formalism and Hagedorn behaviour in external fields, Debye screening, D-brane scattering, thermodynamics of D-branes, and noncommutative field and string theories on D-branes. The electric field instabilities are emphasized throughout and contrasted with the case of magnetic fields. A new derivation of the velocity-dependent potential between moving D-branes is presented, as is a new result for the velocity corrections to the one-loop thermal effective potential.
Geometer energy unified field theory
NASA Astrophysics Data System (ADS)
Rivera, Susana; Rivera, Anacleto
GEOMETER - ENERGY UNIFIED FIELD THEORY Author: Anacleto Rivera Nivón Co-author: Susana Rivera Cabrera This work is an attempt to find the relationship between the Electromagnetic Field and the Gravitational Field. Despite it is based on the existence of Strings of Energy, it is not the same kind of strings that appears on other theories like Superstring Theory, Branas Theory, M - Theory, or any other related string theories. Here, the Strings are concentrated energy lines that vibrates, and experiences shrinking and elongations, absorbing and yielding on each contraction and expansion all that is found in the Universe: matter and antimatter, waves and energy in all manifestations. In contrast to superstring theory, which strings are on the range of the Length of Planck, these Strings can be on the cosmological size, and can contain many galaxies, or clusters, or groups of galaxies; but also they can reach as small sizes as subatomic levels. Besides, and contrary to what it is stated in some other string theories that need the existence of ten or more dimensions, the present proposal sustains in only four particular dimensions. It has been developed a mathematical support that will try to help to improve the understanding of the phenomena that take place at the Universe.
Nonlocal and quasilocal field theories
NASA Astrophysics Data System (ADS)
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi
2016-01-01
Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity. PMID:27336169
Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi
2016-01-01
Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity. PMID:27336169
Fluid Stochastic Petri Nets: Theory, Applications, and Solution
NASA Technical Reports Server (NTRS)
Horton, Graham; Kulkarni, Vidyadhar G.; Nicol, David M.; Trivedi, Kishor S.
1996-01-01
In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.
Rapid Change of Field Line Connectivity and Reconnection in Stochastic Magnetic Fields
NASA Astrophysics Data System (ADS)
Huang, Y. M.; Bhattacharjee, A.; Boozer, A. H.
2014-12-01
Magnetic fields depending on three spatial coordinates generally have the feature that neighboring field lines exponentiate away from each other and become stochastic. Such a generic condition usually occurs in space and astrophysical plasmas, such as coronal magnetic field entangled by photospheric footpoint shuffling, as well as in fusion plasmas in the presence of multiple tearing modes. Under the condition of large exponentiation, the ideal constraint of preserving magnetic field line connectivity becomes exponentially sensitive to small deviations from ideal Ohm's law, which may potentially lead to rapid magnetic reconnection. This idea of breaking field line connectivity by stochasticity is tested with numerical simulations based on reduced magnetohydrodynamics equations with a strong guide field line-tied to two perfectly conducting end plates. Starting from an ideally stable force-free equilibrium, the system is allowed to undergo resistive relaxation. Two distinct phases are identified in the process of resistive relaxation. During the quasi-static phase, it is found that regions of high field line exponentiation (akin to quasi-separatrix-layers) are associated with rapid change of field line connectivity and strong induced flow. However, although the field line connectivity of individual field lines can change rapidly, the overall pattern of footpoint mapping appears to deform gradually. From this perspective, field line exponentiation appears to cause enhanced diffusion rather than reconnection. In some cases, it is found that resistive quasi-static evolution can cause the ideally stable initial equilibrium to cross a stability threshold. Onset of the instability leads to formation of intense current filaments, followed by rapid change of field line mapping into a qualitatively different pattern. It is in this onset phase that the change of field line connectivity may be more appropriately designated as magnetic reconnection. Our results reveal and
NASA Astrophysics Data System (ADS)
Sato, Masanori; Matsubara, Takahiko
2013-06-01
It is crucial to understand and model a behavior of galaxy biasing for future ambitious galaxy redshift surveys. Using 40 large cosmological N-body simulations for a standard ΛCDM cosmology, we study the cross-correlation coefficient between matter and the halo density field, which is an indicator of the stochasticity of bias, over a wide redshift range 0≤z≤3. The cross-correlation coefficient is important to extract information on the matter density field, e.g., by combining galaxy clustering and galaxy-galaxy lensing measurements. We compare the simulation results with integrated perturbation theory (iPT) proposed by one of the present authors and standard perturbation theory combined with a phenomenological model of local bias. The cross-correlation coefficient derived from the iPT agrees with N-body simulation results down to r˜15(10)h-1Mpc within 0.5 (1.0)% for all redshifts and halo masses we consider. The standard perturbation theory with local bias does not explain complicated behaviors on quasilinear scales at low redshifts, while roughly reproduces the general behavior of the cross-correlation coefficient on fully nonlinear scales. The iPT is powerful to predict the cross-correlation coefficient down to quasilinear regimes with a high precision.
NASA Astrophysics Data System (ADS)
Gao, Hong
2013-04-01
Electron heat diffusion across stochastic magnetic fields is studied numerically in order to find out how the magnitude of perturbed magnetic field affect the enhanced heat conductivity and its radial profile in tokomak plasma physics. For these purposes, non-local stochastic magnetic fields are chosen as research objects in our simulation work. From our numerical results, we can find that the effects of the perturbed magnetic field magnitude are dominated parameter on the enhance electron heat transport conductivity wherever the magnetic field is single island or full stochastic field. Also, a theoretical analysis is provided and compared with numerical results.
NASA Astrophysics Data System (ADS)
Petreska, Irina; Pejov, Ljupčo; Kocarev, Ljupčo
2008-07-01
First-principles molecular-orbital theory was used to predict the possibilities to control the single-molecule conductance switching by external electrostatic fields in the case of nondipolar phenylene ethynylene oligomer molecule. External field directed perpendicularly to the molecular plane was shown to induce conductance switching, while field directed along axis lying within the molecular plane and being perpendicular to the principal molecular axis was shown to be capable of controlling the stochastic conductance by a strong modulation of the corresponding classical transition probability. The possibility for tuning the molecular switching properties could be attributed to the changes in the polarizability tensor components induced upon intramolecular torsion. The outlined possibilities are of fundamental importance in molecular engineering and design of single-molecule switches.
Further studies using matched filter theory and stochastic simulation for gust loads prediction
NASA Technical Reports Server (NTRS)
Scott, Robert C.; Pototzky, Anthony S.; Perry, Boyd Iii
1993-01-01
This paper describes two analysis methods -- one deterministic, the other stochastic -- for computing maximized and time-correlated gust loads for aircraft with nonlinear control systems. The first method is based on matched filter theory; the second is based on stochastic simulation. The paper summarizes the methods, discusses the selection of gust intensity for each method and presents numerical results. A strong similarity between the results from the two methods is seen to exist for both linear and nonlinear configurations.
Further studies using matched filter theory and stochastic simulation for gust loads prediction
NASA Technical Reports Server (NTRS)
Scott, Robert C.; Pototzky, Anthony S.; Perry, Boyd, III
1993-01-01
This paper describes two analysis methods - one deterministic, the other stochastic - for computing maximized and time-correlated gust loads for aircraft with nonlinear control systems. The first method is based on matched filter theory; the second is based on stochastic simulation. The paper summarizes the methods, discusses the selection of gust intensity for each method and presents numerical results. A strong similarity between the results from the two methods is seen to exist for both linear and nonlinear configurations.
Fornace, Mark E; Lee, Joonho; Miyamoto, Kaito; Manby, Frederick R; Miller, Thomas F
2015-02-10
We introduce embedded mean-field theory (EMFT), an approach that flexibly allows for the embedding of one mean-field theory in another without the need to specify or fix the number of particles in each subsystem. EMFT is simple, is well-defined without recourse to parameters, and inherits the simple gradient theory of the parent mean-field theories. In this paper, we report extensive benchmarking of EMFT for the case where the subsystems are treated using different levels of Kohn-Sham theory, using PBE or B3LYP/6-31G* in the high-level subsystem and LDA/STO-3G in the low-level subsystem; we also investigate different levels of density fitting in the two subsystems. Over a wide range of chemical problems, we find EMFT to perform accurately and stably, smoothly converging to the high-level of theory as the active subsystem becomes larger. In most cases, the performance is at least as good as that of ONIOM, but the advantages of EMFT are highlighted by examples that involve partitions across multiple bonds or through aromatic systems and by examples that involve more complicated electronic structure. EMFT is simple and parameter free, and based on the tests provided here, it offers an appealing new approach to a multiscale electronic structure.
Resummation in hot field theories
Andersen, Jens O. . E-mail: jensoa@nordita.dk; Strickland, Michael . E-mail: mike@hep.itp.tuwien.ac.at
2005-06-01
There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the perturbative expansion. This effective expansion which is due to Braaten and Pisarski, can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of g. However, it turns out that the weak-coupling expansion for thermodynamic quantities are useless unless the coupling constant is very small. We critically discuss various ways of reorganizing the perturbative series for thermal field theories in order to improve its convergence. These include screened perturbation theory (SPT), hard-thermal-loop perturbation theory, the {phi}-derivable approach, dimensionally reduced (DR) SPT, and the DR {phi}-derivable approach.
The adhesion model as a field theory for cosmological clustering
Rigopoulos, Gerasimos
2015-01-01
The adhesion model has been proposed in the past as an improvement of the Zel'dovich approximation, providing a good description of the formation of the cosmic web. We recast the model as a field theory for cosmological large scale structure, adding a stochastic force to account for power generated from very short, highly non-linear scales that is uncorrelated with the initial power spectrum. The dynamics of this Stochastic Adhesion Model (SAM) is reminiscent of the well known Kardar-Parisi-Zhang equation with the difference that the viscosity and the noise spectrum are time dependent. Choosing the viscosity proportional to the growth factor D restricts the form of noise spectrum through a 1-loop renormalization argument. For this choice, the SAM field theory is renormalizable to one loop. We comment on the suitability of this model for describing the non-linear regime of the CDM power spectrum and its utility as a relatively simple approach to cosmological clustering.
Stochastic theory of the Stokes parameters in randomly twisted fiber
Botet, Robert; Kuratsuji, Hiroshi
2011-03-15
We present the stochastic approach of the polarization state of an electromagnetic wave traveling through randomly twisted optical fiber. We treat the case of the weak randomness. When the geometric torsion of the fiber is distributed as a Gaussian law, we can write explicitly the Fokker-Planck equation for the Stokes parameters of the wave, and find the complete solution of the polarization-state distribution.
Robust synthetic biology design: stochastic game theory approach
Chen, Bor-Sen; Chang, Chia-Hung; Lee, Hsiao-Ching
2009-01-01
Motivation: Synthetic biology is to engineer artificial biological systems to investigate natural biological phenomena and for a variety of applications. However, the development of synthetic gene networks is still difficult and most newly created gene networks are non-functioning due to uncertain initial conditions and disturbances of extra-cellular environments on the host cell. At present, how to design a robust synthetic gene network to work properly under these uncertain factors is the most important topic of synthetic biology. Results: A robust regulation design is proposed for a stochastic synthetic gene network to achieve the prescribed steady states under these uncertain factors from the minimax regulation perspective. This minimax regulation design problem can be transformed to an equivalent stochastic game problem. Since it is not easy to solve the robust regulation design problem of synthetic gene networks by non-linear stochastic game method directly, the Takagi–Sugeno (T–S) fuzzy model is proposed to approximate the non-linear synthetic gene network via the linear matrix inequality (LMI) technique through the Robust Control Toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed robust gene design method. Availability: http://www.ee.nthu.edu.tw/bschen/SyntheticBioDesign_supplement.pdf Contact: bschen@ee.nthu.edu.tw Supplementary information: Supplementary data are available at Bioinformatics online. PMID:19435742
Variational methods for field theories
NASA Astrophysics Data System (ADS)
Ben-Menahem, Shahar
1986-09-01
The thesis is presented in four parts dealing with field theory models: Periodic Quantum Electrodynamics (PQED) in (2+1) dimensions, free scalar field theory in (1+1) dimensions, the Quantum XY model in (1+1) dimensions, and the (1+1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. Free field theory is used as a laboratory for a new variational blocking truncation approximation, in which the high frequency modes in a block are truncated to wave functions that depend on the slower background model (Born Oppenheimer approximation). For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. In the 4th part, the transfer matrix method is used to find a good (non blocking) trial ground state for the Ising model in a transverse magnetic field in (1+1) dimensions.
Stochastic analysis of a field-scale unsaturated transport experiment
NASA Astrophysics Data System (ADS)
Severino, G.; Comegna, A.; Coppola, A.; Sommella, A.; Santini, A.
2010-10-01
Modelling of field-scale transport of chemicals is of deep interest to public as well as private sectors, and it represents an area of active theoretical research in many environmentally-based disciplines. However, the experimental data needed to validate field-scale transport models are very limited due to the numerous logistic difficulties that one faces out. In the present paper, the migration of a tracer (Cl -) was monitored during its movement in the unsaturated zone beneath the surface of 8 m × 50 m sandy soil. Under flux-controlled, steady-state water flow ( Jw = 10 mm/day) was achieved by bidaily sprinkler irrigation. A pulse of 105 g/m 2 KCl was applied uniformly to the surface, and subsequently leached downward by the same (chloride-free) flux Jw over the successive two months. Chloride concentration monitoring was carried out in seven measurement campaigns (each one corresponding to a given time) along seven (parallel) transects. The mass recovery was near 100%, therefore underlining the very good-quality of the concentration data-set. The chloride concentrations are used to test two field-scale models of unsaturated transport: (i) the Advection-Dispersion Equation (ADE), which models transport far from the zone of solute entry, and (ii) the Stochastic- Convective Log- normal (CLT) transfer function model, which instead accounts for transport near the release zone. Both the models provided an excellent representation of the solute spreading at z > 0.45 m (being z = 0.45 m the calibration depth). As a consequence, by the depth z ≈ 50 cm one can regard transport as Fickian. The ADE model dramatically underestimates solute spreading at shallow depths. This is due to the boundary effects which are not captured by the ADE. The CLT model appears to be a more robust tool to mimic transport at every depth.
Introduction to string theory and conformal field theory
Belavin, A. A. Tarnopolsky, G. M.
2010-05-15
A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.
Nonlinear analysis of the cooperation of strategic alliances through stochastic catastrophe theory
NASA Astrophysics Data System (ADS)
Xu, Yan; Hu, Bin; Wu, Jiang; Zhang, Jianhua
2014-04-01
The excitation intervention of strategic alliance may change with the changes in the parameters of circumstance (e.g., external alliance tasks). As a result, the stable cooperation between members may suffer a complete unplanned betrayal at last. However, current perspectives on strategic alliances cannot adequately explain this transition mechanism. This study is a first attempt to analyze this nonlinear phenomenon through stochastic catastrophe theory (SCT). A stochastic dynamics model is constructed based on the cooperation of strategic alliance from the perspective of evolutionary game theory. SCT explains the discontinuous changes caused by the changes in environmental parameters. Theoretically, we identify conditions where catastrophe can occur in the cooperation of alliance members.
Static Magnetic Field Induced Stochastic Resonance in Gene Expression
NASA Astrophysics Data System (ADS)
Brady, Megan; Frisch, Paul; McLeod, Kenneth; Laramee, Craig
2012-02-01
Biological systems are naturally complex, making singular responses difficult to detect. However, when the emergent behavior is investigated, the collective properties may be observed and characterized. These responses to external stimuli at are often evident at the genomic level. When an optimal dose of external noise is used to perturb the system, it may work in synergy with the system's intrinsic noise to produce a change in stable state. This phenomenon, known as stochastic resonance (SR), is responsible for shifts in gene expression. This paper proposes that static magnetic fields (SMFs) elicit a SR genomic response in biological systems under environmentally relevant exposures. Using single reporter biomarkers as well as gene expression microarrays, the responses of three cell model systems (MCF-10A; Rat-1; Caco-2) to SMF exposure were examined. Results show that while responses for a single gene do occur, they are difficult to replicate and are near the detection cutoff limits. However, the system as a whole displays a shift in the pattern of gene expression. The replication of this pattern across different experimental platforms provides evidence that the cells are responding to the noise presented by the SMFs.
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Stochastic regulator theory for a class of abstract wave equations
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1991-01-01
A class of steady-state stochastic regulator problems for abstract wave equations in a Hilbert space - of relevance to the problem of feedback control of large space structures using co-located controls/sensors - is studied. Both the control operator, as well as the observation operator, are finite-dimensional. As a result, the usual condition of exponential stabilizability invoked for existence of solutions to the steady-state Riccati equations is not valid. Fortunately, for the problems considered it turns out that strong stabilizability suffices. In particular, a closed form expression is obtained for the minimal (asymptotic) performance criterion as the control effort is allowed to grow without bound.
Rapid change of field line connectivity and reconnection in stochastic magnetic fields
Huang, Yi-Min; Bhattacharjee, A.; Boozer, Allen H.
2014-10-01
Magnetic fields without a direction of continuous symmetry have the generic feature that neighboring field lines exponentiate away from each other and become stochastic, and hence the ideal constraint of preserving magnetic field line connectivity becomes exponentially sensitive to small deviations from ideal Ohm's law. The idea of breaking field line connectivity by stochasticity as a mechanism for fast reconnection is tested with numerical simulations based on reduced magnetohydrodynamics equations with a strong guide field line-tied to two perfectly conducting end plates. Starting from an ideally stable force-free equilibrium, the system is allowed to undergo resistive relaxation. Two distinct phases are found in the process of resistive relaxation. During the quasi-static phase, rapid change of field line connectivity and strong induced flow are found in regions of high field line exponentiation. However, although the field line connectivity of individual field lines can change rapidly, the overall pattern of field line mapping appears to deform gradually. From this perspective, field line exponentiation appears to cause enhanced diffusion rather than reconnection. In some cases, resistive quasi-static evolution can cause the ideally stable initial equilibrium to cross a stability threshold, leading to formation of intense current filaments and rapid change of field line mapping into a qualitatively different pattern. It is in this onset phase that the change of field line connectivity is more appropriately designated as magnetic reconnection. Our results show that rapid change of field line connectivity appears to be a necessary, but not a sufficient condition for fast reconnection.
ON THEORIES FOR STOCHASTIC ACCELERATION IN THE SOLAR WIND
Fisk, L. A.; Gloeckler, G.; Schwadron, N. A. E-mail: gglo@umich.ed
2010-09-01
The suprathermal tails on the distribution functions of ions in the solar wind are observed to have a common spectral shape in many different circumstances: a power law in particle speed with spectral index of -5. Three possible approaches for explaining these observations are considered: (1) the acceleration mechanism of Fisk and Gloeckler in which energy is redistributed from a core particle population into the suprathermal tail; (2) traditional stochastic acceleration in which particles are accelerated by damping turbulence; and (3) the statistical approach introduced by Schwadron et al. in which the -5 spectrum is formed by averaging over individual spectra. The acceleration mechanism of Fisk and Gloeckler has advantages: (1) it appears to occur in conditions that are readily satisfied: compressive turbulence that is thermally isolated (no large-scale spatial gradients), with a core distribution of particles with a sharp initial cutoff in particle speed, above which particles can spatially diffuse; and (2) it yields spectra that are consistent with observations. Traditional stochastic acceleration has the disadvantage that it is unlikely to yield spectral shapes consistent with observations, and the spectra are dependent upon the plasma conditions and thus unlikely to be the same in different circumstances. The statistical approach of Schwadron et al. can yield the -5 spectrum and is consistent with the results of Fisk and Gloeckler when the assumed distribution functions for individual events and the averaging technique are taken to be compatible with the assumptions and averaging in Fisk and Gloeckler.
Variational methods for field theories
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
Diffeomorphisms in group field theories
Baratin, Aristide; Girelli, Florian; Oriti, Daniele
2011-05-15
We study the issue of diffeomorphism symmetry in group field theories (GFT), using the noncommutative metric representation introduced by A. Baratin and D. Oriti [Phys. Rev. Lett. 105, 221302 (2010).]. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties together the vertex translation invariance of discrete gravity, the flatness constraint of canonical quantum gravity, and the topological (coarse-graining) identities for the 6j symbols. We also show how, for the GFT graphs dual to manifolds, the invariance of the Feynman amplitudes encodes the discrete residual action of diffeomorphisms in simplicial gravity path integrals. We extend the results to GFT models for higher-dimensional BF theories and discuss various insights that they provide on the GFT formalism itself.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro E-mail: mwhite@berkeley.edu
2015-09-01
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.
Topological field theory of dynamical systems
Ovchinnikov, Igor V.
2012-09-15
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the 'edge of chaos.' Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
A kinetic theory for age-structured stochastic birth-death processes
NASA Astrophysics Data System (ADS)
Chou, Tom; Greenman, Chris
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Conversely, current theories that include size-dependent population dynamics (e.g., carrying capacity) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution. NSF.
Theory Learning as Stochastic Search in the Language of Thought
ERIC Educational Resources Information Center
Ullman, Tomer D.; Goodman, Noah D.; Tenenbaum, Joshua B.
2012-01-01
We present an algorithmic model for the development of children's intuitive theories within a hierarchical Bayesian framework, where theories are described as sets of logical laws generated by a probabilistic context-free grammar. We contrast our approach with connectionist and other emergentist approaches to modeling cognitive development. While…
Diffusion of Magnetic Field Lines in Astrophysically-Relevant Stochastic Magnetic Fields
NASA Astrophysics Data System (ADS)
Barghouty, A. F.; Jokipii, J. R.
1996-05-01
We present a simple analytic model in which the KS-entropy for the exponential divergence of two neighboring field lines of an astrophysically-relevant stochastic magnetic field can be estimated. We treat the problem as a diffusive (random-walk) process describable by a Fokker-Planck equation and approximated by the standard nonlinear map. For Kolmogorov-like turbulence, we find that the field lines exhibit a non-Gaussian (or anomalous) diffusion for weak to moderate turbulence strength, consistent with a recent MHD numerical calculation(Zimbardo, G., et al. (1995), Phys. Plasmas 2), 2653., but in sharp contrast with simple quasilinear predictions. For moderate to strong turbulence, however, both our model and the numerical MHD study support such predictions in that the field lines appear to follow a Gaussian-like diffusion. Brief description of the model as well as implications to transport mechanisms of charged particles across turbulent magnetic fields will be presented.
Rearranging Pionless Effective Field Theory
Martin Savage; Silas Beane
2001-11-19
We point out a redundancy in the operator structure of the pionless effective field theory which dramatically simplifies computations. This redundancy is best exploited by using dibaryon fields as fundamental degrees of freedom. In turn, this suggests a new power counting scheme which sums range corrections to all orders. We explore this method with a few simple observables: the deuteron charge form factor, n p -> d gamma, and Compton scattering from the deuteron. Higher dimension operators involving electroweak gauge fields are not renormalized by the s-wave strong interactions, and therefore do not scale with inverse powers of the renormalization scale. Thus, naive dimensional analysis of these operators is sufficient to estimate their contribution to a given process.
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
NASA Astrophysics Data System (ADS)
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Koide, T.; Kodama, T.
2015-09-01
The stochastic variational method (SVM) is the generalization of the variational approach to systems described by stochastic variables. In this paper, we investigate the applicability of SVM as an alternative field-quantization scheme, by considering the complex Klein-Gordon equation. There, the Euler-Lagrangian equation for the stochastic field variables leads to the functional Schrödinger equation, which can be interpreted as the Euler (ideal fluid) equation in the functional space. The present formulation is a quantization scheme based on commutable variables, so that there appears no ambiguity associated with the ordering of operators, e.g., in the definition of Noether charges.
Field theory of pattern identification
NASA Astrophysics Data System (ADS)
Agu, Masahiro
1988-06-01
Based on the psychological experimental fact that images in mental space are transformed into other images for pattern identification, a field theory of pattern identification of geometrical patterns is developed with the use of gauge field theory in Euclidean space. Here, the ``image'' or state function ψ[χ] of the brain reacting to a geometrical pattern χ is made to correspond to the electron's wave function in Minkowski space. The pattern identification of the pattern χ with the modified pattern χ+Δχ is assumed to be such that their images ψ[χ] and ψ[χ+Δχ] in the brain are transformable with each other through suitable transformation groups such as parallel transformation, dilatation, or rotation. The transformation group is called the ``image potential'' which corresponds to the vector potential of the gauge field. An ``image field'' derived from the image potential is found to be induced in the brain when the two images ψ[χ] and ψ[χ+Δχ] are not transformable through suitable transformation groups or gauge transformations. It is also shown that, when the image field exists, the final state of the image ψ[χ] is expected to be different, depending on the paths of modifications of the pattern χ leading to a final pattern. The above fact is interpreted as a version of the Aharonov and Bohm effect of the electron's wave function [A. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959)]. An excitation equation of the image field is also derived by postulating that patterns are identified maximally for the purpose of minimizing the number of memorized standard patterns.
Heat Diffusion in a Non-Local Tokomak Stochastic Magnetic Field
NASA Astrophysics Data System (ADS)
Gao, Hong; Yao, Li; Zhong, Haiyang; Liu, Wei; Yang, Kun; Shao, Ying; Xia, Wenwen; li, Qian
2011-04-01
Heat transport across a non-local stochastic magnetic field was studied for the first time. Eleven incompact low m perturbed magnetic islands were used in our calculation. Parallel heat diffusion coefficient to the perpendicular coefficient was found still to be a key factor in influencing the effective radial heat conductivity and the results in this paper were compared with earlier studies in a local stochastic magnetic field.
Vacuum fluctuations of a scalar field during inflation: Quantum versus stochastic analysis
NASA Astrophysics Data System (ADS)
Onemli, V. K.
2015-05-01
We consider an infrared truncated massless minimally coupled scalar field with a quartic self-interaction in the locally de Sitter background of an inflating universe. We compute the two-point correlation function of the scalar at one- and two-loop order applying quantum field theory. The tree-order correlator at a fixed comoving separation (that is at an increasing physical distance) freezes into a nonzero value. At a fixed physical distance, it grows linearly with the comoving time. The one-loop correlator, which is the dominant quantum correction, implies a negative temporal growth in the correlation function, at this order, at a fixed comoving separation and at a fixed physical distance. We also obtain quantitative results for variance in space and time of one- and two-loop correlators and infer that the contrast between the vacuum expectation value and the variance becomes less pronounced when the loop corrections are included. Finally, we repeat the analysis of the model applying a stochastic field theory and reach the same conclusions.
Variational Methods for Field Theories.
NASA Astrophysics Data System (ADS)
Ben-Menahem, Shahar
The thesis has four parts, dealing with four field theory models: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. In the second part, we use free field theory as a loboratory for a new variational blocking-tuncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes(Born-Oppenheimer approximation). This "adiabatic truncation" method gives very accurate results for ground -state energy density and correlation functions. Without the adiabatic method, a much larger number of state per block must be kept to get comparable results. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Eclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. This transition is a rudimentary version of the actual transition known to occur in the XY model, and is
Transport theory of massless fields
Mrowczynski, S. |
1997-08-01
Using the Schwinger-Keldysh technique we discuss how to derive the transport equations for the system of massless quantum fields. We analyze the scalar field models with quartic and cubic interaction terms. In the {phi}{sup 4} model the massive quasiparticles appear due to the self-interaction of massless bare fields. Therefore, the derivation of the transport equations strongly resembles one of the massive fields, but the subset of diagrams which provides the quasiparticle mass has to be resummed. The kinetic equation for the finite width quasiparticles is found, where, except for the mean-field and collision terms, there are terms which are absent in the standard Boltzmann equation. The structure of these terms is discussed. In the massless {phi}{sup 3} model the massive quasiparticles do not emerge and presumably there is no transport theory corresponding to this model. It is not surprising since the {phi}{sup 3} model is, in any case, ill defined. {copyright} {ital 1997} {ital The American Physical Society}
Diffusion and stochastic island generation in the magnetic field line random walk
Vlad, M.; Spineanu, F.
2014-08-10
The cross-field diffusion of field lines in stochastic magnetic fields described by the 2D+slab model is studied using a semi-analytic statistical approach, the decorrelation trajectory method. We show that field line trapping and the associated stochastic magnetic islands strongly influence the diffusion coefficients, leading to dependences on the parameters that are different from the quasilinear and Bohm regimes. A strong amplification of the diffusion is produced by a small slab field in the presence of trapping. The diffusion regimes are determined and the corresponding physical processes are identified.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Topics in low-dimensional field theory
Crescimanno, M.J.
1991-04-30
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.
On a theory of stability for nonlinear stochastic chemical reaction networks
Smadbeck, Patrick; Kaznessis, Yiannis N.
2015-05-14
We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.
Thermodynamic and stochastic theory of hydrodynamic and power-producing processes
Ross, J.
1992-09-16
Thermodynamics of the transport processes of diffusion, thermal conduction, and viscous flow at a macroscopic level are developed for the simplest cases of one-dimensional transport in fluids for individual linear and nonlinear processes approaching a stationary non-equilibrium state. Formulation has started of thermodynamic and stochastic theory of combinations of transport processes. Global thermodynamic and stochastic theory of open chemical systems frar from equilibrium is continued with analysis of a broad class of isothermal, multicomponent reaction mechanisms with multiple steady states with assumed local equilibrium. Stationary solutions are obtained of the master equation for single and multi-intermediate autocatalytic chemical systems. A kinetic potential is identified that governs the deterministic time evolution of coupled tank reactors. A second-order response theory was developed to investigate the effects of external periodic perturbations on a chemical reaction at a stable steady state in an open reactor.
