Classical-field description of the quantum effects in the light-atom interaction
Rashkovskiy, Sergey A
2016-01-01
In this paper I show that light-atom interaction can be described using purely classical field theory without any quantization. In particular, atom excitation by light that accounts for damping due to spontaneous emission is fully described in the framework of classical field theory. I show that three well-known laws of the photoelectric effect can also be derived and that all of its basic properties can be described within classical field theory.
Classical Electrodynamics without Fields and the Aharonov-Bohm effect
Stefanovich, Eugene V.
2008-01-01
The Darwin-Breit Hamiltonian is applied to the Aharonov-Bohm experiment. In agreement with the standard Maxwell-Lorentz theory, the force acting on electrons from infinite solenoids or ferromagnetic rods vanishes. However, the interaction energies and phase factors of the electron wave packets are non-zero. This allows us to explain the Aharonov-Bohm effect without involvement of electromagnetic potentials, fields, and topological properties of space.
A generalisation of classical electrodynamics for the prediction of scalar field effects
van Vlaenderen, K J
2003-01-01
Within the framework of Classical Electrodynamics (CED) it is common practice to choose freely an arbitrary gauge condition with respect to a gauge transformation of the electromagnetic potentials. The Lorenz gauge condition allows for the derivation of the inhomogeneous potential wave equations (IPWE), but this also means that scalar derivatives of the electromagnetic potentials are considered to be \\emph{unphysical}. However, these scalar expressions might have the meaning of a new physical field, $\\mathsf S$. If this is the case, then a generalised CED is required such that scalar field effects are predicted and such that experiments can be performed in order to verify or falsify this generalised CED. The IPWE are viewed as a generalised Gauss law and a generalised Ampe\\`re law, that also contain derivatives of $\\mathsf S$, after reformulating the IPWE in terms of fields. Some recent experiment show positive results that are in qualitative agreement with the presented predictions of scalar field effects, b...
无
2007-01-01
Based on the cascade two-photon laser dynamic equation derived with the technique of quantum Langevin operators with the considerations of coherently prepared three-level atoms and the classical field injected into the cavity, we numerically study the effects of atomic coherence and classical field on the chaotic dynamics of a two-photon laser. Lyapunov exponent and bifurcation diagram calculations show that the Lorenz chaos and hyperchaos can be induced or inhibited by the atomic coherence and the classical field via crisis or Hopf bifurcations.
Classical and quantum effective theories
Polonyi, Janos
2014-01-01
A generalization of the action principle of classical mechanics, motivated by the Closed Time Path (CTP) scheme of quantum field theory, is presented to deal with initial condition problems and dissipative forces. The similarities of the classical and the quantum cases are underlined. In particular, effective interactions which describe classical dissipative forces represent the system-environment entanglement. The relation between the traditional effective theories and their CTP extension is briefly discussed and few qualitative examples are mentioned.
Advances In Classical Field Theory
Yahalom, Asher
2011-01-01
Classical field theory is employed by physicists to describe a wide variety of physical phenomena. These include electromagnetism, fluid dynamics, gravitation and quantum mechanics. The central entity of field theory is the field which is usually a multi component function of space and time. Those multi component functions are usually grouped together as vector fields as in the case in electromagnetic theory and fluid dynamics, in other cases they are grouped as tensors as in theories of gravitation and yet in other cases they are grouped as complex functions as in the case of quantum mechanic
Classical Ising chain in transverse field
The spin 12 Ising chain in transverse field is considered the prototypical system for quantum phase transitions. However, very little is apparently known in literature about its classical counterpart, not to be confused with the standard classical Ising model: while the latter is constructed from classical discrete variables, the model we consider is a chain of classical vectors of modulus 1, interacting via an Ising-like Hamiltonian. When an uniform field is applied perpendicular to the exchange interaction, both the quantum model and its classical counterpart get to be characterized by a critical field separating a ferromagnetically ordered state of minimal energy from a paramagnetic one. The properties of the classical model, and especially the behaviour of the correlation length, are investigated at low temperature around the critical field and compared with those of the quantum model, in order to single out the role played by quantum and classical fluctuations at finite temperature; the possibility to experimentally observe peculiar quantum critical effects in Ising spin chains is discussed
The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Boedeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot φ4 theory, and elucidate its relation to classical transport theory. (c) 2000 The American Physical Society
Jalilian-Marian, J; Venugopalan, R; Wirstam, J; Jalilian-Marian, Jamal; Jeon, Sangyong; Venugopalan, Raju; Wirstam, Jens
2000-01-01
The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Bödeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot $\\phi^4$ theory, and elucidate its relation to classical transport theory.