Nonlocal stochastic mixing-length theory and the velocity profile in the turbulent boundary layer
NASA Astrophysics Data System (ADS)
Dekker, H.; de Leeuw, G.; Maassen van den Brink, A.
1995-02-01
Turbulence mixing by finite size eddies will be treated by means of a novel formulation of nonlocal K-theory, involving sample paths and a stochastic closure hypothesis, which implies a well defined recipe for the calculation of sampling and transition rates. The connection with the general theory of stochastic processes will be established. The relation with other nonlocal turbulence models (e.g. transilience and spectral diffusivity theory) is also discussed. Using an analytical sampling rate model (satisfying exchange) the theory is applied to the boundary layer (using a scaling hypothesis), which maps boundary layer turbulence mixing of scalar densities onto a nondiffusive (Kubo-Anderson or kangaroo) type stochastic process. The resulting transpport equation for longitudinal momentum P x ≡ ϱ U is solved for a unified description of both the inertial and the viscous sublayer including the crossover. With a scaling exponent ε ≈ 0.58 (while local turbulence would amount to ε → ∞) the velocity profile U+ = ƒ(y +) is found to be in excellent agreement with the experimental data. Inter alia (i) the significance of ε as a turbulence Cantor set dimension, (ii) the value of the integration constant in the logarithmic region (i.e. if y+ → ∞), (iii) linear timescaling, and (iv) finite Reynolds number effects will be investigated. The (analytical) predictions of the theory for near-wall behaviour (i.e. if y+ → 0) of fluctuating quantities also perfectly agree with recent direct numerical simulations.
Linear kinetic theory and particle transport in stochastic mixtures
Pomraning, G.C.
1995-12-31
We consider the formulation of linear transport and kinetic theory describing energy and particle flow in a random mixture of two or more immiscible materials. Following an introduction, we summarize early and fundamental work in this area, and we conclude with a brief discussion of recent results.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Poisson-Vlasov in a strong magnetic field: A stochastic solution approach
Vilela Mendes, R.
2010-04-15
Stochastic solutions are obtained for the Maxwell-Vlasov equation in the approximation where magnetic field fluctuations are neglected and the electrostatic potential is used to compute the electric field. This is a reasonable approximation for plasmas in a strong external magnetic field. Both Fourier and configuration space solutions are constructed.
Horváth, Krisztián; Olajos, Marcell; Felinger, Attila; Hajós, Péter
2008-05-01
The stochastic theory of chromatography and an equilibrium based approach were used for the prediction of peak shape and retention data of anions. This attempt incorporating the potential advantages of two different chromatographic phenomena for analytical purposes. It is an integrated method to estimate kinetic and thermodynamic properties for the same chromatographic run of ions. The stochastic parameters of eluted anions, such as the residence time of the molecule on the surface of the stationary phase, and the average number of adsorption steps were determined on the basis of a retention database of organic and inorganic anions (formate, chloride, bromide, nitrate, sulphate, oxalate, phosphate) obtained by using carbonate/bicarbonate eluent system at different pHs (9-11) and concentrations (7-13 mM). In the investigated IC system the residence times are much higher and the average number of sorption steps is somewhat smaller than in RP-HPLC. The simultaneous application of the stochastic and the multispecies eluent/analyte model was utilized to peak shape simulation and the retention controlling of various anions under elution conditions of practical importance. The similarities between the measured and the calculated chromatograms indicates the predictive and simulation power of the combined application of the stochastic theory and the multiple species eluent/analyte retention model. PMID:17719052
Studies in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bastianelli, Fiorenzo
We analyze several topics in quantum field theory, mainly motivated by their role in the formulation of string theories. The common theme in what follows is the implementation of symmetries, such as local supersymmetry or BRST symmetry, through an action principle and the analysis of anomalies, the latter describing the breakdown of these symmetries at the quantum level. In the first part of this dissertation, we analyze "chiral bosons", i.e. massless scalar fields in a two -dimensional spacetime propagating in only one of the two light-cone directions. We present a general method for constructing couplings for chiral bosons and give details for the coupling to supergravity. The notion of a two dimensional chiral boson is generalized in d = 4k + 2 spacetime dimensions to that of a self-dual antisymmetric tensor field. We derive the coupling to gravity and compute the gravitational anomalies using the Feynman rules obtained from the action. We find agreement with the important work of Alvarez-Gaume and Witten, who conjectured the relevant Feynman rules. Our result therefore completes and justifies the Alvarez-Gaume-Witten findings. For the case of d = 2 we also show how to use the method of Fujikawa for computing anomalies from the non-invariance of the path integral measure. We obtain the full effective action by integrating the anomaly equation. In the second part we focus on a method for computing the consistent anomalies in the Fujikawa scheme. In a first application, we derive the consistent regulators for the various fields of the quantum action of the spinning string in superspace. These regulators produce the anomalies which satisfy the Wess-Zumino consistency conditions. In a second application, we analyze the anomalous structure of the Green-Schwarz formulation of the heterotic string. We find anomalies which generically do not cancel on an arbitrary world-sheet manifold. This raises questions concerning the possible validity of such a formulation of
Instantons in Lifshitz field theories
NASA Astrophysics Data System (ADS)
Fujimori, Toshiaki; Nitta, Muneto
2015-10-01
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.
Fluorescence microscopy image noise reduction using a stochastically-connected random field model
Haider, S. A.; Cameron, A.; Siva, P.; Lui, D.; Shafiee, M. J.; Boroomand, A.; Haider, N.; Wong, A.
2016-01-01
Fluorescence microscopy is an essential part of a biologist’s toolkit, allowing assaying of many parameters like subcellular localization of proteins, changes in cytoskeletal dynamics, protein-protein interactions, and the concentration of specific cellular ions. A fundamental challenge with using fluorescence microscopy is the presence of noise. This study introduces a novel approach to reducing noise in fluorescence microscopy images. The noise reduction problem is posed as a Maximum A Posteriori estimation problem, and solved using a novel random field model called stochastically-connected random field (SRF), which combines random graph and field theory. Experimental results using synthetic and real fluorescence microscopy data show the proposed approach achieving strong noise reduction performance when compared to several other noise reduction algorithms, using quantitative metrics. The proposed SRF approach was able to achieve strong performance in terms of signal-to-noise ratio in the synthetic results, high signal to noise ratio and contrast to noise ratio in the real fluorescence microscopy data results, and was able to maintain cell structure and subtle details while reducing background and intra-cellular noise. PMID:26884148
NASA Astrophysics Data System (ADS)
Magdowski, M.; Siddiqui, S.; Vick, R.
2012-05-01
The coupling of stochastic electromagnetic fields to a straight and uniform transmission line was measured in a reverberation chamber. Such stochastic fields also appear in large and complex overmoded cavities like aircraft fuse- lages and satellite enclosures. The measurements were carried out with different line lengths over a large frequency range. The results are analyzed with respect to the statistical distribution of the characteristics of the coupled voltage and compared to simulated values. The simulation is based on a transmission line model and a plane wave representation of the field.
One-dimensional random field Ising model and discrete stochastic mappings
Behn, U.; Zagrebnov, V.A.
1987-06-01
Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.
Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory
Di Renzo, F.; Ilgenfritz, E.-M.; Perlt, H.; Schiller, A.; Torrero, C.
2011-05-23
We summarize the higher-loop perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim is to compare with results from lattice simulations in order to expose the genuinely non-perturbative content of the latter. By means of Numerical Stochastic Perturbation Theory we compute the ghost and gluon propagators in Landau gauge up to three and four loops. We present results in the infinite volume and a{yields}0 limits, based on a general fitting strategy.
Butler, T.; Graham, L.; Estep, D.; Westerink, J.J.
2015-01-01
The uncertainty in spatially heterogeneous Manning’s n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning’s n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of “condition” for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning’s n parameter and the effect on model predictions is analyzed. PMID:25937695
NASA Astrophysics Data System (ADS)
Butler, T.; Graham, L.; Estep, D.; Dawson, C.; Westerink, J. J.
2015-04-01
The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Towards weakly constrained double field theory
NASA Astrophysics Data System (ADS)
Lee, Kanghoon
2016-08-01
We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon) transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.
Conformal field theories from deformations of theories with Wn symmetry
NASA Astrophysics Data System (ADS)
Babaro, Juan Pablo; Giribet, Gaston; Ranjbar, Arash
2016-10-01
We construct a set of nonrational conformal field theories that consist of deformations of Toda field theory for s l (n ). In addition to preserving conformal invariance, the theories may still exhibit a remnant infinite-dimensional affine symmetry. The case n =3 is used to illustrate this phenomenon, together with further deformations that yield enhanced Kac-Moody symmetry algebras. For generic n we compute N -point correlation functions on the Riemann sphere and show that these can be expressed in terms of s l (n ) Toda field theory ((N -2 )n +2 ) -point correlation functions.
Observation of energetic electron confinement in a largely stochastic reversed-field pinch plasma
NASA Astrophysics Data System (ADS)
Clayton, D. J.; Chapman, B. E.; O'Connell, R.; Almagri, A. F.; Burke, D. R.; Forest, C. B.; Goetz, J. A.; Kaufman, M. C.; Bonomo, F.; Franz, P.; Gobbin, M.; Piovesan, P.
2010-01-01
Runaway electrons with energies >100 keV are observed with the appearance of an m =1 magnetic island in the core of otherwise stochastic Madison Symmetric Torus [Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field-pinch plasmas. The island is associated with the innermost resonant tearing mode, which is usually the largest in the m =1 spectrum. The island appears over a range of mode spectra, from those with a weakly dominant mode to those, referred to as quasi single helicity, with a strongly dominant mode. In a stochastic field, the rate of electron loss increases with electron parallel velocity. Hence, high-energy electrons imply a region of reduced stochasticity. The global energy confinement time is about the same as in plasmas without high-energy electrons or an island in the core. Hence, the region of reduced stochasticity must be localized. Within a numerical reconstruction of the magnetic field topology, high-energy electrons are substantially better confined inside the island, relative to the external region. Therefore, it is deduced that the island provides a region of reduced stochasticity and that the high-energy electrons are generated and well confined within this region.
Phase space theory of quantum–classical systems with nonlinear and stochastic dynamics
Burić, Nikola Popović, Duška B.; Radonjić, Milan; Prvanović, Slobodan
2014-04-15
A novel theory of hybrid quantum–classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum–classical phase space. Both, the quantum and classical descriptions of the respective parts of the hybrid system are treated as fundamental. Therefore, the description of the quantum–classical interaction has to be postulated, and includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement. -- Highlights: •A novel theory of quantum–classical systems is developed. •Framework of quantum constrained dynamical systems is used. •A dynamical description of the measurement induced collapse is obtained.
A Simple Stochastic Model for Generating Broken Cloud Optical Depth and Top Height Fields
NASA Technical Reports Server (NTRS)
Prigarin, Sergei M.; Marshak, Alexander
2007-01-01
A simple and fast algorithm for generating two correlated stochastic twodimensional (2D) cloud fields is described. The algorithm is illustrated with two broken cumulus cloud fields: cloud optical depth and cloud top height retrieved from Moderate Resolution Imaging Spectrometer (MODIS). Only two 2D fields are required as an input. The algorithm output is statistical realizations of these two fields with approximately the same correlation and joint distribution functions as the original ones. The major assumption of the algorithm is statistical isotropy of the fields. In contrast to fractals and the Fourier filtering methods frequently used for stochastic cloud modeling, the proposed method is based on spectral models of homogeneous random fields. For keeping the same probability density function as the (first) original field, the method of inverse distribution function is used. When the spatial distribution of the first field has been generated, a realization of the correlated second field is simulated using a conditional distribution matrix. This paper is served as a theoretical justification to the publicly available software that has been recently released by the authors and can be freely downloaded from http://i3rc.gsfc.nasa.gov/Public codes clouds.htm. Though 2D rather than full 3D, stochastic realizations of two correlated cloud fields that mimic statistics of given fields have proved to be very useful to study 3D radiative transfer features of broken cumulus clouds for better understanding of shortwave radiation and interpretation of the remote sensing retrievals.
Continuum regularization of quantum field theory
Bern, Z.
1986-01-01
Breit, Gupta, and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the fifth-time of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, difficulties arise which, in general, ruins the scheme. A successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest.
Temporal variability in a stochastic precipitation field simulator
NASA Astrophysics Data System (ADS)
Kolberg, Sjur
2016-04-01
The space-time statistics of short-term precipitation is studied for two cities in northern Europe, and related to radiosonde observations. The motivation is to construct the temporally varying parameters needed to drive a stochastic short-term precipitation generator. Moments, intermittency, semivariograms, temporal covariance and advection parameters need to be characterised in order to produce realistic scenario simulations for extreme value estimation at different scales. It is hoped that the temporal variability in these parameters can be related to radiosonde data. Hourly values from 46 precipitation stations within a 100*130 km2 region around Copenhagen during the period 1979-2012 is analysed. Bi-daily radiosonde profiles are present from 1969 to 2006. These soundings (vertical profiles of temperature, dew point and wind vector) describe the atmospheric moisture content and convective potential of the current weather situation. Preliminary analysis show that some of the indices extracted from the 12h radiosonde data show good temporal autocorrelation, supporting interpolation to match the 1-hour precipitation data. The precipitation data show a rapidly decreasing temporal autocorrelation function (typically below 0.5 above approx. 12 km), indicating that there is a high variance fraction below scales that the station network is able to reveal. The second data set consists of 7.5-minute C-band radar data from Trondheim, available from June 2013 to October 2015. During the 2014 and 2015 summer seasons, around 25 tipping-bucket precipitation gauges within a 15*20 km area supply observations with temporal resolution down to minute-scale. Nearby radiosonde data are available bi-daily from 1963 to 2015. These data will be explored to provide insight in high-frequency spatial and temporal variability not detectable from the long-term Copenhagen data set. The analysis is a part of the EU-7FP project "Pearl" (http://www.pearl-fp7.eu/, Greve case study), the Norwegian
Boson formulation of fermion field theories
Ha, Y.K.
1984-04-15
The nonperturbative connection between a canonical Fermi field and a canonical Bose field in two dimensions is developed and its validity verified according to the tenets of quantum field theory. We advocate the point of view that a boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. Many features of the massless theory, such as dynamical mass generation with asymptotic-freedom behavior, hidden chiral symmetry, and connections with models of apparently different internal symmetries, are readily transparent through such fermion-boson metamorphosis.
NASA Astrophysics Data System (ADS)
Wang, Shaojie
2016-07-01
Anomalous current pinch, in addition to the anomalous diffusion due to stochastic magnetic perturbations, is theoretically found, which may qualitatively explain the recent DIII-D experiment on resonant magnetic field perturbation. The anomalous current pinch, which may resolve the long-standing issue of seed current in a fully bootstrapped tokamak, is also discussed for the electrostatic turbulence.
Failure of classical traffic flow theories: Stochastic highway capacity and automatic driving
NASA Astrophysics Data System (ADS)
Kerner, Boris S.
2016-05-01
In a mini-review Kerner (2013) it has been shown that classical traffic flow theories and models failed to explain empirical traffic breakdown - a phase transition from metastable free flow to synchronized flow at highway bottlenecks. The main objective of this mini-review is to study the consequence of this failure of classical traffic-flow theories for an analysis of empirical stochastic highway capacity as well as for the effect of automatic driving vehicles and cooperative driving on traffic flow. To reach this goal, we show a deep connection between the understanding of empirical stochastic highway capacity and a reliable analysis of automatic driving vehicles in traffic flow. With the use of simulations in the framework of three-phase traffic theory, a probabilistic analysis of the effect of automatic driving vehicles on a mixture traffic flow consisting of a random distribution of automatic driving and manual driving vehicles has been made. We have found that the parameters of automatic driving vehicles can either decrease or increase the probability of the breakdown. The increase in the probability of traffic breakdown, i.e., the deterioration of the performance of the traffic system can occur already at a small percentage (about 5%) of automatic driving vehicles. The increase in the probability of traffic breakdown through automatic driving vehicles can be realized, even if any platoon of automatic driving vehicles satisfies condition for string stability.
The stochastic string model as a unifying theory of the term structure of interest rates
NASA Astrophysics Data System (ADS)
Bueno-Guerrero, Alberto; Moreno, Manuel; Navas, Javier F.
2016-11-01
We present the stochastic string model of Santa-Clara and Sornette (2001), as reformulated by Bueno-Guerrero et al. (2015), as a unifying theory of the continuous-time modeling of the term structure of interest rates. We provide several new results, such as: (a) an orthogonality condition for the volatilities in the Heath, Jarrow, and Morton (1992) (HJM) model, (b) the interpretation of multi-factor HJM models as approximations to a full infinite-dimensional model, (c) a result of consistency based on Hilbert spaces, and (d) a theorem for option valuation.
Introduction to conformal field theory and string theory
Dixon, L.J.
1989-12-01
These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs.
NASA Astrophysics Data System (ADS)
Kotchenova, Svetlana Y.; Shabanov, Nikolay V.; Knyazikhin, Yuri; Davis, Anthony B.; Dubayah, Ralph; Myneni, Ranga B.
2003-08-01
Large footprint waveform-recording laser altimeters (lidars) have demonstrated a potential for accurate remote sensing of forest biomass and structure, important for regional and global climate studies. Currently, radiative transfer analyses of lidar data are based on the simplifying assumption that only single scattering contributes to the return signal, which may lead to errors in the modeling of the lower portions of recorded waveforms in the near-infrared spectrum. In this study we apply time-dependent stochastic radiative transfer (RT) theory to model the propagation of lidar pulses through forest canopies. A time-dependent stochastic RT equation is formulated and solved numerically. Such an approach describes multiple scattering events, allows for realistic representation of forest structure including foliage clumping and gaps, simulates off-nadir and multiangular observations, and has the potential to provide better approximations of return waveforms. The model was tested with field data from two conifer forest stands (southern old jack pine and southern old black spruce) in central Canada and two closed canopy deciduous forest stands (with overstory dominated by tulip poplar) in eastern Maryland. Model-simulated signals were compared with waveforms recorded by the Scanning Lidar Imager of Canopies by Echo Recovery (SLICER) over these regions. Model simulations show good agreement with SLICER signals having a slow decay of the waveform. The analysis of the effects of multiple scattering shows that multiply scattered photons magnify the amplitude of the reflected signal, especially that originating from the lower portions of the canopy.
Understanding conformal field theory through parafermions and Chern Simons theory
Hotes, S.A.
1992-11-19
Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.
Fermion boson metamorphosis in field theory
Ha, Y.K.
1982-01-01
In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered.
On causality in polymer scalar field theory
NASA Astrophysics Data System (ADS)
García-Chung, Angel A.; Morales-Técotl, Hugo A.
2011-10-01
The properties of spacetime corresponding to a proposed quantum gravity theory might modify the high energy behavior of quantum fields. Motivated by loop quantum gravity, recently, Hossain et al [1] have considered a polymer field algebra that replaces the standard canonical one in order to calculate the propagator of a real scalar field in flat spacetime. This propagator features Lorentz violations. Motivated by the relation between Lorentz invariance and causality in standard Quantum Field Theory, in this work we investigate the causality behavior of the polymer scalar field.
Stochastic geometry and topology of non-Gaussian fields
Beuman, Thomas H.; Turner, Ari M.; Vitelli, Vincenzo
2012-01-01
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter and cosmology to biomedical imaging. The standard test of non-Gaussianity is to measure higher-order correlation functions. In the present work, we take a different route. We show how geometric and topological properties of Gaussian fields, such as the statistics of extrema, are modified by the presence of a non-Gaussian perturbation. The resulting discrepancies give an independent way to detect and quantify non-Gaussianities. In our treatment, we consider both local and nonlocal mechanisms that generate non-Gaussian fields, both statically and dynamically through nonlinear diffusion. PMID:23169625
Three approaches to classical thermal field theory
Gozzi, E.; Penco, R.
2011-04-15
Research Highlights: > Classical thermal field theory admits three equivalent path integral formulations. > Classical Feynman rules can be derived for all three formulations. > Quantum Feynman rules reduce to classical ones at high temperatures. > Classical Feynman rules become much simpler when superfields are introduced. - Abstract: In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.
Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations
2013-01-01
In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model. Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328
Ostrogradsky in theories with multiple fields
NASA Astrophysics Data System (ADS)
de Rham, Claudia; Matas, Andrew
2016-06-01
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
Constraining Modified Theories of Gravity with Gravitational-Wave Stochastic Backgrounds
NASA Astrophysics Data System (ADS)
Maselli, Andrea; Marassi, Stefania; Ferrari, Valeria; Kokkotas, Kostas; Schneider, Raffaella
2016-08-01
The direct discovery of gravitational waves has finally opened a new observational window on our Universe, suggesting that the population of coalescing binary black holes is larger than previously expected. These sources produce an unresolved background of gravitational waves, potentially observable by ground-based interferometers. In this Letter we investigate how modified theories of gravity, modeled using the parametrized post-Einsteinian formalism, affect the expected signal, and analyze the detectability of the resulting stochastic background by current and future ground-based interferometers. We find the constraints that Advanced LIGO would be able to set on modified theories, showing that they may significantly improve the current bounds obtained from astrophysical observations of binary pulsars.
Constraining Modified Theories of Gravity with Gravitational-Wave Stochastic Backgrounds.
Maselli, Andrea; Marassi, Stefania; Ferrari, Valeria; Kokkotas, Kostas; Schneider, Raffaella
2016-08-26
The direct discovery of gravitational waves has finally opened a new observational window on our Universe, suggesting that the population of coalescing binary black holes is larger than previously expected. These sources produce an unresolved background of gravitational waves, potentially observable by ground-based interferometers. In this Letter we investigate how modified theories of gravity, modeled using the parametrized post-Einsteinian formalism, affect the expected signal, and analyze the detectability of the resulting stochastic background by current and future ground-based interferometers. We find the constraints that Advanced LIGO would be able to set on modified theories, showing that they may significantly improve the current bounds obtained from astrophysical observations of binary pulsars. PMID:27610838
Constraining Modified Theories of Gravity with Gravitational-Wave Stochastic Backgrounds.
Maselli, Andrea; Marassi, Stefania; Ferrari, Valeria; Kokkotas, Kostas; Schneider, Raffaella
2016-08-26
The direct discovery of gravitational waves has finally opened a new observational window on our Universe, suggesting that the population of coalescing binary black holes is larger than previously expected. These sources produce an unresolved background of gravitational waves, potentially observable by ground-based interferometers. In this Letter we investigate how modified theories of gravity, modeled using the parametrized post-Einsteinian formalism, affect the expected signal, and analyze the detectability of the resulting stochastic background by current and future ground-based interferometers. We find the constraints that Advanced LIGO would be able to set on modified theories, showing that they may significantly improve the current bounds obtained from astrophysical observations of binary pulsars.
Metric quantum field theory: A preliminary look
Watson, W.N.
1988-01-01
Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics.
Relativistic mean-field theory
NASA Astrophysics Data System (ADS)
Meng, Jie; Ring, Peter; Zhao, Pengwei
In this chapter, the covariant energy density functional is constructed with both the meson-exchange and the point-coupling pictures. Several widely used functionals with either nonlinear or density-dependent effective interactions are introduced. The applications of covariant density functional theory are demonstrated for infinite nuclear matter and finite nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes. Finally, a relativistic description of the nuclear landscape has been discussed, which is not only important for nuclear structure, but also important for nuclear astrophysics, where we are facing the problem of a reliable extrapolation to the very neutron-rich nuclei.
Pure field theories and MACSYMA algorithms
NASA Technical Reports Server (NTRS)
Ament, W. S.
1977-01-01
A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.
Pion masses in quasiconformal gauge field theories
Dietrich, Dennis D.; Jaervinen, Matti
2009-03-01
We study modifications to Weinberg-like sum rules in quasiconformal gauge field theories. Beyond the two Weinberg sum rules and the oblique S parameter, we study the pion mass and the X parameter. Especially, we evaluate the pion mass for walking technicolor theories, in particular, minimal walking technicolor, and find contributions of the order of up to several hundred GeV.
Reductionism, emergence, and effective field theories
NASA Astrophysics Data System (ADS)
Castellani, Elena
In recent years, a "change in attitude" in particle physics has led to our understanding current quantum field theories as effective field theories (EFTs). The present paper is concerned with the significance of this EFT approach, especially from the viewpoint of the debate on reductionism in science. In particular, I shall show how EFTs provide a new and interesting case study in current philosophical discussion on reduction, emergence, and inter-level relationships in general.
{N}=3 four dimensional field theories
NASA Astrophysics Data System (ADS)
García-Etxebarria, Iñaki; Regalado, Diego
2016-03-01
We introduce a class of four dimensional field theories constructed by quotienting ordinary {N}=4 U(N ) SYM by particular combinations of R-symmetry and SL(2, ℤ) automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions possess an unconventional large N limit described by a non-trivial F-theory fibration with base AdS 5 × (S 5/ ℤ k ). Upon reduction on a circle the {N}=3 theories flow to well-known {N}=6 ABJM theories.
Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression
NASA Astrophysics Data System (ADS)
Yasuhiko Igarashi,; Masafumi Oizumi,; Masato Okada,
2010-08-01
We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing-state variable and a synaptic variable. In these equations, the average product of thesevariables is decoupled as the product of their averages because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight Jij is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady-state equations for a network with uniform connections and for a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady-state solutions. An oscillatory uniform state was observed in the network with uniform connections owing to a Hopf instability. For the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading to two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previously unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. PMID:22654052
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.
NASA Astrophysics Data System (ADS)
Touboul, Jonathan
2012-08-01
In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate stochastic delayed integro-differential McKean-Vlasov equation that remain impenetrable, leaving the stochastic collective dynamics of such networks poorly understood. In order to study these macroscopic dynamics, we analyze networks of firing-rate neurons, i.e. with linear intrinsic dynamics and sigmoidal interactions. In that case, we prove that the solution of the mean-field equation is Gaussian, hence characterized by its two first moments, and that these two quantities satisfy a set of coupled delayed integro-differential equations. These equations are similar to usual neural field equations, and incorporate noise levels as a parameter, allowing analysis of noise-induced transitions. We identify through bifurcation analysis several qualitative transitions due to noise in the mean-field limit. In particular, stabilization of spatially homogeneous solutions, synchronized oscillations, bumps, chaotic dynamics, wave or bump splitting are exhibited and arise from static or dynamic Turing-Hopf bifurcations. These surprising phenomena allow further exploring the role of noise in the nervous system.
NASA Astrophysics Data System (ADS)
Charalambous, Charalambos D.; Kyprianou, Andreas
2005-05-01
Fifty years ago, when Claude Shannon was developing the Mathematical Theory of Communications, for reliable data transmission, which evolved into the subject of information theory, another discipline was developing dealing with Feedback Control of Dynamical System, which evolved into a scientific subject dealing with decision, stability, and optimization. More recently, a separate discipline dealing with robustness of uncertain systems was born in response to the codification of high performance and reliability in the presence of modeling uncertainties. In principle, robustness in dynamical systems is captured through power dissipation via induced norms and dynamic games, while reliable data transmission is captured through measures of information via entropy, relative entropy, and certain laws of Large Deviations theory. The main ingredient in Large Deviations is the rate functional (or action functional in the classical mechanics terminology), often identified through the Cramer or Legendre-Fenchel Transform. On the other hand, robustness of stochastic uncertain systems is currently under development, using information theoretic as well as statistical mechanics concepts, such as, partition functions, free energy, relative entropy, and entropy rate functional. This lecture will summarize certain connections between fundamental concepts of robustness, information theory, and statistical mechanics, and possibly make future projections into the convergence of these disciplines.
Potential and Flux Field Landscape Theory of Spatially Inhomogeneous Non-Equilibrium Systems
NASA Astrophysics Data System (ADS)
Wu, Wei
In this dissertation we establish a potential and flux field landscape theory for studying the global stability and dynamics as well as the non-equilibrium thermodynamics of spatially inhomogeneous non-equilibrium dynamical systems. The potential and flux landscape theory developed previously for spatially homogeneous non-equilibrium stochastic systems described by Langevin and Fokker-Planck equations is refined and further extended to spatially inhomogeneous non-equilibrium stochastic systems described by functional Langevin and Fokker-Planck equations. The probability flux field is found to be crucial in breaking detailed balance and characterizing non-equilibrium effects of spatially inhomogeneous systems. It also plays a pivotal role in governing the global dynamics and formulating a set of non-equilibrium thermodynamic equations for a generic class of spatially inhomogeneous stochastic systems. The general formalism is illustrated by studying more specific systems and processes, such as the reaction diffusion system, the Ornstein-Uhlenbeck process, the Brusselator reaction diffusion model, and the spatial stochastic neuronal model. The theory can be applied to a variety of physical, chemical and biological spatially inhomogeneous non-equilibrium systems abundant in nature.
The Theory of Quantized Fields. II
DOE R&D Accomplishments Database
Schwinger, J.
1951-01-01
The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the time reflection invariance requirement. The consistency of the theory is verified in terms of a criterion involving the various generators of infinitesimal transformations. Following a discussion of charged fields, the electromagnetic field is introduced to satisfy the postulate of general gauge invariance. As an aspect of the latter, it is recognized that the electromagnetic field and charged fields are not kinematically independent. After a discussion of the field-strength commutation relations, the independent dynamical variable of the electromagnetic field are exhibited in terms of a special gauge.