Quantum field theory from classical statistics
Wetterich, C
2011-01-01
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discret...
Casimir Effect The Classical Limit
Feinberg, J; Revzen, M
2001-01-01
We analyze the high temperature limit of the Casimir effect. A simple physical argument suggests that the Casimir energy (as opposed to the Casimir free energy) should vanish in the classical limit. We check the validity of this argument for massless scalar field confined in a cavity with boundaries of arbitrary shape, using path integral formalism. We are able to verify this suggestion only when the boundaries consist of disjoint pieces. Moreover, we find in these cases that the contribution to the Casimir entropy by field modes that depend on that separation, tends, in the classical limit, to a finite asymptotic value which depends only on the geometry of the cavity. Thus the Casimir force between disjoint pieces of the boundary in the classical limit is entropy driven and is governed by a dimensionless number characterizing the arbitrary geometry of the cavity. Contributions to the Casimir thermodynamical quantities due to each individual connected component of the boundary exhibit logarithmic deviations i...
Semi-classical noise investigation for sub-40nm metal-oxide-semiconductor field-effect transistors
Device white noise levels in short channel Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) dictate the performance and reliability of high-frequency circuits ranging from high-speed microprocessors to Low-Noise Amplifiers (LNAs) and microwave circuits. Recent experimental noise measurements with very short devices demonstrate the existence of suppressed shot noise, contrary to the predictions of classical channel thermal noise models. In this work we show that, as the dimensions continue to shrink, shot noise has to be considered when the channel resistance becomes comparable to the barrier resistance at the source-channel junction. By adopting a semi-classical approach and taking retrospectively into account transport, short-channel and quantum effects, we investigate the partitioning between shot and thermal noise, and formulate a predictive model that describes the noise characteristics of modern devices
Semi-classical noise investigation for sub-40nm metal-oxide-semiconductor field-effect transistors
Spathis, C., E-mail: cspathis@ece.upatras.gr; Birbas, A.; Georgakopoulou, K. [Department of Electrical and Computer Engineering, University of Patras, Patras 26500 (Greece)
2015-08-15
Device white noise levels in short channel Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) dictate the performance and reliability of high-frequency circuits ranging from high-speed microprocessors to Low-Noise Amplifiers (LNAs) and microwave circuits. Recent experimental noise measurements with very short devices demonstrate the existence of suppressed shot noise, contrary to the predictions of classical channel thermal noise models. In this work we show that, as the dimensions continue to shrink, shot noise has to be considered when the channel resistance becomes comparable to the barrier resistance at the source-channel junction. By adopting a semi-classical approach and taking retrospectively into account transport, short-channel and quantum effects, we investigate the partitioning between shot and thermal noise, and formulate a predictive model that describes the noise characteristics of modern devices.
Classical spin glass system in external field with taking into account relaxation effects
Full text: (author)It is studied statistical properties of disordered spin systems under the influence of an external field with taking into account relaxation effects. For description of system the spatial ID Heisenberg spin-glass Hamiltonian is used. In addition, we suppose that interactions occur between nearest-neighboring spins and they are random. Exact solutions which define angular configuration of the spin in nodes were obtained from the equations of stationary points of Hamiltonian and the corresponding conditions for the energy local minimum. On the basis of these recurrent solutions an effective parallel algorithm is developed for simulation of stabile spin-chains of an arbitrary length. It is shown that by way of an independent order of N2 numerical simulations (where N is number of spin in the each chain) it is possible to generate ensemble of spin-chains, which is completely ergodic which is equivalent to full self-averaging of spin-chains' vector polarization. Distributions of different parameters (energy, average polarization by coordinates, and spin-spin interaction constant) of unperturbed system are calculated. In particular, analytically is proved and by the numerically is shown, that for the Heisenberg nearest-neighboring Hamiltonian model, the distribution of spin-spin interaction constants as opposed to widely used Gauss-Edwards-Anderson distribution satisfies Le'vy alpha-stable distribution law. This distribution is non analytic function and does not have variance. In the work we have in detail studied critical properties of an ensemble depending on value of external field parameters (from amplitude and frequency) and have shown that even at weak external fields the spin-glass system is strongly frustrated. It is shown that frustrations have fractal behavior, they are self-similar and do not disappear at scale decreasing of area. By the numerical computation is shown that the average polarization of spin-glass on a different coordinates can
Classical spin glass system in external field with taking into account relaxation effects
Gevorkyan, A. S., E-mail: g_ashot@sci.am; Abajyan, H. G. [NAS of Armenia, Institute for Informatics and Automation Problems (Armenia)
2013-08-15
We study statistical properties of disordered spin systems under the influence of an external field with taking into account relaxation effects. For description of system the spatial 1D Heisenberg spin-glass Hamiltonian is used. In addition, we suppose that interactions occur between nearest-neighboring spins and they are random. Exact solutions which define angular configuration of the spin in nodes were obtained from the equations of stationary points of Hamiltonian and the corresponding conditions for the energy local minimum. On the basis of these recurrent solutions an effective parallel algorithm is developed for simulation of stabile spin-chains of an arbitrary length. It is shown that by way of an independent order of N{sup 2} numerical simulations (where N is number of spin in each chain) it is possible to generate ensemble of spin-chains, which is completely ergodic which is equivalent to full self-averaging of spin-chains' vector polarization. Distributions of different parameters (energy, average polarization by coordinates, and spin-spin interaction constant) of unperturbed system are calculated. In particular, analytically is proved and numerically is shown, that for the Heisenberg nearest-neighboring Hamiltonian model, the distribution of spin-spin interaction constants as opposed to widely used Gauss-Edwards-Anderson distribution satisfies Levy alpha-stable distribution law. This distribution is nonanalytic function and does not have variance. In the work we have in detail studied critical properties of an ensemble depending on value of external field parameters (from amplitude and frequency) and have shown that even at weak external fields the spin-glass systemis strongly frustrated. It is shown that frustrations have fractal behavior, they are selfsimilar and do not disappear at scale decreasing of area. By the numerical computation is shown that the average polarization of spin-glass on a different coordinates can have values which can lead
A Time-Dependent Classical Solution of C=1 String Field Theory and Non-Perturbative Effects
Dhar, A; Wadia, S R; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R.
1993-01-01
We describe a real-time classical solution of $c=1$ string field theory written in terms of the phase space density, $u(p,q,t)$, of the equivalent fermion theory. The solution corresponds to tunnelling of a single fermion above the filled fermi sea and leads to amplitudes that go as $\\exp(- C/ \\gst)$. We discuss how one can use this technique to describe non-perturbative effects in the Marinari-Parisi model. We also discuss implications of this type of solution for the two-dimensional black hole.
We study the Casimir energy density of the Klein-Gordon-field in the case of two static geometries. We model the effect by coupling the free quantum field to a static classical scalar field. We work out the dependence on the coupling λ, including the limit λ=∞ (Dirichlet boundary condition). The chosen geometries are described by a δ-funktion (σ(x)=δ(x3)) and a step function of finite height (σ(x)(1)/(2ε)1[ε,ε](x3)), respectively. In the area outside the support of the background the density energy converges; calculations for the distorted area lead to divergent surface terms. (orig.)
A generalisation of classical electrodynamics for the prediction of scalar field effects
van Vlaenderen, Koen J.
2003-01-01
Within the framework of Classical Electrodynamics (CED) it is common practice to choose freely an arbitrary gauge condition with respect to a gauge transformation of the electromagnetic potentials. The Lorenz gauge condition allows for the derivation of the inhomogeneous potential wave equations (IPWE), but this also means that scalar derivatives of the electromagnetic potentials are considered to be \\emph{unphysical}. However, these scalar expressions might have the meaning of a new physical...
On the tomographic description of classical fields
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so-called Gauss–Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.