Equilibration properties of classical integrable field theories
NASA Astrophysics Data System (ADS)
De Luca, Andrea; Mussardo, Giuseppe
2016-06-01
We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as quantum field theories in the regime of high occupation numbers. This observation permits to recover the classical quantities from the quantum ones by taking a proper \\hslash \\to 0 limit. In particular, the time averages of the classical theories can be expressed in terms of a suitable version of the LeClair-Mussardo formula relative to the generalized Gibbs ensemble. For the purposes of handling time averages, our approach provides a solution of the problem of the infinite gap solutions of the inverse scattering method.
Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation.
Durán-Olivencia, Miguel A; Lutsko, James F
2015-09-01
Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately, the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g., Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation, a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J. F. Lutsko and M. A. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013)10.1063/1.4811490] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios, in particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion, or interface transfer.
Sustainable ecosystem management using optimal control theory: part 2 (stochastic systems).
Shastri, Y; Diwekar, U
2006-08-01
Sustainable development of ecosystems through external ecosystem management is assuming importance for the environmentalists. To that effect, previous work by the authors looked at the option of manipulating population dynamics of the species in an ecosystem to achieve sustainability. Fisher information is used as the quantifying measure of sustainability and optimal control theory is used to derive the control profiles. However, that work considered only deterministic systems. Uncertainty being prevalent in all systems, particularly in natural systems, this paper extends that work to analyse uncertain systems. Predator-prey models are used to model the species populations and different control philosophies are compared. Ito mean reverting process is used to model the stochastic process, and stochastic maximum principle is used to derive the control profiles. The results for the objective of FI variance minimization qualitatively agree with those for the deterministic system, while the results for the FI maximization objective differ. It is observed that the instability associated with the FI maximization objective for deterministic systems is absorbed by the noise introduced by the uncertainty. Quantitatively, it is observed that the degree of uncertainty, along with its presence, is also important to identify the most appropriate management strategy.
Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation
NASA Astrophysics Data System (ADS)
Durán-Olivencia, Miguel A.; Lutsko, James F.
2015-09-01
Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately, the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g., Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation, a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J. F. Lutsko and M. A. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013), 10.1063/1.4811490] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios, in particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion, or interface transfer.
From theory to field experiments
NASA Astrophysics Data System (ADS)
de Vos, Bram
2016-04-01
Peter Raats' achievements in Haren (NL) 1986-1997 were based on a solid theoretical insight in hydrology and transport process in soil. However, Peter was also the driving force behind many experimental studies and applied research. This will be illustrated by a broad range of examples ranging from the dynamics of composting processes of organic material; modelling and monitoring nutrient leaching at field-scale; wind erosion; water and nutrient dynamics in horticultural production systems; oxygen diffusion in soils; and processes of water and nutrient uptake by plant roots. Peter's leadership led to may new approaches and the introduction of innovative measurement techniques in Dutch research; ranging from TDR to nutrient concentration measurements in closed fertigation systems. This presentation will give a brief overview how Peter's theoretical and mathematical insights accelerated this applied research.
Phase-space quantization of field theory.
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Generalized metric formulation of double field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Hull, Chris; Zwiebach, Barton
2010-08-01
The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple formulation with manifest T-duality of the double field theory that describes the massless sector of closed strings. The gauge transformations are written in terms of a generalized Lie derivative whose commutator algebra is defined by a double field theory extension of the Courant bracket.
Conformal field theory on affine Lie groups
Clubok, K.S.
1996-04-01
Working directly on affine Lie groups, we construct several new formulations of the WZW model, the gauged WZW model, and the generic affine-Virasoro action. In one formulation each of these conformal field theories (CFTs) is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation each CFT is written as a two-dimensional field theory, with a three- dimensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translation dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional formulations on the Lie group. Using this dictionary, we also express each CFT as a three-dimensional field theory on the Lie group with a four-dimensional WZW term. 36 refs.
Parafermionic conformal field theory on the lattice
NASA Astrophysics Data System (ADS)
Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul
2014-11-01
Finding the precise correspondence between lattice operators and the continuum fields that describe their long-distance properties is a largely open problem for strongly interacting critical points. Here, we solve this problem essentially completely in the case of the three-state Potts model, which exhibits a phase transition described by a strongly interacting ‘parafermion’ conformal field theory. Using symmetry arguments, insights from integrability, and extensive simulations, we construct lattice analogues of nearly all the relevant and marginal physical fields governing this transition. This construction includes chiral fields such as the parafermion. Along the way we also clarify the structure of operator product expansions between order and disorder fields, which we confirm numerically. Our results both suggest a systematic methodology for attacking non-free field theories on the lattice and find broader applications in the pursuit of exotic topologically ordered phases of matter.
NASA Astrophysics Data System (ADS)
Gammaitoni, Luca; Hänggi, Peter; Jung, Peter; Marchesoni, Fabio
1998-01-01
Over the last two decades, stochastic resonance has continuously attracted considerable attention. The term is given to a phenomenon that is manifest in nonlinear systems whereby generally feeble input information (such as a weak signal) can be be amplified and optimized by the assistance of noise. The effect requires three basic ingredients: (i) an energetic activation barrier or, more generally, a form of threshold; (ii) a weak coherent input (such as a periodic signal); (iii) a source of noise that is inherent in the system, or that adds to the coherent input. Given these features, the response of the system undergoes resonance-like behavior as a function of the noise level; hence the name stochastic resonance. The underlying mechanism is fairly simple and robust. As a consequence, stochastic resonance has been observed in a large variety of systems, including bistable ring lasers, semiconductor devices, chemical reactions, and mechanoreceptor cells in the tail fan of a crayfish. In this paper, the authors report, interpret, and extend much of the current understanding of the theory and physics of stochastic resonance. They introduce the readers to the basic features of stochastic resonance and its recent history. Definitions of the characteristic quantities that are important to quantify stochastic resonance, together with the most important tools necessary to actually compute those quantities, are presented. The essence of classical stochastic resonance theory is presented, and important applications of stochastic resonance in nonlinear optics, solid state devices, and neurophysiology are described and put into context with stochastic resonance theory. More elaborate and recent developments of stochastic resonance theory are discussed, ranging from fundamental quantum properties-being important at low temperatures-over spatiotemporal aspects in spatially distributed systems, to realizations in chaotic maps. In conclusion the authors summarize the achievements
Cutkosky rules for superstring field theory
NASA Astrophysics Data System (ADS)
Pius, Roji; Sen, Ashoke
2016-10-01
Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.
Effective Field Theories, Reductionism and Scientific Explanation
NASA Astrophysics Data System (ADS)
Hartmann, Stephan
Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effective field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispensable. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation.
Drop Breakup in Fixed Bed Flows as Model Stochastic Flow Fields
NASA Technical Reports Server (NTRS)
Shaqfeh, Eric S. G.; Mosler, Alisa B.; Patel, Prateek
1999-01-01
We examine drop breakup in a class of stochastic flow fields as a model for the flow through fixed fiber beds and to elucidate the general mechanisms whereby drops breakup in disordered, Lagrangian unsteady flows. Our study consists of two parallel streams of investigation. First, large scale numerical simulations of drop breakup in a class of anisotropic Gaussian fields will be presented. These fields are generated spectrally and have been shown in a previous publication to be exact representations of the flow in a dilute disordered bed of fibers if close interactions between the fibers and the drops are dynamically unimportant. In these simulations the drop shape is represented by second and third order small deformation theories which have been shown to be excellent for the prediction of drop breakup in steady strong flows. We show via these simulations that the mechanisms of drop breakup in these flows are quite different than in steady flows. The predominant mechanism of breakup appears to be very short lived twist breakups. Moreover, the occurrence of breakup events is poorly predicted by either the strength of the local flow in which the drop finds itself at breakup, or the degree of deformation that the drop achieves prior to breakup. It is suggested that a correlation function of both is necessary to be predictive of breakup events. In the second part of our research experiments are presented where the drop deformation and breakup in PDMS/polyisobutylene emulsions is considered. We consider very dilute emulsions such that coalescence is unimportant. The flows considered are simple shear and the flow through fixed fiber beds. Turbidity, small angle light scattering, dichroism and microscopy are used to interrogate the drop deformation process in both flows. It is demonstrated that breakup at very low capillary numbers occurs in both flows but larger drop deformation occurs in the fixed bed flow. Moreover, it is witnessed that breakup in the bed occurs
Nonequilibrium statistical field theory for classical particles: Basic kinetic theory.
Viermann, Celia; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2015-06-01
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010); J. Stat. Phys. 149, 643 (2012); J. Stat. Phys. 152, 159 (2013); Phys. Rev. E 83, 041125 (2011)] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
Resolving magnetic field line stochasticity and parallel thermal transport in MHD simulations
Nishimura, Y.; Callen, J.D.; Hegna, C.C.
1998-12-31
Heat transport along braided, or chaotic magnetic field lines is a key to understand the disruptive phase of tokamak operations, both the major disruption and the internal disruption (sawtooth oscillation). Recent sawtooth experimental results in the Tokamak Fusion Test Reactor (TFTR) have inferred that magnetic field line stochasticity in the vicinity of the q = 1 inversion radius plays an important role in rapid changes in the magnetic field structures and resultant thermal transport. In this study, the characteristic Lyapunov exponents and spatial correlation of field line behaviors are calculated to extract the characteristic scale length of the microscopic magnetic field structure (which is important for net radial global transport). These statistical values are used to model the effect of finite thermal transport along magnetic field lines in a physically consistent manner.
Exceptional field theory: SO(5,5)
NASA Astrophysics Data System (ADS)
Abzalov, Aidar; Bakhmatov, Ilya; Musaev, Edvard T.
2015-06-01
We construct Exceptional Field Theory for the group SO(5, 5) based on the extended (6+16)-dimensional spacetime, which after reduction gives the maximal D = 6 supergravity. We present both a true action and a duality-invariant pseudo-action formulations. All the fields of the theory depend on the complete extended spacetime. The U-duality group SO(5, 5) is made a geometric symmetry of the theory by virtue of introducing the generalised Lie derivative that incorporates a duality transformation. Tensor hierarchy appears as a natural consequence of the algebra of generalised Lie derivatives that are viewed as gauge transformations. Upon truncating different subsets of the extra coordinates, maximal supergravities in D = 11 and D = 10 (type IIB) can be recovered from this theory.
Stochastic heating and acceleration of electrons in colliding laser fields in plasma.
Sheng, Z-M; Mima, K; Sentoku, Y; Jovanović, M S; Taguchi, T; Zhang, J; Meyer-Ter-Vehn, J
2002-02-01
We propose a mechanism that leads to efficient acceleration of electrons in plasma by two counterpropagating laser pulses. It is triggered by stochastic motion of electrons when the laser fields exceed some threshold amplitudes, as found in single-electron dynamics. It is further confirmed in particle-in-cell simulations. In vacuum or tenuous plasma, electron acceleration in the case with two colliding laser pulses can be much more efficient than with one laser pulse only. In plasma at moderate densities, such as a few percent of the critical density, the amplitude of the Raman-backscattered wave is high enough to serve as the second counterpropagating pulse to trigger the electron stochastic motion. As a result, even with one intense laser pulse only, electrons can be heated up to a temperature much higher than the corresponding laser ponderomotive potential.
Internal additive noise effects in stochastic resonance using organic field effect transistor
NASA Astrophysics Data System (ADS)
Suzuki, Yoshiharu; Matsubara, Kiyohiko; Asakawa, Naoki
2016-08-01
Stochastic resonance phenomenon was observed in organic field effect transistor using poly(3-hexylthiophene), which enhances performance of signal transmission with application of noise. The enhancement of correlation coefficient between the input and output signals was low, and the variation of correlation coefficient was not remarkable with respect to the intensity of external noise, which was due to the existence of internal additive noise following the nonlinear threshold response. In other words, internal additive noise plays a positive role on the capability of approximately constant signal transmission regardless of noise intensity, which can be said "homeostatic" behavior or "noise robustness" against external noise. Furthermore, internal additive noise causes emergence of the stochastic resonance effect even on the threshold unit without internal additive noise on which the correlation coefficient usually decreases monotonically.
Can stochastic, dissipative wave fields be treated as random walk generators
NASA Technical Reports Server (NTRS)
Weinstock, J.
1986-01-01
A suggestion by Meek et al. (1985) that the gravity wave field be viewed as stochastic, with significant nonlinearities, is applied to calculate diffusivities. The purpose here is to calculate the diffusivity for stochastic wave model and compare it with previous diffusivity estimates. The researchers do this for an idealized case in which the wind velocity changes but slowly, and for which saturation is the principal mechanism by which wave energy is lost. A related calculation was given in a very brief way (Weinstock, 1976), but the approximations were not fully justified, nor were the physical pre-suppositions clearly explained. The observations of Meek et al. (1985) have clarified the pre-suppositions for the researchers and provided a rationalization and improvement of the approximations employed.
Field Theory for Multi-Particle System
NASA Astrophysics Data System (ADS)
Wang, Shouhong; Ma, Tian
2016-03-01
The main objectives of this talk are 1) to introduce some basic postulates for quantum multi-particle systems, and 2) to develop a universal field theory for interacting multi-particle systems coupling both particle fields and interacting fields. By carefully examining the nature of interactions between multi-particles, we conclude that multi-particle systems must obey i) the gauge symmetry, ii) the principle of interaction dynamics (PID), and iii) the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint, offers a different and natural way of introducing Higgs fields, and is also required by the presence of dark matter and dark energy and the quark confinement. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). Based on these principles, a few basic postulates for multi-particle systems are introduced in this talk, leading to a field theory for interacting multi-particle systems. A direct consequence of the field theory is the derivation of general atomic spectrum equations. Supported in Part by the Office of Naval Research, by the US National Science Foundation, and by the Chinese National Science Foundation.
Caustic Formation in Tachyon Effective Field Theories
NASA Astrophysics Data System (ADS)
Barnaby, Neil
2004-07-01
Certain configurations of D-branes, for example wrong dimensional branes or the brane-antibrane system, are unstable to decay. This instability is described by the appearance of a tachyonic mode in the spectrum of open strings ending on the brane(s). The decay of these unstable systems is described by the rolling of the tachyon field from the unstable maximum to the minimum of its potential. We analytically study the dynamics of the inhomogeneous tachyon field as it rolls towards the true vacuum of the theory in the context of several different tachyon effective actions. We find that the vacuum dynamics of these theories is remarkably similar and in particular we show that in all cases the tachyon field forms caustics where second and higher derivatives of the field blow up. The formation of caustics signals a pathology in the evolution since each of the effective actions considered is not reliable in the vicinity of a caustic. We speculate that the formation of caustics is an artifact of truncating the tachyon action, which should contain all orders of derivatives acting on the field, to a finite number of derivatives. Finally, we consider inhomogeneous solutions in p-adic string theory, a toy model of the bosonic tachyon which contains derivatives of all orders acting on the field. For a large class of initial conditions we conclusively show that the evolution is well behaved in this case. It is unclear if these caustics are a genuine prediction of string theory or not.
The amplitude of quantum field theory
Medvedev, B.V. ); Pavlov, V.P.; Polivanov, M.K. ); Sukhanov, A.D. )
1989-05-01
General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number.
Magnetic monopoles in field theory and cosmology.
Rajantie, Arttu
2012-12-28
The existence of magnetic monopoles is predicted by many theories of particle physics beyond the standard model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic monopoles in quantum field theory and discuss their implications for particle physics and cosmology. I also highlight their differences and similarities with monopoles found in frustrated magnetic systems.
Klinkusch, Stefan; Tremblay, Jean Christophe
2016-05-14
In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN. PMID:27179472
NASA Astrophysics Data System (ADS)
Klinkusch, Stefan; Tremblay, Jean Christophe
2016-05-01
In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.
Klinkusch, Stefan; Tremblay, Jean Christophe
2016-05-14
In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.
Supergeometry in Locally Covariant Quantum Field Theory
NASA Astrophysics Data System (ADS)
Hack, Thomas-Paul; Hanisch, Florian; Schenkel, Alexander
2016-03-01
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc to S* Alg to the category of super-*-algebras, which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc to eS* Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1|1-dimensions and the free Wess-Zumino model in 3|2-dimensions.
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Effective field theory for deformed atomic nuclei
NASA Astrophysics Data System (ADS)
Papenbrock, T.; Weidenmüller, H. A.
2016-05-01
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Dual field theory of strong interactions
Akers, D.
1987-07-01
A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac charge g = (137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector boson W/sup +/-/. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant ..cap alpha.. = 1/137.
Effective field theory for deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2016-04-13
In this paper, we present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. Finally, for rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Coherent states formulation of polymer field theory
Man, Xingkun; Villet, Michael C.; Delaney, Kris T.; Orland, Henri; Fredrickson, Glenn H.
2014-01-14
We introduce a stable and efficient complex Langevin (CL) scheme to enable the first direct numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards’ well-known auxiliary-field (AF) framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields, and the action of the field theory has a fully explicit, semi-local, and finite-order polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF-CL simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.
Astrophysical data analysis with information field theory
Enßlin, Torsten
2014-12-05
Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
NASA Astrophysics Data System (ADS)
Schwen, E. M.; Mazilu, I.; Mazilu, D. A.
2015-03-01
We introduce a stochastic cooperative model for particle deposition and evaporation relevant to ionic self-assembly of nanoparticles with applications in surface fabrication and nanomedicine, and present a method for mapping our model onto the Ising model. The mapping process allows us to use the established results for the Ising model to describe the steady-state properties of our system. After completing the mapping process, we investigate the time dependence of particle density using the mean field approximation. We complement this theoretical analysis with Monte Carlo simulations that support our model. These techniques, which can be used separately or in combination, are useful as pedagogical tools because they are tractable mathematically and they apply equally well to many other physical systems with nearest-neighbour interactions including voter and epidemic models.
Symmetry analysis for anisotropic field theories
Parra, Lorena; Vergara, J. David
2012-08-24
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
Imaging lateral groundwater flow in the shallow subsurface using stochastic temperature fields
NASA Astrophysics Data System (ADS)
Fairley, Jerry P.; Nicholson, Kirsten N.
2006-04-01
Although temperature has often been used as an indication of vertical groundwater movement, its usefulness for identifying horizontal fluid flow has been limited by the difficulty of obtaining sufficient data to draw defensible conclusions. Here we use stochastic simulation to develop a high-resolution image of fluid temperatures in the shallow subsurface at Borax Lake, Oregon. The temperature field inferred from the geostatistical simulations clearly shows geothermal fluids discharging from a group of fault-controlled hydrothermal springs, moving laterally through the subsurface, and mixing with shallow subsurface flow originating from nearby Borax Lake. This interpretation of the data is supported by independent geochemical and isotopic evidence, which show a simple mixing trend between Borax Lake water and discharge from the thermal springs. It is generally agreed that stochastic simulation can be a useful tool for extracting information from complex and/or noisy data and, although not appropriate in all situations, geostatistical analysis may provide good definition of flow paths in the shallow subsurface. Although stochastic imaging techniques are well known in problems involving transport of species, e.g. delineation of contaminant plumes from soil gas survey data, we are unaware of previous applications to the transport of thermal energy for the purpose of inferring shallow groundwater flow.
The Mean-Field Flux Pinning Theory
NASA Astrophysics Data System (ADS)
Stejic, George
We develop the Mean-Field Flux Pinning Theory, designed to model the flux line lattice (FLL) as it interacts with itself, the flux pinning centers and the geometry of the superconductor. Like other mean-field theories, the mean-field flux pinning theory does not attempt to model the FLL completely. Instead, it utilizes a simplified model for the FLL, termed the mean-field FLL, in which the FLL is modelled as a continuous vector field rather than as discrete fluxons as in other theories. By so doing, the interactions of the FLL are greatly simplified and more easily modelled. One application of the mean-field flux pinning theory is to predict J_{c} from microstructural data, which we use to determine the optimal Nb-Ti microstructures with (1) alpha -Ti pinning centers and (2) Nb pinning centers. The microstructure is modelled on a grid in which the local values of T_{c} and kappa reflect the spatial distribution of the pinning centers and the superconductor. Using this model, we solve the G-L equations and calculate the pinning potential defined as the vortex free energy as a function of position. We conclude that the ideal Nb-Ti microstructure with alpha-Ti pinning centers would require 40 volume percent of alpha -Ti and have 6nm thick pinning centers. In the Nb pinning center case, the ideal microstructure requires 50 volume percent of Nb and would have 6nm pinning centers. Another application for the mean-field flux pinning theory is to model the FLL as it interacts with the penetrating magnetic fields within lambda of the superconducting surface. Using this theory, we study the effects of sample geometry on the FLL and J _{c} for the thin film geometry. We find that the FLL becomes increasingly distorted as the film thickness is reduced and that J_{c } increases sharply for dimensions less that lambda. These predictions are experimentally evaluated in Nb-Ti thin films. Our results show that J_{c} values as high as 1/3 of J_{d} and a strong orientational
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ϕ4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ϕ4 theory, consists in substitution of the local fields ϕ(x) by those dependent on both the position x and the resolution a. The substitution of the action S[ϕ(x)] by the action S[ϕa(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=⟨ϕa1(x1)…ϕan(xn)⟩ finite for any given set of regions by means of an effective cutoff scale A=min(a1,…,an).
Integrable structures in quantum field theory
NASA Astrophysics Data System (ADS)
Negro, Stefano
2016-08-01
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q-operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only.
Dual field theories of quantum computation
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2016-06-01
Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N -torus
Logarithmic conformal field theory: beyond an introduction
NASA Astrophysics Data System (ADS)
Creutzig, Thomas; Ridout, David
2013-12-01
This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with the remarkable observation of Cardy that the horizontal crossing probability of critical percolation may be computed analytically within the formalism of boundary conformal field theory. Cardy’s derivation relies on certain implicit assumptions which are shown to lead inexorably to indecomposable modules and logarithmic singularities in correlators. For this, a short introduction to the fusion algorithm of Nahm, Gaberdiel and Kausch is provided. While the percolation logarithmic conformal field theory is still not completely understood, there are several examples for which the formalism familiar from rational conformal field theory, including bulk partition functions, correlation functions, modular transformations, fusion rules and the Verlinde formula, has been successfully generalized. This is illustrated for three examples: the singlet model \\mathfrak {M} (1,2), related to the triplet model \\mathfrak {W} (1,2), symplectic fermions and the fermionic bc ghost system; the fractional level Wess-Zumino-Witten model based on \\widehat{\\mathfrak {sl}} \\left( 2 \\right) at k=-\\frac{1}{2}, related to the bosonic βγ ghost system; and the Wess-Zumino-Witten model for the Lie supergroup \\mathsf {GL} \\left( 1 {\\mid} 1 \\right), related to \\mathsf {SL} \\left( 2 {\\mid} 1 \\right) at k=-\\frac{1}{2} and 1, the Bershadsky-Polyakov algebra W_3^{(2)} and the Feigin-Semikhatov algebras W_n^{(2)}. These examples have been chosen because they represent the most accessible, and most useful, members of the three best-understood families of logarithmic conformal field theories. The logarithmic minimal models \\mathfrak {W} (q,p), the fractional level Wess-Zumino-Witten models, and the Wess-Zumino-Witten models on Lie supergroups (excluding \\mathsf {OSP} \\left( 1 {\\mid} 2n \\right)). In this review, the emphasis lies on the representation theory
Causality constraints in conformal field theory
NASA Astrophysics Data System (ADS)
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-01
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂ ϕ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.
Bipartite field theories from D-branes
NASA Astrophysics Data System (ADS)
Franco, Sebastián; Uranga, Angel
2014-04-01
We develop tools for determining the gauge theory resulting from a configuration of Type IIB D3-branes probing a non-compact, toric Calabi-Yau 3-fold, in the presence of additional flavor D7-branes with general embeddings. Two main ingredients of our approach are dimer models and mirror symmetry. D7-branes with general embeddings are obtained by recombination of elementary D7-brane constituents. These tools are then used to engineer a large set of Bipartite Field Theories, a class of 4d, = 1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. Several explicit examples, including infinite families of models, associated to both planar and non-planar graphs are presented.
Scalar field theory on fuzzy S 4
NASA Astrophysics Data System (ADS)
Medina, Julieta; O'Connor, Denjoe
2003-11-01
Scalar fields are studied on fuzzy S 4 and a solution is found for the elimination of the unwanted degrees of freedom that occur in the model. The resulting theory can be interpreted as a Kaluza-Klein reduction of Bbb CP3 to S 4 in the fuzzy context.
Cross Sections From Scalar Field Theory
NASA Technical Reports Server (NTRS)
Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel
2008-01-01
A one pion exchange scalar model is used to calculate differential and total cross sections for pion production through nucleon- nucleon collisions. The collisions involve intermediate delta particle production and decay to nucleons and a pion. The model provides the basic theoretical framework for scalar field theory and can be applied to particle production processes where the effects of spin can be neglected.
Field Theory of the Quantum Kicked Rotor
Altland, A.; Zirnbauer, M.R.
1996-11-01
The quantum kicked rotor is investigated by field theoretical methods. It is shown that the effective theory describing the long wavelength physics of the system is precisely the supersymmetric nonlinear {sigma} model for quasi-one-dimensional metallic wires. This proves that the analogy between chaotic systems with dynamical localization and disordered metals can indeed be exact. The role of symmetries is discussed.
Dirac-Kaehler Theory and Massless Fields
Pletyukhov, V. A.; Strazhev, V. I.
2010-03-24
Three massless limits of the Dirac-Kaehler theory are considered. It is shown that the Dirac-Kaehler equation for massive particles can be represented as a result of the gauge-invariant mixture (topological interaction) of the above massless fields.
Perturbative quantum gravity in double field theory
NASA Astrophysics Data System (ADS)
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Recent Progress in Group Field Theory
Oriti, Daniele
2009-12-15
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical definition of these models, and possible avenues towards extracting interesting physics from them.
Ross, J.
1992-09-16
Thermodynamics of the transport processes of diffusion, thermal conduction, and viscous flow at a macroscopic level are developed for the simplest cases of one-dimensional transport in fluids for individual linear and nonlinear processes approaching a stationary non-equilibrium state. Formulation has started of thermodynamic and stochastic theory of combinations of transport processes. Global thermodynamic and stochastic theory of open chemical systems frar from equilibrium is continued with analysis of a broad class of isothermal, multicomponent reaction mechanisms with multiple steady states with assumed local equilibrium. Stationary solutions are obtained of the master equation for single and multi-intermediate autocatalytic chemical systems. A kinetic potential is identified that governs the deterministic time evolution of coupled tank reactors. A second-order response theory was developed to investigate the effects of external periodic perturbations on a chemical reaction at a stable steady state in an open reactor.
Quantum field theories on manifolds with curved boundaries: Scalar fields
NASA Astrophysics Data System (ADS)
McAvity, D. M.; Osborn, H.
1993-04-01
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the Green function for second-order differential operators valid in the neighbourhood of the boundary and which is obtained from a corresponding expansion of the associated heat kernel derived earlier for arbitrary mixed Dirichlet and Neumann boundary conditions. The first few leading terms in the expansion are sufficient to calculate all additional divergences present in a perturbative loop expansion as a consequence of the presence of the boundary. The method is applied to a general renormalisable scalar field theory in four dimensions using dimensional regularisation to two loops and expanding about arbitrary background fields. Detailed results are also specialised to an O( n) symmetric model with a single coupling constant. Extra boundary terms are introduced into the action which give rise to either Dirichlet orgeneralized Neumann boundary conditions for the quantum fields. For plane boundaries the resulting renormalisation group functions are in accord with earlier results but here the additional terms depending on the extrinsic curvature of the boundary are found. Various consistency relations are also checked and the implications of conformal invariance at the critical point where the β-function vanishes are also derived. For a general scalar field theory, where the fieldsø attain specified values ϕ in the boundary, the local Schrödinger equation for the wave functional defined by the functional integral under deformations of the boundary is also verified to two loops. The perturbative expansion for the wave functional is defined by expansion around the solution of the classical field equations satisfying the required boundary values and the counterterms necessary to derive a finite hamiltonian operator, which includes a functional Laplace operator on the fields ϕ, are
NASA Astrophysics Data System (ADS)
Eichhorn, Ralf; Aurell, Erik
2014-04-01
theory for small deviations from equilibrium, in which a general framework is constructed from the analysis of non-equilibrium states close to equilibrium. In a next step, Prigogine and others developed linear irreversible thermodynamics, which establishes relations between transport coefficients and entropy production on a phenomenological level in terms of thermodynamic forces and fluxes. However, beyond the realm of linear response no general theoretical results were available for quite a long time. This situation has changed drastically over the last 20 years with the development of stochastic thermodynamics, revealing that the range of validity of thermodynamic statements can indeed be extended deep into the non-equilibrium regime. Early developments in that direction trace back to the observations of symmetry relations between the probabilities for entropy production and entropy annihilation in non-equilibrium steady states [5-8] (nowadays categorized in the class of so-called detailed fluctuation theorems), and the derivations of the Bochkov-Kuzovlev [9, 10] and Jarzynski relations [11] (which are now classified as so-called integral fluctuation theorems). Apart from its fundamental theoretical interest, the developments in stochastic thermodynamics have experienced an additional boost from the recent experimental progress in fabricating, manipulating, controlling and observing systems on the micro- and nano-scale. These advances are not only of formidable use for probing and monitoring biological processes on the cellular, sub-cellular and molecular level, but even include the realization of a microscopic thermodynamic heat engine [12] or the experimental verification of Landauer's principle in a colloidal system [13]. The scientific program Stochastic Thermodynamics held between 4 and 15 March 2013, and hosted by The Nordic Institute for Theoretical Physics (Nordita), was attended by more than 50 scientists from the Nordic countries and elsewhere, amongst them
Extending Gurwitsch's field theory of consciousness.