On the tomographic description of classical fields
Ibort, A., E-mail: albertoi@math.uc3m.es [Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid (Spain); López-Yela, A., E-mail: alyela@math.uc3m.es [Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid (Spain); Man' ko, V.I., E-mail: manko@na.infn.it [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, G., E-mail: marmo@na.infn.it [Dipartimento di Scienze Fisiche dell' Università “Federico II” e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Simoni, A., E-mail: simoni@na.infn.it [Dipartimento di Scienze Fisiche dell' Università “Federico II” e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Sudarshan, E.C.G., E-mail: bhamathig@gmail.com [Physics Department, Center for Particle Physics, University of Texas, Austin, TX 78712 (United States); Ventriglia, F., E-mail: ventriglia@na.infn.it [Dipartimento di Scienze Fisiche dell' Università “Federico II” e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy)
2012-03-26
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so-called Gauss–Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.
On the tomographic description of classical fields
Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Sudarshan, E C G; Ventriglia, F
2012-01-01
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so called Gauss--Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.
Jonathan Miller
2015-01-01
Full Text Available In the framework of quantum field theory, a graviton interacts locally with a quantum state having definite mass, that is, the gravitational mass eigenstate, while a weak boson interacts with a state having definite flavor, that is, the flavor eigenstate. An interaction of a neutrino with an energetic graviton may trigger the collapse of the neutrino to a definite mass eigenstate with probability expressed in terms of PMNS mixing matrix elements. Thus, gravitons would induce quantum decoherence of a coherent neutrino flavor state similarly to how weak bosons induce quantum decoherence of a neutrino in a definite mass state. We demonstrate that such an essentially quantum gravity effect may have strong consequences for neutrino oscillation phenomena in astrophysics due to relatively large scattering cross sections of relativistic neutrinos undergoing large angle radiation of energetic gravitons in gravitational field of a classical massive source (i.e., the quasi-classical case of gravitational Bethe-Heitler scattering. This graviton-induced decoherence is compared to decoherence due to propagation in the presence of the Earth matter effect. Based on this study, we propose a new technique for the indirect detection of energetic gravitons by measuring the flavor composition of astrophysical neutrinos.
In the framework of quantum field theory, a graviton interacts locally with a quantum state having definite mass, that is, the gravitational mass eigenstate, while a weak boson interacts with a state having definite flavor, that is, the flavor eigenstate. An interaction of a neutrino with an energetic graviton may trigger the collapse of the neutrino to a definite mass eigenstate with probability expressed in terms of PMNS mixing matrix elements. Thus, gravitons would induce quantum decoherence of a coherent neutrino flavor state similarly to how weak bosons induce quantum decoherence of a neutrino in a definite mass state. We demonstrate that such an essentially quantum gravity effect may have strong consequences for neutrino oscillation phenomena in astrophysics due to relatively large scattering cross sections of relativistic neutrinos undergoing large angle radiation of energetic gravitons in gravitational field of a classical massive source (i.e., the quasi-classical case of gravitational Bethe-Heitler scattering). This graviton-induced decoherence is compared to decoherence due to propagation in the presence of the Earth matter effect. Based on this study, we propose a new technique for the indirect detection of energetic gravitons by measuring the flavor composition of astrophysical neutrinos
Three Approaches to Classical Thermal Field Theory
Gozzi, E.; Penco, R.
2010-01-01
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.
Three approaches to classical thermal field theory
Gozzi, E.; Penco, R.
2011-04-01
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.
The Effect of Electric Fields In A Classic Introductory Physics Treatment of Eddy Current Forces
Salzman, P J; Lea, S M; Burke, John Robert; Lea, Susan M.
2001-01-01
A simple model of eddy currents in which current is computed solely from magnetic forces acting on electrons proves accessible to introductory students and gives a good qualitative account of eddy current forces. However, this model cannot be complete; it ignores the electric fields that drive current outside regions of significant magnetic field. In this paper we show how to extend the model to obtain a boundary value problem for current density. Solution of this problem in polar coordinates shows that the electric field significantly affects the quantitative results and presents an exercise suitable for upper division students. We apply elliptic cylindrical coordinates to generalize the result and offer an exercise useful for teaching graduate students how to use non-standard coordinate systems.