Yoshimi, Jeff; Vinson, David W
2015-07-01
Aron Gurwitsch's theory of the structure and dynamics of consciousness has much to offer contemporary theorizing about consciousness and its basis in the embodied brain. On Gurwitsch's account, as we develop it, the field of consciousness has a variable sized focus or "theme" of attention surrounded by a structured periphery of inattentional contents. As the field evolves, its contents change their status, sometimes smoothly, sometimes abruptly. Inner thoughts, a sense of one's body, and the physical environment are dominant field contents. These ideas can be linked with (and help unify) contemporary theories about the neural correlates of consciousness, inattention, the small world structure of the brain, meta-stable dynamics, embodied cognition, and predictive coding in the brain.
Effective Field Theory for Jet Processes.
Becher, Thomas; Neubert, Matthias; Rothen, Lorena; Shao, Ding Yu
2016-05-13
Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom that are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the nonglobal logarithms.
NASA Astrophysics Data System (ADS)
Bershadskii, A.
1994-10-01
The quantitative (scaling) results of a recent lattice-gas simulation of granular flows [1] are interpreted in terms of Kolmogorov-Obukhov approach revised for strong space-intermittent systems. Renormalised power spectrum with exponent '-4/3' seems to be an universal spectrum of scalar fluctuations convected by stochastic velocity fields in dissipative systems with inverse energy transfer (some other laboratory and geophysic turbulent flows with this power spectrum as well as an analogy between this phenomenon and turbulent percolation on elastic backbone are pointed out).
Phase-field modeling of epitaxial growth in stochastic systems with interacting adsorbate
NASA Astrophysics Data System (ADS)
Kharchenko, Dmitrii O.; Kharchenko, Vasyl O.; Lysenko, Irina O.
2011-04-01
We study the epitaxial growth of pyramidal patterns in stochastic systems with interacting adsorbate within the framework of the phase-field approach based on the Burton-Cabrera-Frank model. Considering the statistical criteria of pattern formation, it is shown that the system dynamics is governed by the interaction strength of adatoms and the noise intensity of the total flux fluctuations. We have shown that the noise action can crucially change the processes of pyramidal pattern formation. The scaling behavior of the height-height correlation function is discussed.
The effects of noise on binocular rivalry waves: a stochastic neural field model
NASA Astrophysics Data System (ADS)
Webber, Matthew A.; Bressloff, Paul C.
2013-03-01
We analyze the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. We use our analysis to calculate the first-passage-time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation lead to quenched disorder in the neural fields during propagation of a wave.
Inflation and deformation of conformal field theory
Garriga, Jaume; Urakawa, Yuko E-mail: yurakawa@ffn.ub.es
2013-07-01
It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation ζ and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.
Matrix field theory: Applications to superconductivity
NASA Astrophysics Data System (ADS)
Zhou, Lubo
In this thesis a systematic, functional matrix field theory is developed to describe both clean and disordered s-wave and d-wave superconductors and the quantum phase transitions associated with them. The thesis can be divided into three parts. The first part includes chapters 1 to 3. In chapter one a general physical introduction is given. In chapters two and three the theory is developed and used to compute the equation of state as well as the number-density susceptibility, spin-density susceptibility, the sound attenuation coefficient, and the electrical conductivity in both clean and disordered s-wave superconductors. The second part includes chapter four. In this chapter we use the theory to describe the disorder-induced metal - superconductor quantum phase transition. The key physical idea here is that in addition to the superconducting order-parameter fluctuations, there are also additional soft fermionic fluctuations that are important at the transition. We develop a local field theory for the coupled fields describing superconducting and soft fermionic fluctuations. Using simple renormalization group and scaling ideas, we exactly determine the critical behavior at this quantum phase transition. Our theory justifies previous approaches. The third part includes chapter five. In this chapter we study the analogous quantum phase transition in disordered d-wave superconductors. This theory should be related to high Tc superconductors. Surprisingly, we show that in both the underdoped and overdoped regions, the coupling of superconducting fluctuations to the soft disordered fermionic fluctuations is much weaker than that in the s-wave case. The net result is that the disordered quantum phase transition in this case is a strong coupling, or described by an infinite disordered fixed point, transition and cannot be described by the perturbative RG description that works so well in the s-wave case. The transition appears to be related to the one that occurs in
Perturbation theory, effective field theory, and oscillations in the power spectrum
NASA Astrophysics Data System (ADS)
Vlah, Zvonimir; Seljak, Uroš; Yat Chu, Man; Feng, Yu
2016-03-01
We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and if stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with k and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model. We show that if primordial oscillations are localized to a scale q, the wiggles in power spectrum are approximately suppressed as exp[-k2Σ2(q)/2], where Σ(q) is rms displacement of particles separated by q, which saturates on large scales, and decreases as q is reduced. No oscillatory features survive past k ~ 0.5h/Mpc at z = 0.
Alpha particles in effective field theory
Caniu, C.
2014-11-11
Using an effective field theory for alpha (α) particles at non-relativistic energies, we calculate the strong scattering amplitude modified by Coulomb corrections for a system of two αs. For the strong interaction, we consider a momentum-dependent interaction which, in contrast to an energy dependent interaction alone [1], could be more useful in extending the theory to systems with more than two α particles. We will present preliminary results of our EFT calculations for systems with two alpha particles.
Birnbaum; Patton; Lott
1999-01-01
This study tests between two modern theories of decision making. Rank- and sign-dependent utility (RSDU) models, including cumulative prospect theory (CPT), imply stochastic dominance and two cumulative independence conditions. Configural weight models, with parameters estimated in previous research, predict systematic violations of these properties for certain choices. Experimental data systematically violate all three properties, contrary to RSDU but consistent with configural weight models. This study also tests whether violations of stochastic dominance can be explained by violations of transitivity. Violations of transitivity may be evidence of a dominance detecting mechanism. Although some transitivity violations were observed, most choice triads violated stochastic dominance without violating transitivity. Judged differences between gambles were not consistent with the CPT model. Data were not consistent with the editing principles of cancellation and combination. The main findings are interpreted in terms of coalescing, the principle that equal outcomes can be combined in a gamble by adding their probabilities. RSDU models imply coalescing but configural weight models violate it, allowing configural weighting to explain violations of stochastic dominance and cumulative independence. Copyright 1999 Academic Press.
A Field Theory Problem Relating to Questions in Hyperfield Theory
NASA Astrophysics Data System (ADS)
Massouros, Ch. G.
2011-09-01
M. Krasner introduced the notions of the hypefield and the hyperring in 1956. Much later, he constructed the quotient hyperfield/hyperrring, using a field/ring and a subgroup of its multiplicative group/semigroup. The existence of non-quotient hyperfields and hyperrings was an essential question for the self-sufficiency of the theory of hyperfields and hyperrings vis-à-vis that of fields and rings. The momogene hyperfield, which was introduced by the author, is a hyperfield H having the property x - x = H for all x≠0. The existence of non-quotient monogene hyperfields is a hitherto open question. The answer to this question is directly connected with the answer to the question which fields can be expressed as a difference of a subgroup of their multiplicative group from itself and which these subgroups are. These issues, as well as some relevant theorems are presented in this paper.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Weiss mean-field approximation for multicomponent stochastic spatially extended systems.
Kurushina, Svetlana E; Maximov, Valerii V; Romanovskii, Yurii M
2014-08-01
We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system, which describes a well-known model of autocatalytic chemical reaction (brusselator) with spatially correlated multiplicative noise, and to study the evolution of probability density and statistical characteristics of the system in the process of spatial pattern formation. We propose the finite-difference method for the numerical solving of a general class of multivariate nonlinear self-consistent time-dependent Fokker-Planck equations. We illustrate the accuracy and reliability of the method by applying it to an exactly solvable nonlinear Fokker-Planck equation (NFPE) for the Shimizu-Yamada model [Prog. Theor. Phys. 47, 350 (1972)] and nonlinear Fokker-Planck equation [Desai and Zwanzig, J. Stat. Phys. 19, 1 (1978)] obtained for a nonlinear stochastic mean-field model introduced by Kometani and Shimizu [J. Stat. Phys. 13, 473 (1975)]. Taking the problems indicated above as an example, the accuracy of the method is compared with the accuracy of Hermite distributed approximating functional method [Zhang et al., Phys. Rev. E 56, 1197 (1997)]. Numerical study of the NFPE solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple "repumping" of probability density through bimodality. Additionally, we study the behavior of the order parameter of the system under consideration and show that the second type of solution arises in the supercritical region if noise intensity values are close to the values appropriate for the transition from bimodal stationary probability density for the order parameter to the unimodal one. PMID:25215716
Weiss mean-field approximation for multicomponent stochastic spatially extended systems
NASA Astrophysics Data System (ADS)
Kurushina, Svetlana E.; Maximov, Valerii V.; Romanovskii, Yurii M.
2014-08-01
We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system, which describes a well-known model of autocatalytic chemical reaction (brusselator) with spatially correlated multiplicative noise, and to study the evolution of probability density and statistical characteristics of the system in the process of spatial pattern formation. We propose the finite-difference method for the numerical solving of a general class of multivariate nonlinear self-consistent time-dependent Fokker-Planck equations. We illustrate the accuracy and reliability of the method by applying it to an exactly solvable nonlinear Fokker-Planck equation (NFPE) for the Shimizu-Yamada model [Prog. Theor. Phys. 47, 350 (1972), 10.1143/PTP.47.350] and nonlinear Fokker-Planck equation [Desai and Zwanzig, J. Stat. Phys. 19, 1 (1978), 10.1007/BF01020331] obtained for a nonlinear stochastic mean-field model introduced by Kometani and Shimizu [J. Stat. Phys. 13, 473 (1975), 10.1007/BF01013146]. Taking the problems indicated above as an example, the accuracy of the method is compared with the accuracy of Hermite distributed approximating functional method [Zhang et al., Phys. Rev. E 56, 1197 (1997), 10.1103/PhysRevE.56.1197]. Numerical study of the NFPE solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple "repumping" of probability density through bimodality. Additionally, we study the behavior of the order parameter of the system under consideration and show that the second type of solution arises in the supercritical region if noise intensity values are close to the values appropriate for the transition from bimodal stationary probability density
A master functional for quantum field theory
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2013-04-01
We study a new generating functional of one-particle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The usual functional Γ does not behave as a scalar under the transformation law inherited from its very definition as the Legendre transform of W=ln Z, although it does behave as a scalar under an unusual transformation law. The master functional, on the other hand, is the Legendre transform of an improved functional W with respect to the sources coupled to both elementary and composite fields. The inclusion of certain improvement terms in W and Z is necessary to make this new Legendre transform well defined. The master functional behaves as a scalar under the transformation law inherited from its very definition. Moreover, it admits a proper formulation, obtained extending the set of integrated fields to so-called proper fields, which allows us to work without passing through Z, W or Γ. In the proper formulation the classical action coincides with the classical limit of the master functional, and correlation functions and renormalization are calculated applying the usual diagrammatic rules to the proper fields. Finally, the most general change of field variables, including the map relating bare and renormalized fields, is a linear redefinition of the proper fields.
Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes
Buividovich, P. V.
2011-02-15
We propose a stochastic method for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of the so-called nonlinear random processes. The set of all the histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators. We illustrate the method on examples of the matrix-valued scalar field theory and the Weingarten model of random planar surfaces on the lattice. For theories with compact field variables, such as sigma models or non-Abelian lattice gauge theories, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into a self-consistent redefinition of expansion parameters. A stochastic solution of the self-consistency conditions can be implemented as a 'memory' of the random process, so that some parameters of the process are estimated from its previous history. We illustrate this idea on the two-dimensional O(N) sigma model. The extension to non-Abelian lattice gauge theories is discussed.
Relative entropies in conformal field theory.
Lashkari, Nima
2014-08-01
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance.
Relative entropies in conformal field theory.
Lashkari, Nima
2014-08-01
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance. PMID:25126908
Theory of Stochastic Dipolar Recoupling in Solid State Nuclear Magnetic Resonance
Tycko, Robert
2008-01-01
Dipolar recoupling techniques in solid state nuclear magnetic resonance (NMR) consist of radio-frequency (rf) pulse sequences applied in synchrony with magic-angle spinning (MAS) that create non-zero average magnetic dipole-dipole couplings under MAS. Stochastic dipolar recoupling (SDR) is a variant in which randomly chosen rf carrier frequency offsets are introduced to cause random phase modulations of individual pairwise couplings in the dipolar spin Hamiltonian. Several aspects of SDR are investigated through analytical theory and numerical simulations: (1) An analytical expression for the evolution of nuclear spin polarization under SDR in a two-spin system is derived and verified through simulations, which show a continuous evolution from coherent, oscillatory polarization exchange to incoherent, exponential approach to equilibrium as the range of random carrier offsets (controlled by a parameter fmax) increases; (2) In a many-spin system, polarization transfers under SDR are shown to be described accurately by a rate matrix in the limit of large fmax, with pairwise transfer rates that are proportional to the inverse sixth power of pairwise internuclear distances; (3) Quantum mechanical interferences among non-commuting pairwise dipole-dipole couplings, which are a complicating factor in solid state NMR studies of molecular structures by traditional dipolar recoupling methods, are shown to be absent from SDR data in the limit of large fmax, provided that coupled nuclei have distinct NMR chemical shifts. PMID:18085769
Theory of stochastic dipolar recoupling in solid-state nuclear magnetic resonance.
Tycko, Robert
2008-05-15
Dipolar recoupling techniques in solid-state nuclear magnetic resonance (NMR) consist of radio frequency (rf) pulse sequences applied in synchrony with magic-angle spinning (MAS) that create nonzero average magnetic dipole-dipole couplings under MAS. Stochastic dipolar recoupling (SDR) is a variant in which randomly chosen rf carrier frequency offsets are introduced to cause random phase modulations of individual pairwise couplings in the dipolar spin Hamiltonian. Several aspects of SDR are investigated through analytical theory and numerical simulations: (1) An analytical expression for the evolution of nuclear spin polarization under SDR in a two-spin system is derived and verified through simulations, which show a continuous evolution from coherent, oscillatory polarization exchange to incoherent, exponential approach to equilibrium as the range of random carrier offsets (controlled by a parameter f(max)) increases; (2) in a many-spin system, polarization transfers under SDR are shown to be described accurately by a rate matrix in the limit of large f(max), with pairwise transfer rates that are proportional to the inverse sixth power of pairwise internuclear distances; (3) quantum mechanical interferences among noncommuting pairwise dipole-dipole couplings, which are a complicating factor in solid-state NMR studies of molecular structures by traditional dipolar recoupling methods, are shown to be absent from SDR data in the limit of large f(max), provided that coupled nuclei have distinct NMR chemical shifts. PMID:18085769
NASA Astrophysics Data System (ADS)
Rosso, O. A.; Masoller, C.
2009-05-01
We show that Information Theory quantifiers are suitable tools for detecting and for quantifying noise-induced temporal correlations in stochastic resonance phenomena. We use the Bandt & Pompe (BP) method [Phys. Rev. Lett. 88, 174102 (2002)] to define a probability distribution, P, that fully characterizes temporal correlations. The BP method is based on a comparison of neighboring values, and here is applied to the temporal sequence of residence-time intervals generated by the paradigmatic model of a Brownian particle in a sinusoidally modulated bistable potential. The probability distribution P generated via the BP method has associated a normalized Shannon entropy, H[P], and a statistical complexity measure, C[P], which is defined as proposed by Rosso et al. [Phys. Rev. Lett. 99, 154102 (2007)]. The statistical complexity quantifies not only randomness but also the presence of correlational structures, the two extreme circumstances of maximum knowledge (“perfect order") and maximum ignorance (“complete randomness") being regarded an “trivial", and in consequence, having complexity C = 0. We show that both, H and C, display resonant features as a function of the noise intensity, i.e., for an optimal level of noise the entropy displays a minimum and the complexity, a maximum. This resonant behavior indicates noise-enhanced temporal correlations in the sequence of residence-time intervals. The methodology proposed here has great potential for the precise detection of subtle signatures of noise-induced temporal correlations in real-world complex signals.
Interpretation of non-Markovian stochastic Schroedinger equations as a hidden-variable theory
Gambetta, Jay; Wiseman, H.M.
2003-12-01
Do diffusive non-Markovian stochastic Schroedinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function z(t) appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value z(t) even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system 'conditioned' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit.
Electron residual energy due to stochastic heating in field-ionized plasma
Khalilzadeh, Elnaz; Yazdanpanah, Jam Chakhmachi, Amir; Jahanpanah, Jafar; Yazdani, Elnaz
2015-11-15
The electron residual energy originated from the stochastic heating in under-dense field-ionized plasma is investigated here. Initially, the optical response of plasma is modeled by using two counter-propagating electromagnetic waves. In this case, the solution of motion equation of a single electron indicates that by including the ionization, the electron with higher residual energy compared with that without ionization could be obtained. In agreement with chaotic nature of the motion, it is found that the electron residual energy will be significantly changed by applying a minor change in the initial conditions. Extensive kinetic 1D-3V particle-in-cell simulations have been performed in order to resolve full plasma reactions. In this way, two different regimes of plasma behavior are observed by varying the pulse length. The results indicate that the amplitude of scattered fields in a proper long pulse length is high enough to act as a second counter-propagating wave and trigger the stochastic electron motion. On the contrary, the analyses of intensity spectrum reveal the fact that the dominant scattering mechanism tends to Thomson rather than Raman scattering by increasing the pulse length. A covariant formalism is used to describe the plasma heating so that it enables us to measure electron temperature inside and outside of the pulse region.
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Quantitative field theory of the glass transition
Franz, Silvio; Jacquin, Hugo; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco
2012-01-01
We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the hypernetted chain approximation for the Gibbs free energy, and we find results that are consistent with numerical simulations. PMID:23112202
Effective field theory for lattice nuclei.
Barnea, N; Contessi, L; Gazit, D; Pederiva, F; van Kolck, U
2015-02-01
We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in LQCD simulations carried out at pion masses heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron, and triton LQCD energies at m_{π}≈800 MeV, we reproduce the corresponding alpha-particle binding and predict the binding energies of mass-5 and mass-6 ground states. PMID:25699436
Effective Field Theory for Rydberg Polaritons.
Gullans, M J; Thompson, J D; Wang, Y; Liang, Q-Y; Vuletić, V; Lukin, M D; Gorshkov, A V
2016-09-01
We develop an effective field theory (EFT) to describe the few- and many-body propagation of one-dimensional Rydberg polaritons. We show that the photonic transmission through the Rydberg medium can be found by mapping the propagation problem to a nonequilibrium quench, where the role of time and space are reversed. We include effective range corrections in the EFT and show that they dominate the dynamics near scattering resonances in the presence of deep bound states. Finally, we show how the long-range nature of the Rydberg-Rydberg interactions induces strong effective N-body interactions between Rydberg polaritons. These results pave the way towards studying nonperturbative effects in quantum field theories using Rydberg polaritons. PMID:27661685
Double field theory on group manifolds
NASA Astrophysics Data System (ADS)
Blumenhagen, Ralph; Hassler, Falk; Lüst, Dieter
2015-02-01
A new version of double field theory (DFT) is derived for the exactly solvable background of an in general left-right asymmetric WZW model in the large level limit. This generalizes the original DFT that was derived via expanding closed string field theory on a torus up to cubic order. The action and gauge transformations are derived for fluctuations around the generalized group manifold background up to cubic order, revealing the appearance of a generalized Lie derivative and a corresponding C-bracket upon invoking a new version of the strong constraint. In all these quantities a background dependent covariant derivative appears reducing to the partial derivative for a toroidal background. This approach sheds some new light on the conceptual status of DFT, its background (in-)dependence and the up-lift of non-geometric Scherk-Schwarz reductions.
Wu, Wei; Wang, Jin
2013-09-28
We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is
Higher spin double field theory: a proposal
NASA Astrophysics Data System (ADS)
Bekaert, Xavier; Park, Jeong-Hyuck
2016-07-01
We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to O(4, 4) T-duality, doubled diffeomorphisms, Spin(1, 3) local Lorentz symmetry and, separately, HS(4) higher spin gauge symmetry. We identify a minimal set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.
Large gauge transformations in double field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Zwiebach, Barton
2013-02-01
Finite gauge transformations in double field theory can be defined by the exponential of generalized Lie derivatives. We interpret these transformations as `generalized coordinate transformations' in the doubled space by proposing and testing a formula that writes large transformations in terms of derivatives of the coordinate maps. Successive generalized coordinate transformations give a generalized coordinate transformation that differs from the direct composition of the original two. Instead, it is constructed using the Courant bracket. These transformations form a group when acting on fields but, intriguingly, do not associate when acting on coordinates.
Bosonic Dynamical Mean-Field Theory
NASA Astrophysics Data System (ADS)
Snoek, Michiel; Hofstetter, Walter
2013-02-01
We derive the bosonic dynamical mean-field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbours. Hence the theory is applicable in sufficiently high-dimensional lattices. We apply the method to a two-component mixture, for which a rich phase diagram with spin order is revealed.
A dual theory of price and value in a meso-scale economic model with stochastic profit rate
NASA Astrophysics Data System (ADS)
Greenblatt, R. E.
2014-12-01
The problem of commodity price determination in a market-based, capitalist economy has a long and contentious history. Neoclassical microeconomic theories are based typically on marginal utility assumptions, while classical macroeconomic theories tend to be value-based. In the current work, I study a simplified meso-scale model of a commodity capitalist economy. The production/exchange model is represented by a network whose nodes are firms, workers, capitalists, and markets, and whose directed edges represent physical or monetary flows. A pair of multivariate linear equations with stochastic input parameters represent physical (supply/demand) and monetary (income/expense) balance. The input parameters yield a non-degenerate profit rate distribution across firms. Labor time and price are found to be eigenvector solutions to the respective balance equations. A simple relation is derived relating the expected value of commodity price to commodity labor content. Results of Monte Carlo simulations are consistent with the stochastic price/labor content relation.
Backreacted axion field ranges in string theory
NASA Astrophysics Data System (ADS)
Baume, Florent; Palti, Eran
2016-08-01
String theory axions are interesting candidates for fields whose potential might be controllable over super-Planckian field ranges and therefore as possible candidates for inflatons in large field inflation. Axion monodromy scenarios are setups where the axion shift symmetry is broken by some effect such that the axion can traverse a large number of periods potentially leading to super-Planckian excursions. We study such scenarios in type IIA string theory where the axion shift symmetry is broken by background fluxes. In particular we calculate the backreaction of the energy density induced by the axion vacuum expectation value on its own field space metric. We find universal behaviour for all the compactifications studied where up to a certain critical axion value there is only a small backreaction effect. Beyond the critical value the backreaction is strong and implies that the proper field distance as measured by the backreacted metric increases at best logarithmically with the axion vev, thereby placing strong limitations on extending the field distance any further. The critical axion value can be made arbitrarily large by the choice of fluxes. However the backreaction of these fluxes on the axion field space metric ensures a precise cancellation such that the proper field distance up to the critical axion value is flux independent and remains sub-Planckian. We also study an axion alignment scenario for type IIA compactifications on a twisted torus with four fundamental axions mixing to leave an axion with an effective decay constant which is flux dependent. There is a choice of fluxes for which the alignment parameter controlling the effective decay constant is unconstrained by tadpoles and can in principle lead to an arbitrarily large effective decay constant. However we show that these fluxes backreact on the fundamental decay constants so as to precisely cancel any enhancement leaving a sub-Planckian effective decay constant.
Veron, Dana E
2009-03-12
This project had two primary goals: 1) development of stochastic radiative transfer as a parameterization that could be employed in an AGCM environment, and 2) exploration of the stochastic approach as a means for representing shortwave radiative transfer through mixed-phase layer clouds. To achieve these goals, an analysis of the performance of the stochastic approach was performed, a simple stochastic cloud-radiation parameterization for an AGCM was developed and tested, a statistical description of Arctic mixed phase clouds was developed and the appropriateness of stochastic approach for representing radiative transfer through mixed-phase clouds was assessed. Significant progress has been made in all of these areas and is detailed below.
Dana E. Veron
2012-04-09
This project had two primary goals: (1) development of stochastic radiative transfer as a parameterization that could be employed in an AGCM environment, and (2) exploration of the stochastic approach as a means for representing shortwave radiative transfer through mixed-phase layer clouds. To achieve these goals, climatology of cloud properties was developed at the ARM CART sites, an analysis of the performance of the stochastic approach was performed, a simple stochastic cloud-radiation parameterization for an AGCM was developed and tested, a statistical description of Arctic mixed phase clouds was developed and the appropriateness of stochastic approach for representing radiative transfer through mixed-phase clouds was assessed. Significant progress has been made in all of these areas and is detailed in the final report.
The effective field theory of inflation
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Fitzpatrick, A. Liam; Kaplan, Jared; Senatore, Leonardo; Creminelli, Paolo
2008-03-01
We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g^{00} and K_{mu nu}, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.
Pomraning, G.C.
1997-05-01
The goal in this research was to continue the development of a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. Such a theory should predict the ensemble average and higher moments, such as the variance, of the particle or energy density described by the underlying transport/kinetic equation. The statistics studied correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components in the mixture. The mixing statistics considered were Markovian as well as more general statistics. In the absence of time dependence and scattering, the theory is well developed and described exactly by the master (Liouville) equation for Markovian mixing, and by renewal equations for non-Markovian mixing. The intent of this research was to generalize these treatments to include both time dependence and scattering. A further goal of this research was to develop approximate, but simpler, models from any comprehensive theory. In particular, a specific goal was to formulate a renormalized transport/kinetic theory of the usual nonstochastic form, but with effective interaction coefficients and sources to account for the stochastic nature of the problem. In the three and one-half year period of research summarized in this final report, they have made substantial progress in the development of a comprehensive theory of kinetic processes in stochastic mixtures. This progress is summarized in 16 archival journal articles, 7 published proceedings papers, and 2 comprehensive review articles. In addition, 17 oral presentations were made describing these research results.
Du Kai Qiu, Jinniao Tang Shanjian
2012-04-15
This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L{sup p}-theory is given for the Cauchy problem of BSPDEs, separately for the case of p Element-Of (1,2] and for the case of p Element-Of (2,{infinity}). A comparison theorem is also addressed.
Stochastic approach to correlations beyond the mean field with the Skyrme interaction
Fukuoka, Y.; Nakatsukasa, T.; Funaki, Y.; Yabana, K.
2012-10-20
Large-scale calculation based on the multi-configuration Skyrme density functional theory is performed for the light N=Z even-even nucleus, {sup 12}C. Stochastic procedures and the imaginary-time evolution are utilized to prepare many Slater determinants. Each state is projected on eigenstates of parity and angular momentum. Then, performing the configuration mixing calculation with the Skyrme Hamiltonian, we obtain low-lying energy-eigenstates and their explicit wave functions. The generated wave functions are completely free from any assumption and symmetry restriction. Excitation spectra and transition probabilities are well reproduced, not only for the ground-state band, but for negative-parity excited states and the Hoyle state.
3D stochastic inversion and joint inversion of potential fields for multi scale parameters
NASA Astrophysics Data System (ADS)
Shamsipour, Pejman
In this thesis we present the development of new techniques for the interpretation of potential field (gravity and magnetic data), which are the most widespread economic geophysical methods used for oil and mineral exploration. These new techniques help to address the long-standing issue with the interpretation of potential fields, namely the intrinsic non-uniqueness inversion of these types of data. The thesis takes the form of three papers (four including Appendix), which have been published, or soon to be published, in respected international journals. The purpose of the thesis is to introduce new methods based on 3D stochastical approaches for: 1) Inversion of potential field data (magnetic), 2) Multiscale Inversion using surface and borehole data and 3) Joint inversion of geophysical potential field data. We first present a stochastic inversion method based on a geostatistical approach to recover 3D susceptibility models from magnetic data. The aim of applying geostatistics is to provide quantitative descriptions of natural variables distributed in space or in time and space. We evaluate the uncertainty on the parameter model by using geostatistical unconditional simulations. The realizations are post-conditioned by cokriging to observation data. In order to avoid the natural tendency of the estimated structure to lay near the surface, depth weighting is included in the cokriging system. Then, we introduce algorithm for multiscale inversion, the presented algorithm has the capability of inverting data on multiple supports. The method involves four main steps: i. upscaling of borehole parameters (It could be density or susceptibility) to block parameters, ii. selection of block to use as constraints based on a threshold on kriging variance, iii. inversion of observation data with selected block densities as constraints, and iv. downscaling of inverted parameters to small prisms. Two modes of application are presented: estimation and simulation. Finally, a novel
Naruse, Makoto; Akahane, Kouichi; Yamamoto, Naokatsu; Holmström, Petter; Thylén, Lars; Huant, Serge; Ohtsu, Motoichi
2014-04-21
We theoretically and experimentally demonstrate energy transfer mediated by optical near-field interactions in a multi-layer InAs quantum dot (QD) structure composed of a single layer of larger dots and N layers of smaller ones. We construct a stochastic model in which optical near-field interactions that follow a Yukawa potential, QD size fluctuations, and temperature-dependent energy level broadening are unified, enabling us to examine device-architecture-dependent energy transfer efficiencies. The model results are consistent with the experiments. This study provides an insight into optical energy transfer involving inherent disorders in materials and paves the way to systematic design principles of nanophotonic devices that will allow optimized performance and the realization of designated functions.
NASA Astrophysics Data System (ADS)
Sochi, Taha
2016-09-01
Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel-Bulkley, Ellis, Ree-Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.
GAMMA-RAY BURST PROMPT EMISSION: JITTER RADIATION IN STOCHASTIC MAGNETIC FIELD REVISITED
Mao, Jirong; Wang Jiancheng
2011-04-10
We revisit the radiation mechanism of relativistic electrons in the stochastic magnetic field and apply it to the high-energy emissions of gamma-ray bursts (GRBs). We confirm that jitter radiation is a possible explanation for GRB prompt emission in the condition of a large electron deflection angle. In the turbulent scenario, the radiative spectral property of GRB prompt emission is decided by the kinetic energy spectrum of turbulence. The intensity of the random and small-scale magnetic field is determined by the viscous scale of the turbulent eddy. The microphysical parameters {epsilon}{sub e} and {epsilon}{sub B} can be obtained. The acceleration and cooling timescales are estimated as well. Due to particle acceleration in magnetized filamentary turbulence, the maximum energy released from the relativistic electrons can reach a value of about 10{sup 14} eV. The GeV GRBs are possible sources of high-energy cosmic-ray.
Stochastic generation of explicit pore structures by thresholding Gaussian random fields
Hyman, Jeffrey D.; Winter, C. Larrabee
2014-11-15
We provide a description and computational investigation of an efficient method to stochastically generate realistic pore structures. Smolarkiewicz and Winter introduced this specific method in pores resolving simulation of Darcy flows (Smolarkiewicz and Winter, 2010 [1]) without giving a complete formal description or analysis of the method, or indicating how to control the parameterization of the ensemble. We address both issues in this paper. The method consists of two steps. First, a realization of a correlated Gaussian field, or topography, is produced by convolving a prescribed kernel with an initial field of independent, identically distributed random variables. The intrinsic length scales of the kernel determine the correlation structure of the topography. Next, a sample pore space is generated by applying a level threshold to the Gaussian field realization: points are assigned to the void phase or the solid phase depending on whether the topography over them is above or below the threshold. Hence, the topology and geometry of the pore space depend on the form of the kernel and the level threshold. Manipulating these two user prescribed quantities allows good control of pore space observables, in particular the Minkowski functionals. Extensions of the method to generate media with multiple pore structures and preferential flow directions are also discussed. To demonstrate its usefulness, the method is used to generate a pore space with physical and hydrological properties similar to a sample of Berea sandstone. -- Graphical abstract: -- Highlights: •An efficient method to stochastically generate realistic pore structures is provided. •Samples are generated by applying a level threshold to a Gaussian field realization. •Two user prescribed quantities determine the topology and geometry of the pore space. •Multiple pore structures and preferential flow directions can be produced. •A pore space based on Berea sandstone is generated.
A comparison between the quasi-species evolution and stochastic quantization of fields
NASA Astrophysics Data System (ADS)
Bianconi, G.; Rahmede, C.
2012-06-01
The quasi-species equation describes the evolution of the probability that a random individual in a population carries a given genome. Here we map the quasi-species equation for individuals of a self-reproducing population to an ensemble of scalar field elementary units undergoing a creation and annihilation process. In this mapping, the individuals of the population are mapped to field units and their genome to the field value. The selective pressure is mapped to an inverse temperature β of the system regulating the evolutionary dynamics of the fields. We show that the quasi-species equation if applied to an ensemble of field units gives in the small β limit can be put in relation with existing stochastic quantization approaches. The ensemble of field units described by the quasi-species equation relaxes to the fundamental state, describing an intrinsically dissipative dynamics. For a quadratic dispersion relation the mean energy ⟨U⟩ of the system changes as a function of the inverse temperature β. For small values of β the average energy ⟨U⟩ takes a relativistic form, for large values of β, the average energy ⟨U⟩ takes a classical form.
NASA Astrophysics Data System (ADS)
Ghodsi, Seyed Hamed; Kerachian, Reza; Estalaki, Siamak Malakpour; Nikoo, Mohammad Reza; Zahmatkesh, Zahra
2016-02-01
In this paper, two deterministic and stochastic multilateral, multi-issue, non-cooperative bargaining methodologies are proposed for urban runoff quality management. In the proposed methodologies, a calibrated Storm Water Management Model (SWMM) is used to simulate stormwater runoff quantity and quality for different urban stormwater runoff management scenarios, which have been defined considering several Low Impact Development (LID) techniques. In the deterministic methodology, the best management scenario, representing location and area of LID controls, is identified using the bargaining model. In the stochastic methodology, uncertainties of some key parameters of SWMM are analyzed using the info-gap theory. For each water quality management scenario, robustness and opportuneness criteria are determined based on utility functions of different stakeholders. Then, to find the best solution, the bargaining model is performed considering a combination of robustness and opportuneness criteria for each scenario based on utility function of each stakeholder. The results of applying the proposed methodology in the Velenjak urban watershed located in the northeastern part of Tehran, the capital city of Iran, illustrate its practical utility for conflict resolution in urban water quantity and quality management. It is shown that the solution obtained using the deterministic model cannot outperform the result of the stochastic model considering the robustness and opportuneness criteria. Therefore, it can be concluded that the stochastic model, which incorporates the main uncertainties, could provide more reliable results.
Mathematics of small stochastic reaction networks: A boundary layer theory for eigenstate analysis
NASA Astrophysics Data System (ADS)
Mjolsness, Eric; Prasad, Upendra
2013-03-01
We study and analyze the stochastic dynamics of a reversible bimolecular reaction A + B ↔ C called the "trivalent reaction." This reaction is of a fundamental nature and is part of many biochemical reaction networks. The stochastic dynamics is given by the stochastic master equation, which is difficult to solve except when the equilibrium state solution is desired. We present a novel way of finding the eigenstates of this system of difference-differential equations, using perturbation analysis of ordinary differential equations arising from approximation of the difference equations. The time evolution of the state probabilities can then be expressed in terms of the eigenvalues and the eigenvectors.
NASA Astrophysics Data System (ADS)
Ren, W. X.; Lin, Y. Q.; Fang, S. E.
2011-11-01
One of the key issues in vibration-based structural health monitoring is to extract the damage-sensitive but environment-insensitive features from sampled dynamic response measurements and to carry out the statistical analysis of these features for structural damage detection. A new damage feature is proposed in this paper by using the system matrices of the forward innovation model based on the covariance-driven stochastic subspace identification of a vibrating system. To overcome the variations of the system matrices, a non-singularity transposition matrix is introduced so that the system matrices are normalized to their standard forms. For reducing the effects of modeling errors, noise and environmental variations on measured structural responses, a statistical pattern recognition paradigm is incorporated into the proposed method. The Mahalanobis and Euclidean distance decision functions of the damage feature vector are adopted by defining a statistics-based damage index. The proposed structural damage detection method is verified against one numerical signal and two numerical beams. It is demonstrated that the proposed statistics-based damage index is sensitive to damage and shows some robustness to the noise and false estimation of the system ranks. The method is capable of locating damage of the beam structures under different types of excitations. The robustness of the proposed damage detection method to the variations in environmental temperature is further validated in a companion paper by a reinforced concrete beam tested in the laboratory and a full-scale arch bridge tested in the field.
NASA Astrophysics Data System (ADS)
Ohdachi, Satoshi; Watanabe, Kiyomasa; Sakakibara, Satoru; Suzuki, Yasuhiro; Tsuchiya, Hayato; Ming, Tingfeng; Du, Xiaodi; LHD Expriment Group Team
2014-10-01
In the Large Helical Device (LHD), the plasma is surrounded by the so-called magnetic stochastic region, where the Kolmogorov length of the magnetic field lines is very short, from several tens of meters and to thousands meters. Finite pressure gradient are formed in this region and MHD instabilities localized in this region is observed since the edge region of the LHD is always unstable against the pressure driven mode. Therefore, the saturation level of the instabilities is the key issue in order to evaluate the risk of this kind of MHD instabilities. The saturation level depends on the pressure gradient and on the magnetic Reynolds number; there results are similar to the MHD mode in the closed magnetic surface region. The saturation level in the stochastic region is affected also by the stocasticity itself. Parameter dependence of the saturation level of the MHD activities in the region is discussed in detail. It is supported by NIFS budget code ULPP021, 028 and is also partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research 26249144, by the JSPS-NRF-NSFC A3 Foresight Program NSFC: No. 11261140328.
Effective field theory of cosmological perturbations
NASA Astrophysics Data System (ADS)
Piazza, Federico; Vernizzi, Filippo
2013-11-01
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.
Aspects of hot Galilean field theory
NASA Astrophysics Data System (ADS)
Jensen, Kristan
2015-04-01
We reconsider general aspects of Galilean-invariant thermal field theory. Using the proposal of our companion paper, we recast non-relativistic hydrodynamics in a manifestly covariant way and couple it to a background spacetime. We examine the concomitant consequences for the thermal partition functions of Galilean theories on a time-independent, but weakly curved background. We work out both the hydrodynamics and partition functions in detail for the example of parity-violating normal fluids in two dimensions to first order in the gradient expansion, finding results that differ from those previously reported in the literature. As for relativistic field theories, the equality-type constraints imposed by the existence of an entropy current appear to be in one-to-one correspondence with those arising from the existence of a hydrostatic partition function. Along the way, we obtain a number of useful results about non-relativistic hydrodynamics, including a manifestly boost-invariant presentation thereof, simplified Ward identities, the systematics of redefinitions of the fluid variables, and the positivity of entropy production.
Inhomogeneous field theory inside the arctic circle
NASA Astrophysics Data System (ADS)
Allegra, Nicolas; Dubail, Jérôme; Stéphan, Jean-Marie; Viti, Jacopo
2016-05-01
Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic circle phenomenon, namely a spatial phase separation between a critically fluctuating region and a frozen region. Large-scale correlations inside the critical region are expressed in terms of correlators in a (euclidean) two-dimensional massless Dirac field theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac theory in curved space. The technique used to solve the toy-model is then extended to deal with the transfer matrices of other models: dimers on the honeycomb and square lattice, and the six-vertex model at the free fermion point (Δ =0 ). In all cases, explicit expressions are given for the long-range correlations in the critical region, as well as for the underlying Dirac action. Although the setup developed here is heavily based on fermionic observables, the results can be translated into the language of height configurations and of the gaussian free field, via bosonization. Correlations close to the phase boundary and the generic appearance of Airy processes in all these models are also briefly revisited in the appendix.
Causality constraints in conformal field theory
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-17
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well knownmore » sign constraint on the (Φ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. As a result, our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators« less
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio; Meljanac, Stjepan
2010-07-15
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
Lenormand, R.; Thiele, M.R.
1997-08-01
The paper describes the method and presents preliminary results for the calculation of homogenized relative permeabilities
Working Group Report: Lattice Field Theory
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Effective field theory with two Higgs doublets
NASA Astrophysics Data System (ADS)
Crivellin, Andreas; Ghezzi, Margherita; Procura, Massimiliano
2016-09-01
In this article we extend the effective field theory framework describing new physics effects to the case where the underlying low-energy theory is a Two-Higgs-Doublet model. We derive a complete set of independent operators up to dimension six assuming a Z 2-invariant CP-conserving Higgs potential. The effects on Higgs and gauge boson masses, mixing angles in the Higgs sector as well as couplings to fermions and gauge bosons are computed. At variance with the case of a single Higgs doublet, we find that pair production of SM-like Higgses, arising through dimension-six operators, is not fixed by fermion-fermion-Higgs couplings and can therefore be sizable.
The effective field theory of dark energy
NASA Astrophysics Data System (ADS)
Gubitosi, Giulia; Piazza, Federico; Vernizzi, Filippo
2013-02-01
We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.
Nonequilibrium dynamical mean-field theory
NASA Astrophysics Data System (ADS)
Freericks, James
2007-03-01
Dynamical mean-field theory (DMFT) is establishing itself as one of the most powerful approaches to the quantum many-body problem in strongly correlated electron materials. Recently, the formalism has been generalized to study nonequilibrium problems [1,2], such as the evolution of Bloch oscillations in a material that changes from a diffusive metal to a Mott insulator [2,3]. Using a real-time formalism on the Kadanoff-Baym-Keldysh contour, the DMFT algorithm can be generalized to the case of systems that are not time-translation invariant. The computational algorithm has a parallel implementation with essentially a linear scale up when running on thousands of processors. Results on the decay of Bloch oscillations, their change of character within the Mott insulator, and movies on how electrons redistribute themselves due to their response to an external electrical field will be presented. In addition to solid-state applications, this work also applies to the behavior of mixtures of light and heavy cold atoms in optical lattices. [1] V. M. Turkowski and J. K. Freericks, Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields, Phys. Rev. B 075108 (2006); Erratum, Phys. Rev. B 73, 209902(E) (2006). [2] J. K. Freericks, V. M. Turkowski , and V. Zlati'c, Nonlinear response of strongly correlated materials to large electric fields, in Proceedings of the HPCMP Users Group Conference 2006, Denver, CO, June 26--29, 2006 edited by D. E. Post (IEEE Computer Society, Los Alamitos, CA, 2006), to appear. [3] J. K. Freericks, V. M. Turkowski, and V. Zlati'c, Nonequilibrium dynamical mean-field theory, submitted to Phys. Rev. Lett. cond-mat//0607053.
QCD unitarity constraints on Reggeon Field Theory
NASA Astrophysics Data System (ADS)
Kovner, Alex; Levin, Eugene; Lublinsky, Michael
2016-08-01
We point out that the s-channel unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun's Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a "black disk limit" as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature.
Theory of microemulsions in a gravitational field
NASA Technical Reports Server (NTRS)
Jeng, J. F.; Miller, Clarence A.
1989-01-01
A theory of microemulsions developed previously is extended to include the effect of a gravitational field. It predicts variation with position of drop size, drop volume fraction, and area per molecule in the surfactant films within a microemulsion phase. Variation in volume fraction is greatest and occurs in such a way that oil content increases with increasing elevation, as has been found experimentally. Large composition variations are predicted within a middle phase microemulsion near optimal conditions because inversion from the water-continuous to the oil-continuous arrangement occurs with increasing elevation. Generally speaking, gravity reduces solubilization within microemulsions and promotes separation of excess phases.
Temperature Gradient Field Theory of Nucleation
NASA Astrophysics Data System (ADS)
Das, S.; Ain, W. Q.; Azhari, A.; Prasada Rao, A. K.
2016-02-01
According to the proposed theory, ceramic particles present in molten metal, lose heat at a slower rate than the metallic liquid during cooling. Such condition results in the formation of a spherical thermal gradient field (TGF) around each particle. Hence, the interstitials (low temperature) of such TGFs are the regions to reach the nucleation temperature first, owing to low energy barrier than the liquid-particle interface (higher temperature). Analytics also indicate that the nucleation rate is higher at the TGF interstitials, than at the liquid-particle interface. Such TGF network results in simultaneous nucleation throughout the system, resulting in grain refinement.
Purely cubic action for string field theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
A matrix model from string field theory
NASA Astrophysics Data System (ADS)
Zeze, Syoji
2016-09-01
We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and U(N) vectors which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both for finite and large N. Increase of potential height is observed in both cases. The large N matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.
Pauli-Villars regulatization of supergravity and field theory anomalies
Gaillard, M.K.
1995-06-01
A procedure for Pauli-Villars regularization of locally and globally supersymmetric theories is described. Implications for specific theories, especially those obtained from superstrings, are discussed with emphasis on the role of field theory anomalies.
Leonard, T.; Lander, B.; Seifert, U.; Speck, T.
2013-11-28
We discuss the stochastic thermodynamics of systems that are described by a time-dependent density field, for example, simple liquids and colloidal suspensions. For a time-dependent change of external parameters, we show that the Jarzynski relation connecting work with the change of free energy holds if the time evolution of the density follows the Kawasaki-Dean equation. Specifically, we study the work distributions for the compression and expansion of a two-dimensional colloidal model suspension implementing a practical coarse-graining scheme of the microscopic particle positions. We demonstrate that even if coarse-grained dynamics and density functional do not match, the fluctuation relations for the work still hold albeit for a different, apparent, change of free energy.
Ballardini, Mario
2015-10-01
We consider the impact of a stochastic background of primordial magnetic fields with non-vanishing helicity on CMB anisotropies in temperature and polarization. We compute the exact expressions for the scalar, vector and tensor part of the energy-momentum tensor including the helical contribution, by assuming a power-law dependence for the spectra and a comoving cutoff which mimics the damping due to viscosity. We also compute the parity-odd correlator between the helical and non-helical contribution which generate the TB and EB cross-correlation in the CMB pattern. We finally show the impact of including the helical term on the power spectra of CMB anisotropies up to multipoles with ℓ ∼ O(10{sup 3})
1D Runoff-runon stochastic model in the light of queueing theory : heterogeneity and connectivity
NASA Astrophysics Data System (ADS)
Harel, M.-A.; Mouche, E.; Ledoux, E.
2012-04-01
Runoff production on a hillslope during a rainfall event may be simplified as follows. Given a soil of constant infiltrability I, which is the maximum amount of water that the soil can infiltrate, and a constant rainfall intensity R, runoff is observed where R is greater than I. The infiltration rate equals the infiltrability when runoff is produced, R otherwise. When ponding time, topography, and overall spatial and temporal variations of physical parameters, such as R and I, are neglected, the runoff equation remains simple. In this study, we consider soils of spatially variable infiltrability. As runoff can re-infiltrate on down-slope areas of higher infiltrabilities (runon), the resulting process is highly non-linear. The stationary runoff equation is: Qn+1 = max(Qn + (R - In)*Δx , 0) where Qn is the runoff arriving on pixel n of size Δx [L2/T], R and In the rainfall intensity and infiltrability on that same pixel [L/T]. The non-linearity is due to the dependence of infiltration on R and Qn, that is runon. This re-infiltration process generates patterns of runoff along the slope, patterns that organise and connect to each other differently depending on the rainfall intensity and the nature of the soil heterogeneity. The runoff connectivity, assessed using the connectivity function of Allard (1993), affects greatly the dynamics of the runoff hillslope. Our aim is to assess, in a stochastic framework, the runoff organization on 1D slopes with random infiltrabilities (log-normal, exponential, bimodal and uniform distributions) by means of theoretical developments and numerical simulations. This means linking the nature of soil heterogeneity with the resulting runoff organisation. In term of connectivity, we investigate the relations between structural (infiltrability) and functional (runoff) connectivity. A theoretical framework based on the queueing theory is developed. We implement the idea of Jones et al. (2009), who remarked that the above formulation is
PT-Symmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2011-09-01
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
Causality Is Inconsistent With Quantum Field Theory
Wolf, Fred Alan
2011-11-29
Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non-vanishing probabilities for both negative energy particles in the forward-through-time direction and positive energy antiparticles in the backwards-through-time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.
Conformal field theory of critical Casimir forces
NASA Astrophysics Data System (ADS)
Emig, Thorsten; Bimonte, Giuseppe; Kardar, Mehran
2015-03-01
Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two dimensional conformal field theories (CFT) we derive exact results for the Casimir interaction for a deformed strip and for two compact objects of arbitrary shape in terms of the free energy of a standard region (circular ring or flat strip) whose dimension is determined by the mutual capacitance of two conductors with the objects' shape; and a purely geometric energy that is proportional to conformal charge of the CFT, but otherwise super-universal in that it depends only on the shapes and is independent of boundary conditions and other details. The effect of inhomogenous boundary conditions is also discussed.
A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach
NASA Astrophysics Data System (ADS)
Lacroix, Denis; Tanimura, Yusuke; Ayik, Sakir; Yilmaz, Bulent
2016-04-01
The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here that this approach is equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-, ..., N -body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for short time evolution. In that case, it gives information on the evolution time-scale close to a saddle point associated to a quantum phase-transition. For long time evolution and strong coupling, we observed that the simplified BBGKY hierarchy cannot be truncated and only the full SMF with initial sampling leads to reasonable results.
Ramond equations of motion in superstring field theory
NASA Astrophysics Data System (ADS)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo
2015-11-01
We extend the recently constructed NS superstring field theories in the small Hilbert space to give classical field equations for all superstring theories, including Ramond sectors. We also comment on the realization of supersymmetry in this framework.
Entanglement negativity in quantum field theory.
Calabrese, Pasquale; Cardy, John; Tonni, Erik
2012-09-28
We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρ(A)(T(2) of the reduced density matrix of a subsystem [formula: see text], and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=ln//ρ(A)(T(2))//. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E~(c/4)ln[ℓ(1)ℓ(2)/(ℓ(1)+ℓ(2))] for the case of two adjacent intervals of lengths ℓ(1), ℓ(2) in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain.
The effective field theory treatment of quantum gravity
Donoghue, John F.
2012-09-24
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.
Investigations of low-dimensional field theories
NASA Astrophysics Data System (ADS)
Shifrin, Leonid
Spontaneous chiral symmetry breaking plays an important role in the low-energy dynamics of QCD. The nonzero chiral condensate is related to the non-zero density of small Dirac eigenvalues through the Banks-Casher relation. Further, the low-energy QCD Dirac spectrum has to satisfy a family of universal consistency relations called Leutwyler-Smilga (LS) spectral sum rules. We discuss these sum rules in the closely related to QCD but much simpler 2-dimensional Schwinger model. The dynamics of the two theories share chiral anomaly, topologically non-trivial vacuum, instantons, dynamical mass generation and confinement. While LS sum rules are the same for both theories, in the Schwinger model it is possible to achieve a more detailed microscopic understanding of them. We give three different derivations of LS sum rules in the Schwinger Model. The first is based on the clustering property of fermionic correlators and is also valid for 1-flavor QCD. The second is an exact microscopic (field theory) derivation. The third relies on 2D bosonization. Next, we discuss the clustering property for the multi-flavor QCD. It is shown that standard clustering is violated in the chiral limit, and a modified clustering relation is derived. Then we consider multi-flavor Schwinger model, and discuss the spectral density and mass dependence of the chiral condensate in the thermodynamic limit. The relation to Random Fermion models used in condensed matter physics is also discussed here. Relations with the Random Matrix Theory and the so called spectral duality are discussed next. Finally, we comment briefly on the remaining unsolved problems and relevance to lattice studies.
Marginally Relevant Topics in Conformal Field Theories
NASA Astrophysics Data System (ADS)
Cleary, Kevin Francis
We consider a set of topics in conformal field theory. We provide an example of a 4D theory that exhibits the Contino-Pomarol-Rattazzi mechanism, where breaking conformal symmetry by an almost marginal operator leads to a light pseudo-Goldstone boson, the dilaton, and a parametrically suppressed contribution to vacuum energy. We consider SUSY QCD at the edge of the conformal window and break conformal symmetry by weakly gauging a subgroup of the flavor symmetry. Using Seiberg duality we show that for a range of parameters the singlet meson in the dual theory reaches the unitarity bound, however, this theory does not have a stable vacuum. We stabilize the vacuum with soft breaking terms, compute the mass of the dilaton, and determine the range of parameters where the leading contribution to the dilaton mass is from the almost marginal coupling. We also weigh in on a widely held belief that increasing bounds on the gluino mass, which feeds down to the stop mass through renormalization group running, are making a light stop increasingly unlikely. Here we present a counter-example. We examine the case of the Minimal Composite Supersymmetric Standard Model which has a light composite stop. The large anomalous dimension of the stop from strong dynamics pushes the stop mass toward a quasi-fixed point in the infrared, which is smaller than standard estimates by a factor of a large logarithm. The gluino can be about three times heavier than the stop, which is comparable to hierarchy achieved with supersoft Dirac gluino masses. Thus, in this class of models, a heavy gluino is not necessarily indicative of a heavy stop.
Quantum field theory of K-mouflage
NASA Astrophysics Data System (ADS)
Brax, Philippe; Valageas, Patrick
2016-08-01
We consider K-mouflage models, which are K-essence theories coupled to matter. We analyze their quantum properties and in particular the quantum corrections to the classical Lagrangian. We setup the renormalization program for these models and show that, contrary to renormalizable field theories where renormalization by infinite counterterms can be performed in one step, K-mouflage theories involve a recursive construction whereby each set of counterterms introduces new divergent quantum contributions which in turn must be subtracted by new counterterms. This tower of counterterms can be in principle constructed step by step by recursion and allows one to calculate the finite renormalized action of the model. In particular, it can be checked that the classical action is not renormalized and that the finite corrections to the renormalized action contain only higher-derivative operators. We concentrate then on the regime where calculability is ensured, i.e., when the corrections to the classical action are negligible. We establish an operational criterion for classicality and show that this is satisfied in cosmological and astrophysical situations for (healthy) K-mouflage models which pass the solar system tests. These results rely on perturbation theory around a background and are only valid when the background configuration is quantum stable. We analyze the quantum stability of astrophysical and cosmological backgrounds and find that models that pass the solar system tests are quantum stable. We then consider the possible embedding of the K-mouflage models in an UV completion. We find that the healthy models which pass the solar system tests all violate the positivity constraint which would follow from the unitarity of the putative UV completion, implying that these healthy K-mouflage theories have no UV completion. We then analyze their behavior at high energy, and we find that the classicality criterion is satisfied in the vicinity of a high-energy collision
Combining Wind-Tunnel and Field Measurements of Street-Canyon Flow via Stochastic Estimation
NASA Astrophysics Data System (ADS)
Perret, Laurent; Blackman, Karin; Savory, Eric
2016-06-01
We demonstrate how application of the stochastic estimation method can be employed to combine spatially well-resolved wind-tunnel particle image velocimetry measurements with instantaneous velocity signals from a limited number of sensors (six sonic anemometers located within the canyon in the present case) to predict full-scale flow dynamics in an entire street-canyon cross-section. The investigated configuration corresponds to a street-canyon flow in a neutrally stratified atmospheric boundary layer with the oncoming flow being perpendicular to the main canyon axis. Data were obtained during both full-scale and 1:200-scale wind-tunnel experiments. The performance of the proposed method is investigated using both wind-tunnel data and signals from five sonic anemometers to predict the velocity from the sixth one. In particular, based on analysis of the influence of the high-frequency velocity fluctuations on the quality of the reconstruction, it is shown that stochastic estimation is able to correctly reproduce the large-scale temporal features of the flow with the present set-up. The full dataset is then used to spatially extrapolate the instantaneous flow measured by the six sonic anemometers and perform detailed analysis of instantaneous flow features. The main features of the flow, such as the presence of the shear layer that develops over the canyon and the intermittent ejection and penetration events across the canyon opening, are well predicted by stochastic estimation. In addition, thanks to the high spatial resolution made possible by the technique, the intermittency of the main vortical structure existing within the canyon is demonstrated, as well as its meandering motion in the canyon cross-section. It is also shown that the canyon flow, particularly its spanwise component, is affected by large-scale fluctuations of low temporal frequency along the canyon axis. Finally, the proposed techniques based on wind-tunnel data can prove useful for a priori
Stochastic generation of explicit pore structures by thresholding Gaussian random fields
NASA Astrophysics Data System (ADS)
Hyman, Jeffrey D.; Winter, C. Larrabee
2014-11-01
We provide a description and computational investigation of an efficient method to stochastically generate realistic pore structures. Smolarkiewicz and Winter introduced this specific method in pores resolving simulation of Darcy flows (Smolarkiewicz and Winter, 2010 [1]) without giving a complete formal description or analysis of the method, or indicating how to control the parameterization of the ensemble. We address both issues in this paper. The method consists of two steps. First, a realization of a correlated Gaussian field, or topography, is produced by convolving a prescribed kernel with an initial field of independent, identically distributed random variables. The intrinsic length scales of the kernel determine the correlation structure of the topography. Next, a sample pore space is generated by applying a level threshold to the Gaussian field realization: points are assigned to the void phase or the solid phase depending on whether the topography over them is above or below the threshold. Hence, the topology and geometry of the pore space depend on the form of the kernel and the level threshold. Manipulating these two user prescribed quantities allows good control of pore space observables, in particular the Minkowski functionals. Extensions of the method to generate media with multiple pore structures and preferential flow directions are also discussed. To demonstrate its usefulness, the method is used to generate a pore space with physical and hydrological properties similar to a sample of Berea sandstone.
Stochastic conversions of TeV photons into axion-like particles in extragalactic magnetic fields
Mirizzi, Alessandro; Montanino, Daniele E-mail: daniele.montanino@le.infn.it
2009-12-01
Very-high energy photons emitted by distant cosmic sources are absorbed on the extragalactic background light (EBL) during their propagation. This effect can be characterized in terms of a photon transfer function at Earth. The presence of extragalactic magnetic fields could also induce conversions between very high-energy photons and hypothetical axion-like particles (ALPs). The turbulent structure of the extragalactic magnetic fields would produce a stochastic behaviour in these conversions, leading to a statistical distribution of the photon transfer functions for the different realizations of the random magnetic fields. To characterize this effect, we derive new equations to calculate the mean and the variance of this distribution. We find that, in presence of ALP conversions, the photon transfer functions on different lines of sight could have relevant deviations with respect to the mean value, producing both an enhancement or a suppression in the observable photon flux with respect to the expectations with only absorption. As a consequence, the most striking signature of the mixing with ALPs would be a reconstructed EBL density from TeV photon observations which appears to vary over different directions of the sky: consistent with standard expectations in some regions, but inconsistent in others.
Stochastic properties of the geomagnetic field across the 210 mm chain
NASA Astrophysics Data System (ADS)
Wanliss, J. A.; Shiokawa, K.; Yumoto, K.