Classical theory of electric and magnetic fields
Good, Roland H
1971-01-01
Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction. The book also focuses on electrostatics and the general methods for solving electrostatic problems concerning images, inversion, complex variable, or separation of variables. The text also explains ma
Classical-field theory of thermal radiation
Rashkovskiy, Sergey A
2016-01-01
In this paper, using the viewpoint that quantum mechanics can be constructed as a classical field theory without any quantization I build a fully classical theory of thermal radiation. Planck's law for the spectral energy density of thermal radiation and the Einstein A-coefficient for spontaneous emission are derived in the framework of classical field theory without using the concept of "photon". It is shown that the spectral energy density of thermal radiation is apparently not a universal function of frequency, as follows from the Planck's law, but depends weakly on the nature of atoms, while Planck's law is valid only as an approximation in the limit of weak excitation of atoms.
Introducing quantum effects in classical theories
Fabris, J C; Rodrigues, D C; Daouda, M H
2015-01-01
In this paper, we explore two different ways of implementing quantum effects in a classical structure. The first one is through an external field. The other one is modifying the classical conservation laws. In both cases, the consequences for the description of the evolution of the universe are discussed.
Casimir Effect - The Classical Limit
The temperature dependence of the Casimir effect for the radiation field confined between two conducting plates is analysed; The Casimir energy is shown to decline exponentially with temperature while the Casimir entropy which is defined in the text is shown to approach a limit which depends only on the geometry of the constraining plates. The result is shown to hold, for a scalar field, for arbitrary geometry. The high temperature (T) expansion is shown to be ''robust'', i.e. it does not have any nonvanishing correction to the ''classical' result where the latter is defined by the validity of the Rayleigh - Jeans law. We show that validity of the Rayleigh - Jeans law implies the vanishing of the Casimir energy, hence the high temperature Casimir force, for a wide variety of geometries, is purely entropic
The classical pion field in a nucleus
Ripka, Georges
2007-01-01
A self-consistent symmetry arises when the nucleon angular momentum j and the isospin t are coupled to a grand spin G. Closed G shells become sources of a classical pion field with a hedgehog shape. Although the amplitude of the pion field, as measured by the chiral angle, is small, it is found to perturb significantly the energies of the nucleon orbits.
Casimir effect: The classical limit
We analyze the high temperature (or classical) limit of the Casimir effect. A useful quantity which arises naturally in our discussion is the 'relative Casimir energy', which we define for a configuration of disjoint conducting boundaries of arbitrary shapes, as the difference of Casimir energies between the given configuration and a configuration with the same boundaries infinitely far apart. Using path integration techniques, we show that the relative Casimir energy vanishes exponentially fast in temperature. This is consistent with a simple physical argument based on Kirchhoff's law. As a result the 'relative Casimir entropy', which we define in an obviously analogous manner, tends, in the classical limit, to a finite asymptotic value which depends only on the geometry of the boundaries. Thus the Casimir force between disjoint pieces of the boundary, in the classical limit, is entropy driven and is governed by a dimensionless number characterizing the geometry of the cavity. Contributions to the Casimir thermodynamical quantities due to each individual connected component of the boundary exhibit logarithmic deviations in temperature from the behavior just described. These logarithmic deviations seem to arise due to our difficulty to separate the Casimir energy (and the other thermodynamical quantities) from the 'electromagnetic' self-energy of each of the connected components of the boundary in a well defined manner. Our approach to the Casimir effect is not to impose sharp boundary conditions on the fluctuating field, but rather take into consideration its interaction with the plasma of 'charge carriers' in the boundary, with the plasma frequency playing the role of a physical UV cutoff. This also allows us to analyze deviations from a perfect conductor behavior
The classical theory of fields electromagnetism
Helrich, Carl S
2012-01-01
The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green’s Functions and Laplace’s Equation and a discussion of Faraday’s Experiment further deepen the understanding. The chapter on Einstein’s relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dis...
Classical lifting processes and multiplicative vector fields
Mackenzie, Kirill; Xu, Ping
1997-01-01
We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to include also the classical process of complete lifting from arbitrary manifolds to tangent and cotangent bundles. Using this calculus we give a new description of the Lie bialgebroid structure associated with a Poisson groupoid.
Quantum Back Reaction on a Classical Field
Brout, R; Popescu, S; Parentani, R; Spindel, P; Spindel, Ph.