2013-12-01
We explore the stochastic fractal qualities of the geomagnetic field from 210 mm ground-based magnetometers during quiet and active magnetospheric conditions. We search through 10 years of these data to find events that qualify. Quiet intervals are defined by Kp ≤ 1 for 1,440 consecutive minutes. Similarly, active intervals require Kp ≥ 4 for 1,440 consecutive minutes. The total for quiet intervals is ~4.3×106 minutes and 2×108 minutes for active data points. With this large number of events compiled we then characterize changes in the nonlinear statistics of the geomagnetic field via measurements of a fractal scaling exponent. A clear difference in statistical behavior during quiet and active intervals is implied through analysis of the scaling exponents; active intervals generally have larger values of scaling exponents. This means that although 210 mm data appears monofractal on shorter timescales, it is more properly described as a multifractional Brownian motion. Long-range statistical behavior of the geomagnetic field at a local observation site can be described as a multifractional Brownian motion, thus suggesting the statistical structure required of mathematical models of magnetospheric activity. We also find that low-latitudes have scaling exponents that are consistently larger than for high-latitudes.
An overview of stochastic modeling of groundwater flow and transport: From theory to applications
NASA Astrophysics Data System (ADS)
Dagan, Gedeon
The stochastic modeling of groundwater has developed considerably in the last twenty years and a large body of knowledge has accumulated. However, there is also room for criticism: the community has evolved into a specialized one and research has started to address esoteric topics. Furthermore, in spite of its expansion, the stochastic approach hasn't yet become a routine tool of hydrological modeling.The main message of this article is an appeal for application of stochastic modeling to practical problems on a regular basis (see motto above). This is regarded as a task of utmost importance and high priority Furthermore, in spite of outstanding problems, it is surmised that the accumulated knowledge makes it possible.
Laboratory evidence for stochastic plasma-wave growth.
Austin, D R; Hole, M J; Robinson, P A; Cairns, Iver H; Dallaqua, R
2007-11-16
The first laboratory confirmation of stochastic growth theory is reported. Floating potential fluctuations are measured in a vacuum arc centrifuge using a Langmuir probe. Statistical analysis of the energy density reveals a lognormal distribution over roughly 2 orders of magnitude, with a high-field nonlinear cutoff whose spatial dependence is consistent with the predicted eigenmode profile. These results are consistent with stochastic growth and nonlinear saturation of a spatially extended eigenmode, the first evidence for stochastic growth of an extended structure.
Laboratory Evidence for Stochastic Plasma-Wave Growth
NASA Astrophysics Data System (ADS)
Austin, D. R.; Hole, M. J.; Robinson, P. A.; Cairns, Iver H.; Dallaqua, R.
2007-11-01
The first laboratory confirmation of stochastic growth theory is reported. Floating potential fluctuations are measured in a vacuum arc centrifuge using a Langmuir probe. Statistical analysis of the energy density reveals a lognormal distribution over roughly 2 orders of magnitude, with a high-field nonlinear cutoff whose spatial dependence is consistent with the predicted eigenmode profile. These results are consistent with stochastic growth and nonlinear saturation of a spatially extended eigenmode, the first evidence for stochastic growth of an extended structure.
Laboratory Evidence for Stochastic Plasma-Wave Growth
Austin, D. R.; Hole, M. J.; Robinson, P. A.; Cairns, Iver H.; Dallaqua, R.
2007-11-16
The first laboratory confirmation of stochastic growth theory is reported. Floating potential fluctuations are measured in a vacuum arc centrifuge using a Langmuir probe. Statistical analysis of the energy density reveals a lognormal distribution over roughly 2 orders of magnitude, with a high-field nonlinear cutoff whose spatial dependence is consistent with the predicted eigenmode profile. These results are consistent with stochastic growth and nonlinear saturation of a spatially extended eigenmode, the first evidence for stochastic growth of an extended structure.
Stochastic Simulation of Precipitation Fields Conditioned on Radar and Gauge Information
NASA Astrophysics Data System (ADS)
Pfaff, T.; Bárdossy, A.
2009-04-01
Precipitation is the main input variable for hydrological modelling. Operational precipitation data are usually provided by rain gauges, weather radar and sometimes satellite observations., Precipitation data with very high spatial and temporal resolution is necessary especially for flash flood forecasting in small catchments. Usually these can neither be provided by rain gauge networks nor satellite measurements. However, radar data has not been used widely in operational flood forecasting yet. Modelling results obtained with radar derived precipitation forcing still don't show a better skill than those obtained by using gauge observations. Radar data suffers from a set of errors. The common ones are uncertainties in the Z-R relation, attenuation effects and uncertain vertical profiles of reflectivity. Corrections for any of these errors have been devised but it has also been shown that some corrections just shift the uncertainty from one source to another. Since the 'true' rainfall field cannot be known, true error statistics cannot be calculated. A measure of uncertainty can be obtained by comparing radar (R) and gauge data (G). Recent developments towards radar ensemble generation focus on the generation of relative uncertainty fields. They are based on comparisons of radar data with gauge data or of radar fields with reference fields obtained by gauge adjustment. The generated fields are then multiplied with the radar field to create the realizations. The proposed approach aims at stochastic simulation of precipitation fields conditioned on radar data In addition, the approach incorporates the additional information available from gauge measurements similarly to radar gauge adjustment. If radar data is adjusted by gauge data using either a multiplicative or an additive correction term, this single correction term can produce unrealistic results when it is regionalized to the radar cells surrounding the reference gauge. This problem can be avoided by splitting
Quadratic α‧-corrections to heterotic double field theory
NASA Astrophysics Data System (ADS)
Lee, Kanghoon
2015-10-01
We investigate α‧-corrections of heterotic double field theory up to quadratic order in the language of supersymmetric O (D, D + dim G) gauged double field theory. After introducing double-vielbein formalism with a parametrization which reproduces heterotic supergravity, we show that supersymmetry for heterotic double field theory up to leading order α‧-correction is obtained from supersymmetric gauged double field theory. We discuss the necessary modifications of the symmetries defined in supersymmetric gauged double field theory. Further, we construct supersymmetric completion at quadratic order in α‧.
Machine Learning for Dynamical Mean Field Theory
NASA Astrophysics Data System (ADS)
Arsenault, Louis-Francois; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Littlewood, P. B.; Millis, Andy
2014-03-01
Machine Learning (ML), an approach that infers new results from accumulated knowledge, is in use for a variety of tasks ranging from face and voice recognition to internet searching and has recently been gaining increasing importance in chemistry and physics. In this talk, we investigate the possibility of using ML to solve the equations of dynamical mean field theory which otherwise requires the (numerically very expensive) solution of a quantum impurity model. Our ML scheme requires the relation between two functions: the hybridization function describing the bare (local) electronic structure of a material and the self-energy describing the many body physics. We discuss the parameterization of the two functions for the exact diagonalization solver and present examples, beginning with the Anderson Impurity model with a fixed bath density of states, demonstrating the advantages and the pitfalls of the method. DOE contract DE-AC02-06CH11357.
Takiff superalgebras and conformal field theory
NASA Astrophysics Data System (ADS)
Babichenko, Andrei; Ridout, David
2013-03-01
A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an Abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalization of Sugawara’s construction is shown to give rise to a copy of the Virasoro algebra and so, presumably, to a conformal field theory. Evidence for this is detailed for the extension of the affinization of the superalgebra \\mathfrak {gl} ( 1 \\vert 1): its highest weight irreducible modules are classified using spectral flow, the irreducible supercharacters are computed and a continuum version of the Verlinde formula is verified to give non-negative integer structure coefficients. Interpreting these coefficients as those of the Grothendieck ring of fusion, partial results on the true fusion ring and its indecomposable structures are deduced.
Generalized Gibbs ensembles for quantum field theories
NASA Astrophysics Data System (ADS)
Essler, F. H. L.; Mussardo, G.; Panfil, M.
2015-05-01
We consider the nonequilibrium dynamics in quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In the presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra)local in the usual sense of QFTs, but fulfill a significantly weaker form of locality. We discuss the implications of our results for integrable QFTs in one spatial dimension.
Effective field theory analysis of Higgs naturalness
Bar-Shalom, Shaouly; Soni, Amarjit; Wudka, Jose
2015-07-20
Assuming the presence of physics beyond the Standard Model ( SM) with a characteristic scale M ~ O (10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the leading 1 -loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff, and determine t he constraints on the corresponding operator coefficients for these effects to alleviate the little hierarchy problem up to the scale of the effective action Λ < M , a condition we denote by “EFT-naturalness”. We also determine the types of physics that can lead to EFT-naturalness and show that these types of new physics are best probed in vector-boson and multiple-Higgs production. The current experimental constraints on these coefficients are also discussed.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field. PMID:25215973
The $\\hbar$ Expansion in Quantum Field Theory
Brodsky, Stanley J.; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
NASA Astrophysics Data System (ADS)
Nogueira, M.; Barros, A. P.; Miranda, P. M.
2012-04-01
Atmospheric fields can be extremely variable over wide ranges of spatial scales, with a scale ratio of 109-1010 between largest (planetary) and smallest (viscous dissipation) scale. Furthermore atmospheric fields with strong variability over wide ranges in scale most likely should not be artificially split apart into large and small scales, as in reality there is no scale separation between resolved and unresolved motions. Usually the effects of the unresolved scales are modeled by a deterministic bulk formula representing an ensemble of incoherent subgrid processes on the resolved flow. This is a pragmatic approach to the problem and not the complete solution to it. These models are expected to underrepresent the small-scale spatial variability of both dynamical and scalar fields due to implicit and explicit numerical diffusion as well as physically based subgrid scale turbulent mixing, resulting in smoother and less intermittent fields as compared to observations. Thus, a fundamental change in the way we formulate our models is required. Stochastic approaches equipped with a possible realization of subgrid processes and potentially coupled to the resolved scales over the range of significant scale interactions range provide one alternative to address the problem. Stochastic multifractal models based on the cascade phenomenology of the atmosphere and its governing equations in particular are the focus of this research. Previous results have shown that rain and cloud fields resulting from both idealized and realistic numerical simulations display multifractal behavior in the resolved scales. This result is observed even in the absence of scaling in the initial conditions or terrain forcing, suggesting that multiscaling is a general property of the nonlinear solutions of the Navier-Stokes equations governing atmospheric dynamics. Our results also show that the corresponding multiscaling parameters for rain and cloud fields exhibit complex nonlinear behavior
NASA Technical Reports Server (NTRS)
Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.
2006-01-01
In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.
Euler-Poincare reduction for discrete field theories
Vankerschaver, Joris
2007-03-15
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed.
Traveling pulses in a stochastic neural field model of direction selectivity.
Bressloff, Paul C; Wilkerson, Jeremy
2012-01-01
We analyze the effects of extrinsic noise on traveling pulses in a neural field model of direction selectivity. The model consists of a one-dimensional scalar neural field with an asymmetric weight distribution consisting of an offset Mexican hat function. We first show how, in the absence of any noise, the system supports spontaneously propagating traveling pulses that can lock to externally moving stimuli. Using a separation of time-scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the wave from its uniformly translating position at long time-scales, and fluctuations in the wave profile around its instantaneous position at short time-scales. In the case of freely propagating pulses, the wandering is characterized by pure Brownian motion, whereas in the case of stimulus-locked pulses, it is given by an Ornstein-Uhlenbeck process. This establishes that stimulus-locked pulses are more robust to noise. PMID:23181018
Topological and differential geometrical gauge field theory
NASA Astrophysics Data System (ADS)
Saaty, Joseph
Recent Quantum Field Theory books have defined the topological charge (Q) in terms of the winding number (N). Contrary to this definition, my proof defines Q in terms of the quantum number (n). Defining Q in terms of n, instead of in terms of N, enables me to determine a precise value for Q. The solutions of all kinds of homotopy classification are referred to as instanton solutions, hence the terms homotopy classification and instanton solution will be used interchangeably. My proof replaces the use of these techniques with the use of the Dirac quantization condition, the covariant Dirac's equation, and the covariant Maxwell's equation. Unlike the earlier approaches, my proof accounts for the concept of the spin quantum number and the concept of time. Using the three methods noted above, my proof yields results not obtained by earlier methods. I have dealt similarly with the Pontryagin Index. I have used the Covariant Electrodynamics, in place of homotopy classification techniques, to create for the Pontryagin Index a proof that is alternative to the one cited in recent literature. The homotopy classification techniques gives an expression that excludes the fact that particles have spin quantum number. Therefore, the homotopy classification techniques does not really describe what the topological charge is in reality. I did derive an expression which does include the spin quantum numbers for particles and this has not been done before. Therefore, this will give a better idea for theoretical physicists about the nature of the topological charge. Contribution to knowledge includes creativity. I created an alternative method to the instanton solution for deriving an expression for the topological charge and this method led to new discoveries as a contribution to knowledge in which I found that topological charge for fermions cannot be quantized (to be quantized means to take discrete values only in integer steps), whereas the instanton solution cannot distinguish
NASA Astrophysics Data System (ADS)
Khmaladze, E. V.
1982-12-01
CONTENTS § 1. Introduction § 2. Martingale methods in the theory of testing hypotheses § 3. Martingale limit theorems in the theory of decomposable and similar statistics § 4. Martingale methods in reliability theory References
The field theory of specific heat
NASA Astrophysics Data System (ADS)
Gusev, Yu. V.
2016-01-01
Finite temperature quantum field theory in the heat kernel method is used to study the heat capacity of condensed matter. The lattice heat is treated à la P. Debye as energy of the elastic (sound) waves. The dimensionless functional of free energy is re-derived with a cut-off parameter and used to obtain the specific heat of crystal lattices. The new dimensionless thermodynamical variable is formed as Planck's inverse temperature divided by the lattice constant. The dimensionless constant, universal for the class of crystal lattices, which determines the low temperature region of molar specific heat, is introduced and tested with the data for diamond lattice crystals. The low temperature asymptotics of specific heat is found to be the fourth power in temperature instead of the cubic power law of the Debye theory. Experimental data for the carbon group elements (silicon, germanium) and other materials decisively confirm the quartic law. The true low temperature regime of specific heat is defined by the surface heat, therefore, it depends on the geometrical characteristics of the body, while the absolute zero temperature limit is geometrically forbidden. The limit on the growth of specific heat at temperatures close to critical points, known as the Dulong-Petit law, appears from the lattice constant cut-off. Its value depends on the lattice type and it is the same for materials with the same crystal lattice. The Dulong-Petit values of compounds are equal to those of elements with the same crystal lattice type, if one mole of solid state matter were taken as the Avogadro number of the composing atoms. Thus, the Neumann-Kopp law is valid only in some special cases.
Luxmoore, R.J.; Jardine, P.M.; Gardner, R.H. ); Wilson, G.V. . Dept. of Plant and Soil Science)
1990-01-01
Investigations of rain-fed solute transport have been conducted at a forested hillslope site by using an in situ soil pedon and a subsurface hydrologic monitoring facility. Complementary solute transport studies on undisturbed soil columns taken from the field site have not provided data that can be directly applied to the field situation. Scaling up from columns to pedons and from pedons to hillslopes is being evaluated with percolation theory and Latin hypercube sampling methods. Percolation theory provides a means of identifying mobile zones and stagnant zones for given soil structural attributes which can be compared with column dye tracing results. The generation of frequency distributions of backwater and backbone porosities for a range of total soil porosities and pore arrangements may provide a stochastic representation of soil systems suitable for scaling up from the column scale to the pedon using the Latin hypercube sampling method. 9 refs.
NASA Astrophysics Data System (ADS)
Suo, M. Q.; Li, Y. P.; Huang, G. H.
2011-09-01
In this study, an inventory-theory-based interval-parameter two-stage stochastic programming (IB-ITSP) model is proposed through integrating inventory theory into an interval-parameter two-stage stochastic optimization framework. This method can not only address system uncertainties with complex presentation but also reflect transferring batch (the transferring quantity at once) and period (the corresponding cycle time) in decision making problems. A case of water allocation problems in water resources management planning is studied to demonstrate the applicability of this method. Under different flow levels, different transferring measures are generated by this method when the promised water cannot be met. Moreover, interval solutions associated with different transferring costs also have been provided. They can be used for generating decision alternatives and thus help water resources managers to identify desired policies. Compared with the ITSP method, the IB-ITSP model can provide a positive measure for solving water shortage problems and afford useful information for decision makers under uncertainty.
NASA Astrophysics Data System (ADS)
Teodorescu, Razvan
2009-10-01
Systems of oscillators coupled non-linearly (stochastically or not) are ubiquitous in nature and can explain many complex phenomena: coupled Josephson junction arrays, cardiac pacemaker cells, swarms or flocks of insects and birds, etc. They are know to have a non-trivial phase diagram, which includes chaotic, partially synchronized, and fully synchronized phases. A traditional model for this class of problems is the Kuramoto system of oscillators, which has been studied extensively for the last three decades. The model is a canonical example for non-equilibrium, dynamical phase transitions, so little understood in physics. From a stochastic analysis point of view, the transition is described by the large deviations principle, which offers little information on the scaling behavior near the critical point. I will discuss a special case of the model, which allows a rigorous analysis of the critical properties of the model, and reveals a new, anomalous scaling behavior in the vicinity of the critical point.
A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization
NASA Astrophysics Data System (ADS)
Liu, Shuang; Hu, Xiangyun; Liu, Tianyou
2014-07-01
Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.
Gravitational consequences of modern field theories
NASA Technical Reports Server (NTRS)
Horowitz, Gary T.
1989-01-01
Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.
Double field theory and mathcal{N} = {4} gauged supergravity
NASA Astrophysics Data System (ADS)
Geissbühler, David
2011-11-01
Double Field Theory describes the NS-NS sector of string theory and lives on a doubled spacetime. The theory has a local gauge symmetry generated by a generalization of the Lie derivative for doubled coordinates. For the action to be invariant under this symmetry, a differential constraint is imposed on the fields and gauge parameters, reducing their possible dependence in the doubled coordinates. We perform a Scherk-Schwarz reduction of Double Field Theory, yielding electric gaugings of half-maximal supergravity in four dimensions when integrability conditions are assumed. The residual symmetries of the compactified theory are mapped with the symmetries of the effective theory and the differential constraints of Double Field Theory are compared with the algebraic conditions on the embedding tensor. It is found that only a weaker form of the differential constraint has to be imposed on background fields to ensure the local gauge symmetry of the reduced action.
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Beverland, Michael E.; Buerschaper, Oliver; Koenig, Robert; Pastawski, Fernando; Preskill, John; Sijher, Sumit
2016-02-01
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Superconformal field theory and Jack superpolynomials
NASA Astrophysics Data System (ADS)
Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre
2012-09-01
We uncover a deep connection between the {N} = {1} superconformal field theory in 2 D and eigenfunctions of the supersymmetric Sutherland model known as Jack super-polynomials (sJacks). Specifically, the singular vector at level rs/2 of the Kac module labeled by the two integers r and s are given explicitly as a sum of sJacks whose indexing diagrams are contained in a rectangle with r columns and s rows. As a second compelling evidence for the distinguished status of the sJack-basis in SCFT, we find that the degenerate Whittaker vectors (Gaiotto states) can be expressed as a remarkably simple linear combination of sJacks. As a consequence, we are able to reformulate the supersymmetric version of the (degenerate) AGT conjecture in terms of the combinatorics of sJacks. The closed-form formulas for the singular vectors and the degenerate Whittaker vectors, although only conjectured in general, have been heavily tested (in some cases, up to level 33/2). Both the Neveu-Schwarz and Ramond sectors are treated.
Gravitational Descendants in Symplectic Field Theory
NASA Astrophysics Data System (ADS)
Fabert, Oliver
2011-02-01
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov and Pandharipande (Ann Math 163(2):517-560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak and Latschev (
Quantifying truncation errors in effective field theory
NASA Astrophysics Data System (ADS)
Furnstahl, R. J.; Klco, N.; Phillips, D. R.; Wesolowski, S.
2015-08-01
Bayesian procedures designed to quantify truncation errors in perturbative calculations of quantum chromodynamics observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions ("priors") for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We first demonstrate the calculation of Bayesian probability distributions for the EFT truncation error in some representative examples and then focus on the application of chiral EFT to neutron-proton scattering. Epelbaum, Krebs, and Meißner recently articulated explicit rules for estimating truncation errors in such EFT calculations of few-nucleon-system properties. We find that their basic procedure emerges generically from one class of naturalness priors considered and that all such priors result in consistent quantitative predictions for 68% DOB intervals. We then explore several methods by which the convergence properties of the EFT for a set of observables may be used to check the statistical consistency of the EFT expansion parameter.
Quantifying truncation errors in effective field theory
NASA Astrophysics Data System (ADS)
Furnstahl, R. J.; Klco, N.; Phillips, D. R.; Wesolowski, S.
2015-10-01
Bayesian procedures designed to quantify truncation errors in perturbative calculations of QCD observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions (``priors'') for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We demonstrate the calculation of Bayesian DOB intervals for the EFT truncation error in some representative cases and explore several methods by which the convergence properties of the EFT for a set of observables may be used to check the statistical consistency of the EFT expansion parameter. Supported in part by the NSF and the DOE.
Could reggeon field theory be an effective theory for QCD in the Regge limit?
NASA Astrophysics Data System (ADS)
Bartels, Jochen; Contreras, Carlos; Vacca, G. P.
2016-03-01
In this paper we investigate the possibility whether, in the extreme limit of high energies and large transverse distances, reggeon field theory might serve as an effective theory of high energy scattering for strong interactions. We analyse the functional renormalization group equations (flow equations) of reggeon field theory and search for fixed points in the space of (local) reggeon field theories. We study in complementary ways the candidate for the scaling solution, investigate its main properties and briefly discuss possible physical interpretations.
Stochastic models for climate field reconstruction over the Euro-Mediterranean region
NASA Astrophysics Data System (ADS)
Werner, Johannes; Toreti, Andrea; Luterbacher, Juerg
2014-05-01
Over the last decades, several different methods have been used to reconstruct past climatic change. These methods consist of an - often statistical - model and a related inference step. While recently a lot of the discussion has been focused on the latter (Smerdon et al. 2011, Christiansen et al. 2011), the focus on more appropriate models seems promising. In a series of recent pseudoproxy experiments (PPE) for climate field reconstructions (Tingley+Huybers 2010a,b; Werner et al. 2013), Bayesian inference was used toghether with a localised stochastic description of the spatio-temporal evolution of annual temperature fields. In contrast to other methods that are based on large scale patterns over the full reconstruction domain, the local temporal evolution and spatial dependencies are modelled. The models are based on simple assumptions about the spatio-temporal evolution and have been shown to perform well for temperature reconstructions, at least in pseudo proxy experiments. We show in this contribution how localised climate models can be checked using the Kramers Moyal expansion. We apply this method to estimate models for temperature and precipitation over Europe and the Mediterranean. While such simple models fare well enough for temperatures, precipitation poses new problems. We show that while the model mismatch does indeed introduce errors, it can be neglected when compared to the influence of the proxy data. The effect of noisy proxy time series and spatial sparseness still remains the most prominent source of errors. Smerdon J.E. et al., J Clim 24, 1284-1309 (2011) Tingley M.P. and Huybers P., J Clim 10, 2759-2781, 2782-2800 (2010a,b) Christiansen B. and Ljundqvist F.C., J Clim 24, 6013-6034 (2011) Werner J.P. et al., J Clim 26, 824 (2013)
NASA Technical Reports Server (NTRS)
Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.
2007-01-01
In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.
A stochastic aerodynamic model for stationary blades in unsteady 3D wind fields
NASA Astrophysics Data System (ADS)
Fluck, Manuel; Crawford, Curran
2016-09-01
Dynamic loads play an important roll in the design of wind turbines, but establishing the life-time aerodynamic loads (e.g. extreme and fatigue loads) is a computationally expensive task. Conventional (deterministic) methods to analyze long term loads, which rely on the repeated analysis of multiple different wind samples, are usually too expensive to be included in optimization routines. We present a new stochastic approach, which solves the aerodynamic system equations (Lagrangian vortex model) in the stochastic space, and thus arrive directly at a stochastic description of the coupled loads along a turbine blade. This new approach removes the requirement of analyzing multiple different realizations. Instead, long term loads can be extracted from a single stochastic solution, a procedure that is obviously significantly faster. Despite the reduced analysis time, results obtained from the stochastic approach match deterministic result well for a simple test-case (a stationary blade). In future work, the stochastic method will be extended to rotating blades, thus opening up new avenues to include long term loads into turbine optimization.
NASA Astrophysics Data System (ADS)
Zatloukal, Václav
2016-04-01
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. The general method is illustrated with three examples: non-relativistic Hamiltonian mechanics, De Donder-Weyl scalar field theory, and string theory.
Stochastic differential equations
Sobczyk, K. )
1990-01-01
This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshore structures.
Note on the stochastic theory of a self-catalytic chemical reaction. II
NASA Astrophysics Data System (ADS)
Dambrine, S.; Moreau, M.
1981-04-01
The general results of article I on the stochastic representation of the macroscopic stationary state of a self-catalytic chemical system are applied to a step-by-step chemical reaction. The relaxation times to the quasi-stationary state and to the final stationary state are computed by evaluating the first two non-trivial eigenvalues of the transition matrix. The previous results of Oppenheim, Shuler and Weiss are confirmed, precised and extended. The critical and subcritical cases are treated by the same method.
Modeling the net flows of U.S. mutual funds with stochastic catastrophe theory
NASA Astrophysics Data System (ADS)
Clark, A.
2006-04-01
Using the recent work of Hartelman, van der Maas, and Wagenmakers, we demonstrate the use of invariant stochastic catastrophe models in finance for modeling net flows (the difference between purchases and redemptions of fund shares) of U.S. mutual funds. We validate Goetzmann et al. and others' work concerning the importance of sentiment variables on stock fund flows. We also answer some of the questions Goetzmann et al. and Brown et al. pose at the end of their respective papers. We end with possible experiments for experimental economists and sociophysicists.
Magnetism and rotation in relativistic field theory
NASA Astrophysics Data System (ADS)
Mameda, Kazuya; Yamamoto, Arata
2016-09-01
We investigate the analogy between magnetism and rotation in relativistic theory. In nonrelativistic theory, the exact correspondence between magnetism and rotation is established in the presence of an external trapping potential. Based on this, we analyze relativistic rotation under external trapping potentials. A Landau-like quantization is obtained by considering an energy-dependent potential.
The State of the Field: Interdisciplinary Theory
ERIC Educational Resources Information Center
Newell, William H.
2013-01-01
This chronological overview of the development of interdisciplinary theory starts with the pre-cursors of theory: the development and elaboration of the definition of interdisciplinary studies, influential but problematic images of interdisciplinary studies proposed by Donald Campbell and Erich Jantsch, and best practices in interdisciplinary…
Cruz, Roberto de la; Guerrero, Pilar; Spill, Fabian; Alarcón, Tomás
2016-10-21
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance
Gauge field theory for the Poincaré-Weyl group
NASA Astrophysics Data System (ADS)
Babourova, O. V.; Frolov, B. N.; Zhukovsky, V. Ch.
2006-09-01
On the basis of the general principles of a gauge field theory, the gauge theory for the Poincaŕe-Weyl group is constructed. It is shown that tetrads are not true gauge fields, but represent functions of true gauge fields: Lorentzian, translational, and dilatational ones. The equations for gauge fields are obtained. Geometrical interpretation of the theory is developed demonstrating that as a result of localization of the Poincaré-Weyl group the space-time becomes a Weyl-Cartan space. The geometrical interpretation of a dilaton field as a component of the metric tensor of a tangent space in Weyl-Cartan geometry is also proposed.
Field theory on R× S 3 topology. VI: Gravitation
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-04-01
We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.
Dynamics of polymers: A mean-field theory
Fredrickson, Glenn H.; Orland, Henri
2014-02-28
We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ρ and a conjugate MSR response field ϕ, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamics involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.
Effective field theory of broken spatial diffeomorphisms
Lin, Chunshan; Labun, Lance Z.
2016-03-17
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constantmore » for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. In conclusion, we discuss several examples relevant to theories of massive gravity.« less
Effective field theory of broken spatial diffeomorphisms
NASA Astrophysics Data System (ADS)
Lin, Chunshan; Labun, Lance Z.
2016-03-01
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constant for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. We discuss several examples relevant to theories of massive gravity.
Electroweak Sudakov Corrections using Effective Field Theory
Chiu Juiyu; Golf, Frank; Kelley, Randall; Manohar, Aneesh V.
2008-01-18
Electroweak Sudakov corrections of the form {alpha}{sup n}log{sup m}s/M{sub W,Z}{sup 2} are summed using renormalization group evolution in soft-collinear effective theory. Results are given for the scalar, vector, and tensor form factors for fermion and scalar particles. The formalism for including massive gauge bosons in soft-collinear effective theory is developed.
Theory on the Mechanism of DNA Renaturation: Stochastic Nucleation and Zipping
Niranjani, Gnanapragasam; Murugan, Rajamanickam
2016-01-01
Renaturation of the complementary single strands of DNA is one of the important processes that requires better understanding in the view of molecular biology and biological physics. Here we develop a stochastic dynamical model on the DNA renaturation. According to our model there are at least three steps in the renaturation process viz. nonspecific-contact formation, correct-contact formation and nucleation, and zipping. Most of the earlier two-state models combined nucleation with nonspecific-contact formation step. In our model we suggest that it is considerably meaningful when we combine the nucleation with the zipping since nucleation is the initial step of zipping and nucleated and zipping molecules are indistinguishable. Nonspecific contact formation step is a pure three-dimensional diffusion controlled collision process. Whereas nucleation involves several rounds of one-dimensional slithering and internal displacement dynamics of one single strand of DNA on the other complementary strand in the process of searching for the correct-contact and then initiate nucleation. Upon nucleation, the stochastic zipping follows to generate a fully renatured double stranded DNA. It seems that the square-root dependency of the overall renaturation rate constant on the length of reacting single strands originates mainly from the geometric constraints in the diffusion controlled nonspecific-contact formation step. Further the inverse scaling of the renaturation rate on the viscosity of reaction medium also originates from nonspecific contact formation step. On the other hand the inverse scaling of the renaturation rate with the sequence complexity originates from the stochastic zipping which involves several rounds of crossing over the free-energy barrier at microscopic levels. When the sequence of renaturing single strands of DNA is repetitive with less complexity then the cooperative effects will not be noticeable since the parallel zipping will be a dominant enhancing
Stability in higher-derivative matter fields theories
NASA Astrophysics Data System (ADS)
Tretyakov, Petr V.
2016-09-01
We discuss possible instabilities in higher-derivative matter field theories. These theories have two free parameters β _1 and β _4. By using a dynamical system approach we explicitly demonstrate that for the stability of Minkowski space in an expanding universe we need the condition β _4<0. By using the quantum field theory approach we also find an additional restriction for the parameters, β _1>-1/3β _4, which is needed to avoid a tachyon-like instability.
GravitoMagnetic Field in Tensor-Vector-Scalar Theory
Exirifard, Qasem
2013-04-01
We study the gravitomagnetism in the TeVeS theory. We compute the gravitomagnetic field that a slow moving mass distribution produces in its Newtonian regime. We report that the consistency between the TeVeS gravitomagnetic field and that predicted by the Einstein-Hilbert theory leads to a relation between the vector and scalar coupling constants of the theory. We translate the Lunar Laser Ranging measurement's data into a constraint on the deviation from this relation.
Economic policy optimization based on both one stochastic model and the parametric control theory
NASA Astrophysics Data System (ADS)
Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit
2016-06-01
A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)
Topological field theory for 2+1 TRI TSC
NASA Astrophysics Data System (ADS)
Gu, Yingfei; Qi, Xiaoliang
2014-03-01
Time-reversal invariant topological superconductors (TRI TSC) are gapped TRI superconductors with topologically robust gapless modes on the boundary. In the work by X. L. Qi et al, [PRB, 87, 134519(2013)], a topological field theory description was proposed for 3+1-dimensional TRI TSC, which contains an axionic coupling between superconducting phase and electromagnetic field. In my talk, I will describe a generalization of this theory to the 2+1 dimensional TRI TSC. The 2+1d topological field theory describes a topological coupling between electromagnetic field, superconducting phase fluctuation and magneto-electric polarization. I will also talk about the corresponding physical consequences.
Mean-field theory for Bose-Hubbard model under a magnetic field
Oktel, M. Oe.; Tanatar, B.; Nita, M.
2007-01-15
We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.
NASA Astrophysics Data System (ADS)
Morita, Shigeru; Oishi, Tetsutarou; Zhang, Hongming; Kobayashi, Masahiro; Goto, Motoshi; Kawamura, Gakushi; Huang, Xianli
2014-10-01
Edge stochastic magnetic field layer of Large Helical Device (LHD) consists of short and long open magnetic fields ranging in 10 <= Lc <= 2000 m. When the edge density increases, the friction force along magnetic field is entirely dominant in outer region of the stochastic magnetic layer which leads to the impurity screening. In order to study the parallel impurity transport two-dimensional impurity emissions from several impurity spices have been measured in EUV wavelength range (10-500 Å) and a clear impurity footprint along poloidal X-point trajectory is observed. The poloidal impurity footprint, e.g. CIV, is separated into double trajectories at high-density discharges (ne >= 5×1013cm-3) , whereas it shows single trajectory at low-density discharges (ne <= 2×1013cm-3) . The result clearly indicates the presence of the friction force. The 2-D distribution analyzed by 3-D edge transport code, EMC3-EIRENE is discussed on the friction force and temperature gradient force along magnetic fields. This work was partly supported by the JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (NSFC: No. 11261140328, NRF : No. 2012K2A2A6000443).
Heavy Quarks, QCD, and Effective Field Theory
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi eld theoretic de nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
Field Theory Model of the Flyby Anomaly
Lewis, R. A
2009-03-16
Precision tracking of spacecraft on interplanetary missions has turned up several anomalous deviations from predictions of general relativity. The Flyby Anomaly, wherein spacecraft gain or lose energy in an earth-centric frame after an encounter with earth, is clearly associated with the rotation of the earth. The possibility that the missing ingredient is a new type of potential field surrounding the earth is assessed in this write-up. A scalar field with the kinetic energy distribution of the earth as a source is evaluated numerically, with an amplitude parameter adjusted to match the data of Anderson et al.(2008). The new field can be interpreted as a coupling between kinetic energies of objects, a field analogous to fluid mechanics, or a field coupled to acceleration. The potential field violates various aspects of standard physics, such as energy non-conservation.
Quantum field theory of the Casimir effect for real media
Mostepanenko, V.M.; Trunov, N.N.
1985-11-01
The quantum field theory is developed for the corrections to the Casimir force arising when the field penetrates the material of the plates. A new type of divergence arising from the corresponding modification of the boundary conditions is analyzed. General expressions are obtained for the vacuum energy of the electromagnetic field in the space between nonideal plates, and the actual corrections to the Casimir force are calculated in first-order perturbation theory in the penetration depth.
Open superstring field theory on the restricted Hilbert space
NASA Astrophysics Data System (ADS)
Konopka, Sebastian; Sachs, Ivo
2016-04-01
It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert space for the Ramond sector or to introduce auxiliary fields with picture -3/2. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.
Time-Ordered Product Expansions for Computational Stochastic Systems Biology
Mjolsness, Eric
2013-01-01
The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie’s Stochastic Simulation Algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differ-ential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion (TOPE) can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems. PMID:23735739
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt
2009-07-15
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just 'how much' Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [Phys. Rev. D 79, 084008 (2009)] on 3+1 dimensional quantum gravity.
On the stability of the asymptotically free scalar field theories
Shalaby, A M.
2015-03-30
Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.
Applying Power Theories to Field Settings.
ERIC Educational Resources Information Center
Liss, Lora
To test theories presented in the sociology course "Social Policies and Community Power Structure," a team of undergraduate students and their instructor attended a national professional conference. The following are examples of those concepts the students observed in operation at the conference: Social structure affects social policies; the…
A class of effective field theory models of cosmic acceleration
Bloomfield, Jolyon K.; Flanagan, Éanna É. E-mail: eef3@cornell.edu
2012-10-01
We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher derivative terms and exploiting the field redefinition freedom, we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found in similar theories of single-field inflation, where matter is not present. We discuss several different representations of the theory that can be obtained using the field redefinition freedom. For perturbations to the quintessence field today on subhorizon lengthscales larger than the Compton wavelength of the heavy fields, the theory is weakly coupled and natural in the sense of t'Hooft. The theory admits a regime where the perturbations become modestly nonlinear, but very strong nonlinearities lie outside its domain of validity.
NASA Astrophysics Data System (ADS)
Wang, Hui; Wellmann, Florian
2016-04-01
It is generally accepted that 3D geological models inferred from observed data will contain a certain amount of uncertainties. The uncertainty quantification and stochastic sampling methods are essential for gaining the insight into the geological variability of subsurface structures. In the community of deterministic or traditional modelling techniques, classical geo-statistical methods using boreholes (hard data sets) are still most widely accepted although suffering certain drawbacks. Modern geophysical measurements provide us regional data sets in 2D or 3D spaces either directly from sensors or indirectly from inverse problem solving using observed signal (soft data sets). We propose a stochastic modelling framework to extract subsurface heterogeneity from multiple and complementary types of data. In the presented work, subsurface heterogeneity is considered as the "hidden link" among multiple spatial data sets as well as inversion results. Hidden Markov random field models are employed to perform 3D segmentation which is the representation of the "hidden link". Finite Gaussian mixture models are adopted to characterize the statistical parameters of the multiple data sets. The uncertainties are quantified via a Gibbs sampling process under the Bayesian inferential framework. The proposed modelling framework is validated using two numerical examples. The model behavior and convergence are also well examined. It is shown that the presented stochastic modelling framework is a promising tool for the 3D data fusion in the communities of geological modelling and geophysics.
The Theory of Field Parameters for Helmholtz Coil
NASA Astrophysics Data System (ADS)
Wang, Jin; Li, Guofeng; Liang, Ke; Gao, Xianhu
In this paper, the field parameters for the magnetic field of a Helmholtz coil is defined, as predicted by the theory of magnetic multipolar fields. In accordance with Biot-Savart law, eleven series of field parameters for the Helmholtz coil are calculated and the effect of each parameter thoroughly analyzed. This is then shown to provide a theoretical basis for obtaining a uniform magnetic field.
Studies on the formulation of thermodynamics and stochastic theory for systems far from equilibrium
Ross, J.
1995-12-31
We have been working for some time on the formulation of thermodynamics and the theory of fluctuations in systems far from equilibrium and progress in several aspects of that development are reported here.
Gerdes, Frank; Finette, Steven
2012-10-01
A modeling and simulation study is performed in a littoral ocean waveguide subject to uncertainty in four quantities: source depth, tidal forcing, initial thermocline structure, and sediment sound speed. In this partially known shelf-break environment, tidal forcing over a density-stratified water column produces internal tides and solitary wave packets. The resulting uncertainty in the space-time oceanographic field is mapped into the sound speed distribution which, in turn, introduces uncertainty into the acoustic wave field. The latter is treated as a stochastic field whose intensity is described by a polynomial chaos expansion. The expansion coefficients are estimated through constrained multivariate linear regression, and an analysis of the chaos coefficients provides insight into the relative contribution of the uncertain acoustic and oceanographic quantities. Histograms of acoustic intensity are estimated and compared to a reference solution obtained through Latin Hypercube sampling. A sensitivity analysis is performed to illustrate the relative importance of the four contributions of incomplete information about the environment. The simulation methodology represents an end-to-end analysis approach including both oceanographic and acoustic field uncertainty where the latter is quantified using stochastic basis expansions in the form of a polynomial chaos representation.
Gerdes, Frank; Finette, Steven
2012-10-01
A modeling and simulation study is performed in a littoral ocean waveguide subject to uncertainty in four quantities: source depth, tidal forcing, initial thermocline structure, and sediment sound speed. In this partially known shelf-break environment, tidal forcing over a density-stratified water column produces internal tides and solitary wave packets. The resulting uncertainty in the space-time oceanographic field is mapped into the sound speed distribution which, in turn, introduces uncertainty into the acoustic wave field. The latter is treated as a stochastic field whose intensity is described by a polynomial chaos expansion. The expansion coefficients are estimated through constrained multivariate linear regression, and an analysis of the chaos coefficients provides insight into the relative contribution of the uncertain acoustic and oceanographic quantities. Histograms of acoustic intensity are estimated and compared to a reference solution obtained through Latin Hypercube sampling. A sensitivity analysis is performed to illustrate the relative importance of the four contributions of incomplete information about the environment. The simulation methodology represents an end-to-end analysis approach including both oceanographic and acoustic field uncertainty where the latter is quantified using stochastic basis expansions in the form of a polynomial chaos representation. PMID:23039422
Unambiguous formalism for higher order Lagrangian field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris
2009-11-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. 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. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Toward a quantum theory of tachyon fields
NASA Astrophysics Data System (ADS)
Schwartz, Charles
2016-03-01
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space-time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.
Botet, Robert; Kuratsuji, Hiroshi
2010-03-01
We present a framework for the stochastic features of the polarization state of an electromagnetic wave propagating through the optical medium with both deterministic (controlled) and disordered birefringence. In this case, the Stokes parameters obey a Langevin-type equation on the Poincaré sphere. The functional integral method provides for a natural tool to derive the Fokker-Planck equation for the probability distribution of the Stokes parameters. We solve the Fokker-Planck equation in the case of a random anisotropic active medium submitted to a homogeneous electromagnetic field. The possible dissipation and relaxation phenomena are studied in general and in various cases, and we give hints about how to validate experimentally the corresponding phenomenological equations.
Botet, Robert; Kuratsuji, Hiroshi
2010-03-15
We present a framework for the stochastic features of the polarization state of an electromagnetic wave propagating through the optical medium with both deterministic (controlled) and disordered birefringence. In this case, the Stokes parameters obey a Langevin-type equation on the Poincare sphere. The functional integral method provides for a natural tool to derive the Fokker-Planck equation for the probability distribution of the Stokes parameters. We solve the Fokker-Planck equation in the case of a random anisotropic active medium submitted to a homogeneous electromagnetic field. The possible dissipation and relaxation phenomena are studied in general and in various cases, and we give hints about how to validate experimentally the corresponding phenomenological equations.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Killing vector fields and harmonic superfield theories
Groeger, Josua
2014-09-15
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Theory and Simulation of Field Error Transport.
NASA Astrophysics Data System (ADS)
Dubin, D. H. E.
2007-11-01
The rate at which a plasma escapes across an applied magnetic field B due to symmetry-breaking electric or magnetic ``field errors'' is revisited. Such field errors cause plasma loss (or compression) in stellarators, tokamaks,ootnotetextH.E. Mynick, Ph Plas 13 058102 (2006). and nonneutral plasmas.ootnotetextEggleston, Ph Plas 14 012302 (07); Danielson et al., Ph Plas 13 055706. We study this process using idealized simulations that follow guiding centers in given trap fields, neglecting their collective effect on the evolution, but including collisions. Also, the Fokker-Planck equation describing the particle distribution is solved, and the predicted transport agrees with simulations in every applicable regime. When a field error of the form δφ(r, θ, z ) = ɛ(r) e^i m θ kz is applied to an infinite plasma column, the transport rates fall into the usual banana, plateau and fluid regimes. When the particles are axially confined by applied trap fields, the same three regimes occur. When an added ``squeeze'' potential produces a separatrix in the axial motion, the transport is enhanced, scaling roughly as ( ν/ B )^1/2 δ2̂ when ν< φ. For φ< ν< φB (where φ, ν and φB are the rotation, collision and axial bounce frequencies) there is also a 1/ ν regime similar to that predicted for ripple-enhanced transport.^1
No resonant tunneling in standard scalar quantum field theory
NASA Astrophysics Data System (ADS)
Copeland, Edmund J.; Padilla, Antonio; Saffin, Paul M.
2008-01-01
We investigate the nature of resonant tunneling in standard scalar Quantum Field Theory. Following the pioneering work of Banks, Bender and Wu we describe the quantum field theory in terms of infinite dimensional quantum mechanics and utilize the ``Most probable escape path'' (MPEP) as the class of paths which dominate the path integral in the classically forbidden region. Considering a 1+1 dimensional field theory example we show that there are five conditions that any associated bound state in the classically allowed region must satisfy if resonant tunnelling is to occur, and we then proceed to show that it is impossible to satisfy all five conditions simultaneously.
Gravity Dual for Reggeon Field Theory and Nonlinear Quantum Finance
NASA Astrophysics Data System (ADS)
Nakayama, Yu
We study scale invariant but not necessarily conformal invariant deformations of nonrelativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the nonrelativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and nonlinear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.
Doubled Field Theory, T-Duality and Courant-Brackets
NASA Astrophysics Data System (ADS)
Zwiebach, Barton
In these lecture notes we give a simple introduction into double field theory. We show that the presence of momentum and winding excitations in toroidal backgrounds of closed string theory makes it natural to consider double field theories. A tool-kit is developed based on the Courant-bracket and generalized Lie derivatives. We construct a background independent action which represents a T-duality covariantization of the Einstein-Hilbert action for gravity coupled to an antisymmetric tensor field and a dilaton.
Linear processes in stochastic population dynamics: theory and application to insect development.
Solari, Hernán G; Natiello, Mario A
2014-01-01
We consider stochastic population processes (Markov jump processes) that develop as a consequence of the occurrence of random events at random time intervals. The population is divided into subpopulations or compartments. The events occur at rates that depend linearly on the number of individuals in the different described compartments. The dynamics is presented in terms of Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously proposed, higher-order approximations are completely new. Further, we analyse a model for insect development as a sequence of E developmental stages regulated by rates that are linear in the implied subpopulations. Transition to the next stage competes with death at all times. The process ends at a predetermined stage, for example, pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time.
Stochastic gradient processes: A survey of convergence theory using Lyapunov second method
Nakonechnyi, A.N.
1995-09-01
In the present article, our aim is to provide a comprehensive survey and analysis of the convergence conditions of known gradient type algorithms described by process in terms of the Lyapunov function v(z) = min/y {element_of} Y {parallel} z - y {parallel}{sup 2}, where Y is a closed bounded subset in R{sup l}, i.e., the conditions that ensure the equality P (lim/k{r_arrow}{infinity} min/y{element_of}Y {parallel} z{sup k}-y{parallel}{sup 2} = O) = 1. Alongside qualitative results, the article also focuses on comparison of specific gradient type stochastic algorithms on test examples, practical evaluation of the accuracy of the results, and acceleration of convergence by the averaging operation on the trajectory, which is defined by the recurrence u{sup k+1}=u{sup {center_dot}k} + (z{sup k}-u{sup k})/k, k {ge} 1, u{sup 1} = z{sup 1}.
Linear Processes in Stochastic Population Dynamics: Theory and Application to Insect Development
Solari, Hernán G.; Natiello, Mario A.
2014-01-01
We consider stochastic population processes (Markov jump processes) that develop as a consequence of the occurrence of random events at random time intervals. The population is divided into subpopulations or compartments. The events occur at rates that depend linearly on the number of individuals in the different described compartments. The dynamics is presented in terms of Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously proposed, higher-order approximations are completely new. Further, we analyse a model for insect development as a sequence of E developmental stages regulated by rates that are linear in the implied subpopulations. Transition to the next stage competes with death at all times. The process ends at a predetermined stage, for example, pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time. PMID:24696664
NASA Astrophysics Data System (ADS)
Kim, S.; Lee, A.; Keem, M.; Shin, H.
2009-12-01
For better understanding of soil water and plant water stress dynamics, a stochastic soil water and plant water stress model will be proposed and applied to climate change impact assessment. The proposed model is derived by using cumulant expansion theory from a stochastic differential equation with stochastic rainfall forcings. This model has the advantage of providing the probabilistic solution in the form of a probability distribution function, from which the ensemble average behavior of the system can be obtained easily. Also, since this model uses only the statistics of rainfall time series, the effect of different climate conditions on the soil water and plant water stress dynamics can be incorporated effectively. The simulation result of soil water confirms that the proposed model can reproduce the observation properly and shows that the soil water behaves with consistent cycle based on the precipitation pattern. In order to understand the impact of climate change on soil water and plant water stress behaviors, the RCM data developed by Korean Meteorological Administration (KMA RCM) and the third GCM by Canadian Centre for Climate Modeling and Analysis(CGCM3) are used with two time periods of 2051~2060 and 2091~2100. With all the simulation results, it can be conclude that the simulation results will be different with what climate change scenario is selected since different climate change model predicts different soil water and plant water stress behaviors. This analysis can be expected as a starting point for better understanding of the effect of soil water on ecosystem dynamics such as climate-soil-vegetation interaction. Figure 1. The evolution of the soil water PDF. The soil water PDFs have two different patterns according to wet season from June to September and dry season from October to May. From such result, it can be inferred that the mechanisms which influence the soil water behavior are different in wet and dry seasons. That is to say, in wet
Hitchin equation, singularity, and N = 2 superconformal field theories
NASA Astrophysics Data System (ADS)
Nanopoulos, Dimitri; Xie, Dan
2010-03-01
We argue that Hitchin’s equation determines not only the low energy effective theory but also describes the UV theory of four dimensional N = 2 superconformal field theories when we compactify six dimensional A N (0, 2) theory on a punctured Riemann surface. We study singular solutions to Hitchin’s equation and the Highs field of equation has a simple pole at the punctures; We show that the massless theory is associated with Higgs field whose residue is a nilpotent element; We identify the flavor symmetry associated with the puncture by studying the singularity of closure of the moduli space of solutions with the appropriate boundary conditions. For mass-deformed theory the residue of the Higgs field is a semi-simple element, we identify the semi-simple element by arguing that the moduli space of solutions of mass-deformed theory must be a deformation of the closure of the moduli space of massless theory. We also study the Seiberg-Witten curve by identifying it as the spectral curve of the Hitchin’s system. The results are all in agreement with Gaiotto’s results derived from studying the Seiberg-Witten curve of four dimensional quiver gauge theory.
Venugopal, Mamatha; van Es, Peter; Manohar, Srirang; Roy, Debasish; Vasu, Ram Mohan
2016-09-15
We present, perhaps for the first time, a stochastic search algorithm in quantitative photoacoustic tomography (QPAT) for a one-step recovery of the optical absorption map from time-resolved photoacoustic signals. Such a direct recovery is free of the numerical inaccuracies inherent in conventional two-step approaches that depend on an accurate estimation of the absorbed energy distribution. The absorption profile parameterized as a vector stochastic process is additively updated over time recursions so as to drive the measurement-prediction misfit to a zero-mean white noise. The derivative-free additive update is a welcome departure from the conventional gradient-based methods requiring evaluation of Jacobians at every recursion. The quantitative accuracy of the recovered absorption map from both numerical and experimental data is good with an overall error of less than 10%.
Venugopal, Mamatha; van Es, Peter; Manohar, Srirang; Roy, Debasish; Vasu, Ram Mohan
2016-09-15
We present, perhaps for the first time, a stochastic search algorithm in quantitative photoacoustic tomography (QPAT) for a one-step recovery of the optical absorption map from time-resolved photoacoustic signals. Such a direct recovery is free of the numerical inaccuracies inherent in conventional two-step approaches that depend on an accurate estimation of the absorbed energy distribution. The absorption profile parameterized as a vector stochastic process is additively updated over time recursions so as to drive the measurement-prediction misfit to a zero-mean white noise. The derivative-free additive update is a welcome departure from the conventional gradient-based methods requiring evaluation of Jacobians at every recursion. The quantitative accuracy of the recovered absorption map from both numerical and experimental data is good with an overall error of less than 10%. PMID:27628357
NASA Technical Reports Server (NTRS)
Coffey, Victoria; Chandler, Michael; Singh, Nagendra
2008-01-01
The role that the cleft/cusp has in ionosphere/magnetosphere coupling makes it a very dynamic region having similar fundamental processes to those within the auroral regions. With Polar passing through the cusp at 1 Re in the Spring of 1996, we observe a strong correlation between ion heating and broadband ELF (BBELF) emissions. This commonly observed relationship led to the study of the coupling of large field-aligned currents, burst electric fields, and the thermal O+ ions. We demonstrate the role of these measurements to Alfvenic waves and stochastic ion heating. Finally we will show the properties of the resulting density cavities.
The Theory of Quantized Fields. III
DOE R&D Accomplishments Database
Schwinger, J.
1953-05-01
In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.
A New Lorentz Violating Nonlocal Field Theory From String-Theory
Ganor, Ori J.
2007-10-04
A four-dimensional field theory with a qualitatively new type of nonlocality is constructed from a setting where Kaluza-Klein particles probe toroidally compactified string theory with twisted boundary conditions. In this theory fundamental particles are not pointlike and occupy a volume proportional to their R-charge. The theory breaks Lorentz invariance but appears to preserve spatial rotations. At low energies, it is approximately N=4 Super Yang-Mills theory, deformed by an operator of dimension seven. The dispersion relation of massless modes in vacuum is unchanged, but under certain conditions in this theory, particles can travel at superluminal velocities.
Lattice Study of Magnetic Catalysis in Graphene Effective Field Theory
NASA Astrophysics Data System (ADS)
Winterowd, Christopher; Detar, Carleton; Zafeiropoulos, Savvas
2016-03-01
The discovery of graphene ranks as one of the most important developments in condensed matter physics in recent years. As a strongly interacting system whose low-energy excitations are described by the Dirac equation, graphene has many similarities with other strongly interacting field theories, particularly quantum chromodynamics (QCD). Graphene, along with other relativistic field theories, have been predicted to exhibit spontaneous symmetry breaking (SSB) when an external magnetic field is present. Using nonperturbative methods developed to study QCD, we study the low-energy effective field theory (EFT) of graphene subject to an external magnetic field. We find strong evidence supporting the existence of SSB at zero-temperature and characterize the dependence of the chiral condensate on the external magnetic field. We also present results for the mass of the Nambu-Goldstone boson and the dynamically generated quasiparticle mass that result from the SSB.
Screening of scalar fields in Dirac-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Burrage, Clare; Khoury, Justin
2014-07-01
We study a new screening mechanism which is present in Dirac-Born-Infeld (DBI)-like theories. A scalar field with a DBI-like Lagrangian is minimally coupled to matter. In the vicinity of sufficiently dense sources, nonlinearities in the scalar dominate and result in an approximately constant acceleration on a test particle, thereby suppressing the scalar force relative to gravity. Unlike generic P(X) or chameleon theories, screening happens within the regime of validity of the effective field theory thanks to the DBI symmetry. We derive an exact form for the field profile around multiple sources and determine the constraints on the theory parameters from tests of gravity. Perturbations around the spherically-symmetric background propagate superluminally, but we argue for a chronology protection analogous to Galileons. This is the first example of a screening mechanism for which quantum corrections to the theory are under control and exact solutions to cosmological N-body problems can be found.
Topological Field Theory of Time-Reversal Invariant Insulators
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
NASA Astrophysics Data System (ADS)
Yushkevich, A. A.; Chitashvili, R. Ya
1982-12-01
CONTENTSIntroduction Chapter I. Foundations of the general theory of controlled random sequences and Markov chains with the expected reward criterion § 1. Controlled random sequences, Markov chains, and models § 2. Necessary and sufficient conditions for optimality § 3. The Bellman equation for the value function and the existence of (ε-) optimal strategies Chapter II. Some problems in the theory of controlled homogeneous Markov chains § 4. Description of the solutions of the Bellman equation, a characterization of the value function, and the Bellman operator § 5. Sufficiency of stationary strategies in homogeneous Markov models § 6. The lexicographic Bellman equation References
Conceptual Developments of 20th Century Field Theories
NASA Astrophysics Data System (ADS)
Cao, Tian Yu
1998-06-01
This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of theoretical physics. It will also provide professional historians and philosophers of science, particularly philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject.
Conceptual Developments of 20th Century Field Theories
NASA Astrophysics Data System (ADS)
Cao, Tian Yu
1997-02-01
This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of theoretical physics. It will also provide professional historians and philosophers of science, particularly philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject.
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Mann, Robert
2013-02-01
Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is
NASA Astrophysics Data System (ADS)
Lu, B.; Darmon, M.; Leymarie, N.; Chatillon, S.; Potel, C.
2012-05-01
In-service inspection of Sodium-Cooled Fast Reactors (SFR) requires the development of non-destructive techniques adapted to the harsh environment conditions and the examination complexity. From past experiences, ultrasonic techniques are considered as suitable candidates. The ultrasonic telemetry is a technique used to constantly insure the safe functioning of reactor inner components by determining their exact position: it consists in measuring the time of flight of the ultrasonic response obtained after propagation of a pulse emitted by a transducer and its interaction with the targets. While in-service the sodium flow creates turbulences that lead to temperature inhomogeneities, which translates into ultrasonic velocity inhomogeneities. These velocity variations could directly impact the accuracy of the target locating by introducing time of flight variations. A stochastic simulation model has been developed to calculate the propagation of ultrasonic waves in such an inhomogeneous medium. Using this approach, the travel time is randomly generated by a stochastic process whose inputs are the statistical moments of travel times known analytically. The stochastic model predicts beam deviations due to velocity inhomogeneities, which are similar to those provided by a determinist method, such as the ray method.
Lu, B.; Darmon, M.; Leymarie, N.; Chatillon, S.; Potel, C.
2012-05-17
In-service inspection of Sodium-Cooled Fast Reactors (SFR) requires the development of non-destructive techniques adapted to the harsh environment conditions and the examination complexity. From past experiences, ultrasonic techniques are considered as suitable candidates. The ultrasonic telemetry is a technique used to constantly insure the safe functioning of reactor inner components by determining their exact position: it consists in measuring the time of flight of the ultrasonic response obtained after propagation of a pulse emitted by a transducer and its interaction with the targets. While in-service the sodium flow creates turbulences that lead to temperature inhomogeneities, which translates into ultrasonic velocity inhomogeneities. These velocity variations could directly impact the accuracy of the target locating by introducing time of flight variations. A stochastic simulation model has been developed to calculate the propagation of ultrasonic waves in such an inhomogeneous medium. Using this approach, the travel time is randomly generated by a stochastic process whose inputs are the statistical moments of travel times known analytically. The stochastic model predicts beam deviations due to velocity inhomogeneities, which are similar to those provided by a determinist method, such as the ray method.