1995-01-01
We show how to apply post selection in the context of weak measurement of Aharonov and collaborators to construct the quantum back reaction on a classical field. The particular case which we study in this paper is pair creation in an external electric field and the back reaction is the counter field produced by the pair \\underline {as} it is made. The construction leads to a complex electric field obtained from non diagonal matrix elements of the current operator, the interpretation of which is clear in terms of weak measurement. The analogous construction applied to black hole physics (thereby leading to a complex metric) is relegated to a future paper.
Extended phase space. I. Classical fields
Classical field theory is developed in the arena of extended phase space V8, the space of position, time, momentum, and energy. This enables one to incorporate Born's reciprocity which demands equal status for the variables q and p. The present formulation is covariant under the extended Poincare group P8 acting in V8. Variational methods for classical field theory are generalized. Besides the usual concept of the total 4-momentum, one encounters the notion of average position and time of the field distributions. The total charge emerges from a dynamical viewpoint. The Dirac and Duffin--Kemmer algebras are generalized in this setting. The corresponding wave equations would lead to a dynamical theory of the elementary particles. The symplectic structure is not considered because of the difficulties to represent spinors
Classical solutions in quantum field theories
Quantum field theories are difficult to solve because they are governed by nonlinear operator equations. A one-dimensional example, termed the kink, is presented of a classical solution. Topological and nontopological solitons in more than one spatial dimension are also discussed. Euclidean solutions and barrier penetration are also reviewed, focusing on vacuum decay by tunneling, Yang-Mills Instantons, the physical consequences of vacuum tunneling, and thermal fluctuations and sphalerons. 119 refs., 2 figs
Classical Gauged Massless Rarita-Schwinger Fields
Adler, Stephen L
2015-01-01
We show that, in contrast to known results in the massive case, a minimally gauged massless Rarita-Schwinger field yields a consistent classical theory, with a generalized fermionic gauge invariance realized as a canonical transformation. To simplify the algebra, we study a two-component left chiral reduction of the massless theory. We formulate the classical theory in both Lagrangian and Hamiltonian form for a general non-Abelian gauging, and analyze the constraints and the Rarita-Schwinger gauge invariance of the action. An explicit wave front calculation for Abelian gauge fields shows that wave-like modes do not propagate with superluminal velocities. An analysis of Rarita-Schwinger spinor scattering from gauge fields shows that adiabatic decoupling fails in the limit of zero gauge field amplitude, invalidating various "no-go" theorems based on "on-shell" methods that claim to show the impossibility of gauging Rarita-Schwinger fields. Quantization of Rarita-Schwinger fields, using many formulas from this p...
Introduction to classical and quantum field theory
This is the first introductory textbook on quantum field theory to be written from the point of view of condensed matter physics. As such, it presents the basic concepts and techniques of statistical field theory, clearly explaining how and why they are integrated into modern quantum (and classical) field theory, and includes the latest developments. Written by an expert in the field, with a broad experience in teaching and training, it manages to present such substantial topics as phases and phase transitions or solitons and instantons in an accessible and concise way. Divided into three parts, the first part covers fundamental physics and the mathematics background needed by students in order to enter the field, while the second part introduces more advanced concepts and techniques. Part III discusses applications of quantum field theory to a few basic problems. The emphasis here lies on how modern concepts of quantum field theory are embedded in these approaches, and also on the limitations of standard quantum field theory techniques in facing, 'real' physics problems. Throughout there are numerous end-of-chapter problems, and a free solutions manual is available for lecturers. (orig.)
Quantum to classical transition in quantum field theory
Lombardo, F C
1998-01-01
We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the cri...
Effective dynamics of a classical point charges
Polonyi, Janos
2013-01-01
The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham-Lorentz force is recovered and its similarity to anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-pole of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out.
Momentum Maps and Classical Relativistic Fields; 1, Covariant Field Theory
Gotay, M J; Marsden, J E; Gotay, Mark J.; Isenberg, James; Marsden, Jerrold E.
1998-01-01
This is the first paper of a four part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge transformations in such theories (either relativistic or not). To do this, in the course of these four papers, we develop and use a number of tools from symplectic and multisymplectic geometry. Of central importance in our analysis is the notion of the ``energy-momentum map'' associated to the gauge group of a given classical field theory. We hope to demonstrate that many different and apparently unrelated facets of field theories can be thereby tied together and understood in an essentially new way. In Part I we develop some of the basic theory of classical fields from a spacetime covariant viewpoint. We begin with a study of the covariant Lagrangian and Hamiltonian formalisms, on jet bundles and multisymplectic manifolds, respectively. Then we discuss symmetries, conserva...