NASA Astrophysics Data System (ADS)
Loll, Per; Moldrup, Per
2000-04-01
Field-scale pesticide leaching risk assessments were performed by incorporating a numerical, one-dimensional, water and pesticide transport and fate model into the two-step stochastic modeling approach by Loll and Moldrup [1998]. The numerical model included first-order pesticide degradation, linear equilibrium adsorption, and plant uptake of water and pesticide. Simazine was used as a model pesticide, and leaching risk was expressed as the cumulative mass fraction of applied pesticide leached below 100 cm after 1 year. Spatial variability in soil physical and biochemical data, as well as measured meteorological data from an average and a relatively wet year, was considered for two Danish field sites: (1) a coarse sandy soil, with relatively small variability in hydraulic properties, and (2) a sandy loam, with large variability in hydraulic properties. The two-step stochastic modeling approach was used to investigate the relative impact of spatial variability in saturated hydraulic conductivity Ks, soil-water retention through the Campbell [974] soil-water retention parameter b, and pesticide sorption through the organic carbon content (OC). For the coarse sandy soil, field-scale spatial variability in OC was the single most important parameter influencing leaching risk, whereas for the sandy loam, Ks was found more important than OC. The relative impact of field-scale spatial variability in these parameters was found independent of the meteorological conditions, whereas the absolute level of leaching risk was highly dependent on the meteorological conditions. Assuming a linear dependency between pesticide half-life and OC, a unified approach to modeling simultaneous field-scale variability in biodegradation and adsorption was proposed. Leaching risk assessments based on this approach showed that the parts of the field with both low biological activity and low adsorption capacity contributed with a dramatic increase in leaching risk, and suggested that field
Theory of back-surface-field solar cells
NASA Technical Reports Server (NTRS)
Vonroos, O.
1979-01-01
Report describes simple concise theory of back-surface-field (BSF) solar cells (npp + junctions) based on Shockley's depletion-layer approximation and cites superiority of two-junction devices over conventional unijunction cells.
Perturbation Theory of Massive Yang-Mills Fields
DOE R&D Accomplishments Database
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
A Guided Inquiry Activity for Teaching Ligand Field Theory
ERIC Educational Resources Information Center
Johnson, Brian J.; Graham, Kate J.
2015-01-01
This paper will describe a guided inquiry activity for teaching ligand field theory. Previous research suggests the guided inquiry approach is highly effective for student learning. This activity familiarizes students with the key concepts of molecular orbital theory applied to coordination complexes. Students will learn to identify factors that…
Constrained variational calculus for higher order classical field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David
2010-11-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Scalar field theory in {kappa}-Minkowski spacetime from twist
Kim, Hyeong-Chan; Lee, Youngone; Rim, Chaiho; Yee, Jae Hyung
2009-10-15
Using the twist deformation of U(igl(4,R)), the linear part of the diffeomorphism, we define a scalar function and construct a free scalar field theory in four-dimensional {kappa}-Minkowski spacetime. The action in momentum space turns out to differ only in the integration measure from the commutative theory.
An extremal ${\\mathcal{N}}=2$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; Kachru, Shamit
2015-11-16
Here, we provide an example of an extremal chiral ${\\mathcal{N}}$ = 2 superconformal field theory at c = 24. The construction is based on a ${{\\mathbb{Z}}}_{2}$ orbifold of the theory associated to the ${A}_{1}^{24}$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.
An extremal $${\\mathcal{N}}=2$$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; Kachru, Shamit
2015-11-16
Here, we provide an example of an extremal chiralmore » $${\\mathcal{N}}$$ = 2 superconformal field theory at c = 24. The construction is based on a $${{\\mathbb{Z}}}_{2}$$ orbifold of the theory associated to the $${A}_{1}^{24}$$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.« less
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.
Quantum Field Theory in Coordinate Space
NASA Astrophysics Data System (ADS)
Erdogan, Ahmet Ozan
In order to provide a new coordinate-space perspective applicable to scattering amplitudes, in the first part of this dissertation, the structure of singularities in perturbative massless gauge theories is investigated in coordinate space. The pinch singularities in coordinate-space integrals occur at configurations of vertices which have a direct interpretation in terms of physical scattering of particles in real space-time in the same way as for the loop momenta in the case of momentum-space singularities. In the analysis of vertex functions in coordinate space, the well-known factorization into hard, soft, and jet functions is found. By power-counting arguments, it is found that coordinate-space integrals of vertex functions have logarithmic divergences at worst. The `hard-collinear' and `soft-collinear' approximations that allow the application of gauge theory Ward identities in the formal proof of factorization in coordinate space are introduced. In the second part, the perturbative cusp and closed polygons of Wilson lines for massless gauge theories are analyzed in coordinate space, and expressed as exponentials of two-dimensional integrals. These integrals have geometric interpretations, which link renormalization scales with invariant distances. A direct perturbative prescription for the logarithm of the cusp and related cross sections treated in eikonal approximation is provided by web diagrams. The sources of their ultraviolet poles in coordinate space associated with their nonlocal collinear divergences are identified by the power-counting technique explained in the first part. In the study of the coordinate-space matrix elements that correspond to scattering amplitudes involving partons and Wilson lines in coordinate space, a series of subtractions is developed to eliminate their divergences and to show their factorization in coordinate space. The ultraviolet finiteness of the web integrand is shown by relating the web expansion to the application of
J.A. Krommes
2009-05-19
Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-χ theorem is discussed. An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.
Effective hydrodynamic field theory and condensation picture of topological insulators
NASA Astrophysics Data System (ADS)
Chan, AtMa P. O.; Kvorning, Thomas; Ryu, Shinsei; Fradkin, Eduardo
2016-04-01
While many features of topological band insulators are commonly discussed at the level of single-particle electron wave functions, such as the gapless Dirac boundary spectrum, it remains elusive to develop a hydrodynamic or collective description of fermionic topological band insulators in 3+1 dimensions. As the Chern-Simons theory for the 2+1-dimensional quantum Hall effect, such a hydrodynamic effective field theory provides a universal description of topological band insulators, even in the presence of interactions, and that of putative fractional topological insulators. In this paper, we undertake this task by using the functional bosonization. The effective field theory in the functional bosonization is written in terms of a two-form gauge field, which couples to a U (1 ) gauge field that arises by gauging the continuous symmetry of the target system [the U (1 ) particle number conservation]. Integrating over the U (1 ) gauge field by using the electromagnetic duality, the resulting theory describes topological band insulators as a condensation phase of the U (1 ) gauge theory (or as a monopole condensation phase of the dual gauge field). The hydrodynamic description of the surface of topological insulators and the implication of its duality are also discussed. We also touch upon the hydrodynamic theory of fractional topological insulators by using the parton construction.
Free Quantum Field Theory from Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
On the renormalization of non-commutative field theories
NASA Astrophysics Data System (ADS)
Blaschke, Daniel N.; Garschall, Thomas; Gieres, François; Heindl, Franz; Schweda, Manfred; Wohlgenannt, Michael
2013-01-01
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [ j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.
Conformal field theories with infinitely many conservation laws
Todorov, Ivan
2013-02-15
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th
Stochastic Models of Human Growth.
ERIC Educational Resources Information Center
Goodrich, Robert L.
Stochastic difference equations of the Box-Jenkins form provide an adequate family of models on which to base the stochastic theory of human growth processes, but conventional time series identification methods do not apply to available data sets. A method to identify structure and parameters of stochastic difference equation models of human…
Fluctuations as stochastic deformation
NASA Astrophysics Data System (ADS)
Kazinski, P. O.
2008-04-01
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.
Fluctuations as stochastic deformation.
Kazinski, P O
2008-04-01
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.
Statistical field theory description of inhomogeneous polarizable soft matter
NASA Astrophysics Data System (ADS)
Martin, Jonathan M.; Li, Wei; Delaney, Kris T.; Fredrickson, Glenn H.
2016-10-01
We present a new molecularly informed statistical field theory model of inhomogeneous polarizable soft matter. The model is based on fluid elements, referred to as beads, that can carry a net monopole of charge at their center of mass and a fixed or induced dipole through a Drude-type distributed charge approach. The beads are thus polarizable and naturally manifest attractive van der Waals interactions. Beyond electrostatic interactions, beads can be given soft repulsions to sustain fluid phases at arbitrary densities. Beads of different types can be mixed or linked into polymers with arbitrary chain models and sequences of charged and uncharged beads. By such an approach, it is possible to construct models suitable for describing a vast range of soft-matter systems including electrolyte and polyelectrolyte solutions, ionic liquids, polymerized ionic liquids, polymer blends, ionomers, and block copolymers, among others. These bead models can be constructed in virtually any ensemble and converted to complex-valued statistical field theories by Hubbard-Stratonovich transforms. One of the fields entering the resulting theories is a fluctuating electrostatic potential; other fields are necessary to decouple non-electrostatic interactions. We elucidate the structure of these field theories, their consistency with macroscopic electrostatic theory in the absence and presence of external electric fields, and the way in which they embed van der Waals interactions and non-uniform dielectric properties. Their suitability as a framework for computational studies of heterogeneous soft matter systems using field-theoretic simulation techniques is discussed.
Democracy of internal symmetries in supersymmetrical quantum field theory
Lopuszanski, J.T.
1981-12-01
The freedom of choice of some discrete and internal symmetries in the supersymmetric, massive, interacting quantum field theory is discussed. It is shown that the discrete symmetry consisting of changing the sign of some (not all) scalar fields is incompatible with the supersymmetric structure of the theory. It is further demonstrated that an internal symmetry which transforms only some of the fields of fixed spin leaving the other fields invariant and which acts nontrivially on the supercharges can not be admitted as a symmetry; although it can be a good internal symmetry in absence of supersymmetric covariance. Moreover, in case of a model consisting of scalar, spinor and vector fields even a symmetry which transforms all of the scalar (vector) fields leaving spinor and vector (scalar) fields unaffected is ruled out provided it acts nontrivially on some of the supercharges.
Low energy signatures of nonlocal field theories
NASA Astrophysics Data System (ADS)
Belenchia, Alessio; Benincasa, Dionigi M. T.; Martín-Martínez, Eduardo; Saravani, Mehdi
2016-09-01
The response of inertial particle detectors coupled to a scalar field satisfying nonlocal dynamics described by nonanalytic functions of the d'Alembertian operator □ is studied. We show that spontaneous emission processes of a low energy particle detector are very sensitive to high-energy nonlocality scales. This allows us to suggest a nuclear physics experiment (˜MeV energy scales) that outperforms the sensitivity of LHC experiments by many orders of magnitude. This may have implications for the falsifiability of theoretical proposals of quantum gravity.
NASA Technical Reports Server (NTRS)
Cairns, Iver H.; Robinson, P. A.
1998-01-01
Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for
Very special relativity as a background field theory
NASA Astrophysics Data System (ADS)
Ilderton, Anton
2016-08-01
We consider violation of Lorentz invariance in QED induced by a very high frequency background wave. An effective theory is obtained by averaging observables over the rapid field oscillations. This preserves Ward identities and restores translation invariance below the high-frequency scale, but only partial Lorentz invariance: we show that the effective theory is C-invariant SIM(2)-QED in very special relativity. Averaging leads to the nonlocal terms familiar from SIM(2) theories, while the short-distance behavior of the background field fermion propagator generates the infinite number of higher-order vertices of SIM(2)-QED.
An action for F-theory: {SL}(2){{{R}}}^{+} exceptional field theory
NASA Astrophysics Data System (ADS)
Berman, David S.; Blair, Chris D. A.; Malek, Emanuel; Rudolph, Felix J.
2016-10-01
We construct the 12-dimensional exceptional field theory (EFT) associated to the group {SL}(2)× {{{R}}}+. Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that must be imposed on all fields. This constraint has two inequivalent solutions, one giving rise to 11-dimensional supergravity and the other leading to F-theory. Thus {SL}(2)× {{{R}}}+ EFT contains both F-theory and M-theory in a single 12-dimensional formalism.
NASA Astrophysics Data System (ADS)
Jangi, Mehdi; Lucchini, Tommaso; Gong, Cheng; Bai, Xue-Song
2015-09-01
An Eulerian stochastic fields (ESF) method accelerated with the chemistry coordinate mapping (CCM) approach for modelling spray combustion is formulated, and applied to model diesel combustion in a constant volume vessel. In ESF-CCM, the thermodynamic states of the discretised stochastic fields are mapped into a low-dimensional phase space. Integration of the chemical stiff ODEs is performed in the phase space and the results are mapped back to the physical domain. After validating the ESF-CCM, the method is used to investigate the effects of fuel cetane number on the structure of diesel spray combustion. It is shown that, depending of the fuel cetane number, liftoff length is varied, which can lead to a change in combustion mode from classical diesel spray combustion to fuel-lean premixed burned combustion. Spray combustion with a shorter liftoff length exhibits the characteristics of the classical conceptual diesel combustion model proposed by Dec in 1997 (http://dx.doi.org/10.4271/970873), whereas in a case with a lower cetane number the liftoff length is much larger and the spray combustion probably occurs in a fuel-lean-premixed mode of combustion. Nevertheless, the transport budget at the liftoff location shows that stabilisation at all cetane numbers is governed primarily by the auto-ignition process.
NASA Astrophysics Data System (ADS)
Panzeri, Marco; Riva, Monica; Guadagnini, Alberto; Neuman, Shlomo P.
2014-05-01
The ensemble Kalman filter (EnKF) enables one to assimilate newly available data in transient groundwater and other temporal earth system models through real-time Bayesian updating of system states (e.g., hydraulic heads) and parameters (e.g., hydraulic conductivities). It has become common to treat spatially varying hydraulic conductivities as autocorrelated random fields conditioned on measured conductivities and/or heads. Doing so renders the corresponding groundwater flow equations stochastic. Assimilating data in such equations via traditional EnKF entails computationally intensive Monte Carlo (MC) simulation. We have previously illustrated a methodology to circumvent the need for MC. Our methodology is grounded on (1) an approximate direct solution of nonlocal (integrodifferential) equations that govern the space-time evolution of conditional ensemble means (statistical expectations) and covariances of hydraulic heads and fluxes and (2) the embedding of these moments in EnKF. This provides sequential updates of conductivity and head estimates throughout the space-time domain of interest, does not suffer from inbreeding issues and, as an additional benefit, obviates the need for computationally intensive batch inverse solution of the moment equations as we have been doing previously. We compare the performance of our new EnKF approach based on stochastic moment equation and of the traditional Monte Carlo approach. We do so for a field scale scenario involving a sequence of pumping tests performed in a heterogeneous alluvial test site located near the city of Tuebingen, Germany.
Generating functionals for quantum field theories with random potentials
NASA Astrophysics Data System (ADS)
Jain, Mudit; Vanchurin, Vitaly
2016-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.
DBI scalar field theory for QGP hydrodynamics
NASA Astrophysics Data System (ADS)
Nastase, Horatiu
2016-07-01
A way to describe the hydrodynamics of the quark-gluon plasma using a Dirac-Born-Infeld (DBI) action is proposed, based on the model found by Heisenberg for high energy scattering of nucleons. The expanding plasma is described as a shockwave in a DBI model for a real scalar standing in for the pion, and I show that one obtains a fluid description in terms of a relativistic fluid that near the shock is approximately ideal (η ≃0 ) and conformal. One can introduce an extra term inside the square root of the DBI action that generates a shear viscosity term in the energy-momentum tensor near the shock, as well as a bulk viscosity, and regulates the behavior of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with uμ,ρ ,P ,η defined in terms of ϕ and its derivatives. One finds a relation between the parameters of the theory and the quark-gluon plasma thermodynamics, α /β2=η /(s T ), and by fixing α and β from usual (low multiplicity) particle scattering, one finds T ∝mπ.
Graphene, Lattice Field Theory and Symmetries
Drissi, L. B.; Bousmina, M.; Saidi, E. H.
2011-02-15
Borrowing ideas from tight binding model, we propose a board class of lattice field models that are classified by non simply laced Lie algebras. In the case of A{sub N-1{approx_equal}}su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice L{sub suN} are governed by the complex fundamental representations N-bar and N of su(N) and the second nearest neighbor interactions are described by its adjoint N-bar x N. The lattice models associated with the leading su(2), su(3), and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe the electronic properties of the acetylene chain and the graphene, respectively. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the A{sub N} roots {alpha} through the typical dependence N/2+{Sigma}{sub roots} cos(k.{alpha} with k the wave vector.Other features such as the SO(2N) extension and other applications are also discussed.
Mean-Field Theory of the Symmetry Breaking Model for X Chromosome Inactivation
NASA Astrophysics Data System (ADS)
Scialdone, A.; Barbieri, M.; Pallotti, D.; Nicodemi, M.
X Chromosome Inactivation (XCI) is the process in mammal femalecells whereby one of the X chromosomes is silenced to compensate dosage with respect to males. It is still mysterious how precisely one X chromosome is randomly chosen for inactivation. We discuss here a mean-field theory of the Symmetry Breaking (SB) model of XCI, a Statistical Mechanics model introduced to explain that process. The SB model poses that a single regulatory factor, an aggregate of molecules, is produced which acts to preserve from inactivation one of the X's. The model illustrates a physical mechanism, originating from a thermodynamic phase transition, for the self-assembling of such a single super-molecular aggregate which can spontaneously break the binding symmetry of equivalent targets. This results in a sharp, yet stochastic, regulatory mechanism of XCI. In particular, we focus here on how the model can predict the effects of genetic deletions.
Field Theoretic Formulation of Kinetic Theory: Basic Development
NASA Astrophysics Data System (ADS)
Das, Shankar P.; Mazenko, Gene F.
2012-11-01
We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. The need for a self-consistent approach is suggested by our interest in investigating ergodic-nonergodic transitions in dense fluids. The formal structure we develop has been implemented in detail for the simpler case of Smoluchowski dynamics. One aspect of the approach is the identification of a core problem spanned by the variables ρ the number density and B a response density. In this paper we set up the perturbation theory expansion with explicit development at zeroth and first order. We also determine all of the cumulants in the noninteracting limit among the core variables ρ and B.
Group field theories for all loop quantum gravity
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Ryan, James P.; Thürigen, Johannes
2015-02-01
Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.
Stochastic theory of nonequilibrium steady states. Part II: Applications in chemical biophysics
NASA Astrophysics Data System (ADS)
Ge, Hao; Qian, Min; Qian, Hong
2012-01-01
The mathematical theory of nonequilibrium steady state (NESS) has a natural application in open biochemical systems which have sustained source(s) and sink(s) in terms of a difference in their chemical potentials. After a brief introduction in Section 1, in Part II of this review, we present the widely studied biochemical enzyme kinetics, the workhorse of biochemical dynamic modeling, in terms of the theory of NESS (Section 2.1). We then show that several phenomena in enzyme kinetics, including a newly discovered activation-inhibition switching (Section 2.2) and the well-known non-Michaelis-Menten-cooperativity (Section 2.3) and kinetic proofreading (Section 2.4), are all consequences of the NESS of driven biochemical systems with associated cycle fluxes. Section 3 is focused on nonlinear and nonequilibrium systems of biochemical reactions. We use the phosphorylation-dephosphorylation cycle (PdPC), one of the most important biochemical signaling networks, as an example (Section 3.1). It starts with a brief introduction of the Delbrück-Gillespie process approach to mesoscopic biochemical kinetics (Sections 3.2 and 3.3). We shall discuss the zeroth-order ultrasensitivity of PdPC in terms of a new concept - the temporal cooperativity (Sections 3.4 and 3.5), as well as PdPC with feedback which leads to biochemical nonlinear bistability (Section 3.6). Also, both are nonequilibrium phenomena. PdPC with a nonlinear feedback is kinetically isomorphic to a self-regulating gene expression network, hence the theory of NESS discussed here could have wide applications to many other biochemical systems.
Some equivalences between the auxiliary field method and envelope theory
Buisseret, Fabien; Semay, Claude; Silvestre-Brac, Bernard
2009-03-15
The auxiliary field method has been recently proposed as an efficient technique to compute analytical approximate solutions of eigenequations in quantum mechanics. We show that the auxiliary field method is completely equivalent to the envelope theory, which is another well-known procedure to analytically solve eigenequations, although relying on different principles a priori. This equivalence leads to a deeper understanding of both frameworks.
3D quantum gravity and effective noncommutative quantum field theory.
Freidel, Laurent; Livine, Etera R
2006-06-01
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
Thomas, Philipp; Straube, Arthur V; Grima, Ramon
2010-11-21
Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.
NASA Astrophysics Data System (ADS)
Thomas, Philipp; Straube, Arthur V.; Grima, Ramon
2010-11-01
Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.
Rotariu, O; Strachan, N J C; Bădescu, V
2004-09-01
The method of immunomagnetic separation (IMS) has become an established technique to concentrate and separate animal cells, biologically active compounds and pathogenic micro-organisms from clinical, food and environmental matrices. One drawback of this technique is that the analysis is only possible for small sample volumes. We have developed a stochastic model that involves numerical simulations to optimize the process of concentration of pathogenic micro-organisms onto superparamagnetic carrier particles (SCPs) in a gradient magnetic field. Within the range of the system parameters varied in the simulations, optimal conditions favour larger particles with higher magnetite concentrations. The dependence on magnetic field intensity and gradient together with concentration of particles and micro-organisms was found to be less important for larger SCPs but these parameters can influence the values of the collision time for small particles. These results will be useful in aiding the design of apparatus for immunomagnetic separation from large volume samples.
Long-range interactions in lattice field theory
Rabin, J.M.
1981-06-01
Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.
NASA Astrophysics Data System (ADS)
Marie, S.; Irving, J. D.; Looms, M. C.; Nielsen, L.; Holliger, K.
2011-12-01
Geophysical methods such as ground-penetrating radar (GPR) can provide valuable information on the hydrological properties of the vadose zone. In particular, there is evidence to suggest that the stochastic inversion of such data may allow for significant reductions in uncertainty regarding subsurface van-Genuchten-Mualem (VGM) parameters, which characterize unsaturated hydrodynamic behaviour as defined by the combination of the water retention and hydraulic conductivity functions. A significant challenge associated with the use of geophysical methods in a hydrological context is that they generally exhibit an indirect and/or weak sensitivity to the hydraulic parameters of interest. A novel and increasingly popular means of addressing this issue involves the acquisition of geophysical data in a time-lapse fashion while changes occur in the hydrological condition of the probed subsurface region. Another significant challenge when attempting to use geophysical data for the estimation of subsurface hydrological properties is the inherent non-linearity and non-uniqueness of the corresponding inverse problems. Stochastic inversion approaches have the advantage of providing a comprehensive exploration of the model space, which makes them ideally suited for addressing such issues. In this work, we present the stochastic inversion of time-lapse zero-offset-profile (ZOP) crosshole GPR traveltime data, collected during a forced infiltration experiment at the Arreneas field site in Denmark, in order to estimate subsurface VGM parameters and their corresponding uncertainties. We do this using a Bayesian Markov-chain-Monte-Carlo (MCMC) inversion approach. We find that the Bayesian-MCMC methodology indeed allows for a substantial refinement in the inferred posterior parameter distributions of the VGM parameters as compared to the corresponding priors. To further understand the potential impact on capturing the underlying hydrological behaviour, we also explore how the posterior
Mean field analysis of a spatial stochastic model of a gene regulatory network.
Sturrock, M; Murray, P J; Matzavinos, A; Chaplain, M A J
2015-10-01
A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatio-temporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatio-temporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steady-state analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatio-temporal and spatially-homogeneous models.
Dualities among one-time field theories with spin, emerging from a unifying two-time field theory
Bars, Itzhak; Quelin, Guillaume
2008-06-15
The relation between two-time physics (2T-physics) and the ordinary one-time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the standard model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdS{sub d-k}xS{sup k}, and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure.
Quantum field theory constrains traversable wormhole geometries
Ford, L.H. |; Roman, T.A. |
1996-05-01
Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty-principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable. {copyright} {ital 1996 The American Physical Society.}
A gauge field theory of fermionic continuous-spin particles
NASA Astrophysics Data System (ADS)
Bekaert, X.; Najafizadeh, M.; Setare, M. R.
2016-09-01
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang-Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
Massive basketball diagram for a thermal scalar field theory
NASA Astrophysics Data System (ADS)
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-01
The ``basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a φ4 interaction to three-loop order.
Quantum Field Theory in Curved Spacetime
NASA Astrophysics Data System (ADS)
Reynolds, Sally C.; Gallagher, Andrew
2012-03-01
List of contributors; Foreword J. T. Francis Thackeray; 1. African genesis: an evolving paradigm Sally C. Reynolds; 2. Academic genealogy Peter Ungar and Phillip V. Tobias; Part I. In Search of Origins: Evolutionary Theory, New Species, and Paths into the Past: 3. Speciation in hominin evolution Colin Groves; 4. Searching for a new paradigm for hominid origins in Chad (Central Africa) Michel Brunet; 5. From hominoid arboreality to hominid bipedalism Brigitte Senut; 6. Orrorin and the African ape/hominid dichotomy Martin Pickford; 7. A brief history and results of 40 years of Sterkfontein excavations Ronald J. Clarke; Part II. Hominin Morphology Through Time: Brains, Bodies and Teeth: 8. Hominin brain evolution, 1925-2011: an emerging overview Dean Falk; 9. The issue of brain reorganisation in Australopithecus and early hominids: Dart had it right Ralph L. Holloway; 10. The mass of the human brain: is it a spandrel? Paul R. Manger, Jason Hemingway, Muhammad Spocter and Andrew Gallagher; 11. Origin and diversity of early hominin bipedalism Henry M. McHenry; 12. Forelimb adaptations in Australopithecus afarensis Michelle S. M. Drapeau; 13. Hominin proximal femur morphology from the Tugen Hills to Flores Brian G. Richmond and William L. Jungers; 14. Daily rates of dentine formation and root extension rates in Paranthropus boisei, KNM-ER 1817, from Koobi Fora, Kenya M. Christopher Dean; 15. On the evolutionary development of early hominid molar teeth and the Gondolin Paranthropus molar Kevin L. Kuykendall; 16. Digital South African fossils: morphological studies using reference-based reconstruction and electronic preparation Gerhard W. Weber, Philipp Gunz, Simon Neubauer, Philipp Mitteroecker and Fred L. Bookstein; Part III. Modern Human Origins: Patterns, and Processes: 17. Body size in African Middle Pleistocene Homo Steven E. Churchill, Lee R. Berger, Adam Hartstone-Rose and Headman Zondo; 18. The African origin of recent humanity Milford H. Wolpoff and Sang-Hee Lee
Correlation theory of delayed feedback in stochastic systems below Andronov-Hopf bifurcation.
Pototsky, Andrey; Janson, Natalia
2007-11-01
Here we address the effect of large delay on the statistical characteristics of noise-induced oscillations in a nonlinear system below Andronov-Hopf bifurcation. In particular, we introduce a theory of these oscillations that does not involve the eigenmode expansion, and can therefore be used for arbitrary delay time. In particular, we show that the correlation matrix (CM) oscillates on two different time scales: on the scale of the main period of noise-induced oscillations, and on the scale close to the delay time. At large values of the delay time, the CM is shown to decay exponentially only for large values of its argument, while for the arguments comparable with the value of the delay, the CM remains finite disregarding the delay time. The definition of the correlation time of the system with delay is discussed.
Janiszewski, Stefan; Karch, Andreas
2013-02-22
We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Hořava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit.
Faugeras, Olivier; Touboul, Jonathan; Cessac, Bruno
2008-01-01
We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the time variations of their membrane potentials. They are coupled by synaptic connections acting on their resulting activity, a nonlinear function of their membrane potential. At the second (mesoscopic) scale, interacting populations of neurons are described individually by similar equations. The equations describing the dynamical and the stationary mean-field behaviors are considered as functional equations on a set of stochastic processes. Using this new point of view allows us to prove that these equations are well-posed on any finite time interval and to provide a constructive method for effectively computing their unique solution. This method is proved to converge to the unique solution and we characterize its complexity and convergence rate. We also provide partial results for the stationary problem on infinite time intervals. These results shed some new light on such neural mass models as the one of Jansen and Rit (1995): their dynamics appears as a coarse approximation of the much richer dynamics that emerges from our analysis. Our numerical experiments confirm that the framework we propose and the numerical methods we derive from it provide a new and powerful tool for the exploration of neural behaviors at different scales. PMID:19255631
Consistent constraints on the Standard Model Effective Field Theory
NASA Astrophysics Data System (ADS)
Berthier, Laure; Trott, Michael
2016-02-01
We develop the global constraint picture in the (linear) effective field theory generalisation of the Standard Model, incorporating data from detectors that operated at PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II, as well as low energy precision data. We fit one hundred and three observables. We develop a theory error metric for this effective field theory, which is required when constraints on parameters at leading order in the power counting are to be pushed to the percent level, or beyond, unless the cut off scale is assumed to be large, Λ ≳ 3 TeV. We more consistently incorporate theoretical errors in this work, avoiding this assumption, and as a direct consequence bounds on some leading parameters are relaxed. We show how an S, T analysis is modified by the theory errors we include as an illustrative example.
Thermodynamics of perfect fluids from scalar field theory
NASA Astrophysics Data System (ADS)
Ballesteros, Guillermo; Comelli, Denis; Pilo, Luigi
2016-07-01
The low-energy dynamics of relativistic continuous media is given by a shift-symmetric effective theory of four scalar fields. These scalars describe the embedding in spacetime of the medium and play the role of Stückelberg fields for spontaneously broken spatial and time translations. Perfect fluids are selected imposing a stronger symmetry group or reducing the field content to a single scalar. We explore the relation between the field theory description of perfect fluids to thermodynamics. By drawing the correspondence between the allowed operators at leading order in derivatives and the thermodynamic variables, we find that a complete thermodynamic picture requires the four Stückelberg fields. We show that thermodynamic stability plus the null-energy condition imply dynamical stability. We also argue that a consistent thermodynamic interpretation is not possible if any of the shift symmetries is explicitly broken.