Mathematical aspects of classical nonlinear field equations
In these notes we review some important advances in the mathematical analysis of classical nonlinear field equations. Our particular interest will be devoted to the nonlinear Schroedinger equation and the nonlinear Klein-Gordon equation. Since specifically nonlinear phenomena only become evident in the long-time behavior we are mainly concerned with global results rather than with solutions of these equations for a short time. We start with a thorough discussion of the nonlinear Schroedinger equation and its application to the theory of lasers and its bound states. In the following we study the general question of the existence of solutions of the nonlinear Klein-Gordon equation and other relativistic wave equations. The next section outlines the importance of the conservation laws which follow from the invariance properties of the equations. Special consideration is given to the Yang-Mills equations. The final section exposes a discussion of scattering theory mainly in the context of the nonlinear Klein-Gordon equation and summarizes the exciting development in recent years which has taken place in the nonlinear inverse scattering problem. (HJ)
Classical behavior of a scalar field in the inflationary universe
Extending the coarse-graining approach of Starobinsky, we formulate a theory to deal with the dynamics of a scalar field in inflationary universe models. We find a set of classical Langevin equations which describes the large scale behavior of the scalar field, provided that the coarse-grained size is greater than the effective compton wavelength of the scalar field. The corresponding Fokker-Planck equation is also derived which is defined on the phase space of the scalar field. We show that our theory is essentially equivalent to the one-loop field theory in de Sitter space and reduces to that of Starobinsky in a strong limit of the slow roll-over condition. Analysis of a simple Higgs potential model is done and the implications are discussed. (author)
Restrictions imposed on relativistic two-body interactions by classical relativistic field theory
We show that various relativistic potential models (all sharing exact relativistic two-body kinematics and a common nonrelativistic limit) can be distinguished by agreement or disagreement with relativistic corrections produced by classical field theory. We find that the only one of these models whose relativisic corrections duplicate those of classical field theory is the minimal Todorov equation. Conversely, we derive the Todorov equation from the semirelativistic dynamics of classical field theory, thus exposing the classical field-theoretic origins of its characteristic minimal potential structures and dependences on effective one-body variables
The traversable wormhole with classical scalar fields
Kim, S. -W; Kim, S. P.
1999-01-01
We study the Lorentzian static traversable wormholes coupled to quadratic scalar fields. We also obtain the solutions of the scalar fields and matters in the wormhole background and find that the minimal size of the wormhole should be quantized under the appropriate boundary conditions for the positive non-minimal massive scalar field.
Wu, Ning; Zhang, Dahua
2005-01-01
A systematic method is developed to study classical motion of a mass point in gravitational gauge field. First, the formulation of gauge theory of gravity in arbitrary curvilinear coordinates is given. Then in spherical coordinates system, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the Schwarzschild solution. In gauge theory of gravity, the equation of motion of a classical mass point in gravitational gauge field is given by Ne...
PREFACE: Particles and Fields: Classical and Quantum
Asorey, M.; Clemente-Gallardo, J.; Marmo, G.
2007-07-01
This volume contains some of the contributions to the Conference Particles and Fields: Classical and Quantum, which was held at Jaca (Spain) in September 2006 to honour George Sudarshan on his 75th birthday. Former and current students, associates and friends came to Jaca to share a few wonderful days with George and his family and to present some contributions of their present work as influenced by George's impressive achievements. This book summarizes those scientific contributions which are presented as a modest homage to the master, collaborator and friend. At the social ceremonies various speakers were able to recall instances of his life-long activity in India, the United States and Europe, adding colourful remarks on the friendly and intense atmosphere which surrounded those collaborations, some of which continued for several decades. This meeting would not have been possible without the financial support of several institutions. We are deeply indebted to Universidad de Zaragoza, Ministerio de Educación y Ciencia de España (CICYT), Departamento de Ciencia, Tecnología y Universidad del Gobierno de Aragón, Universitá di Napoli 'Federico II' and Istituto Nazionale di Fisica Nucleare. Finally, we would like to thank the participants, and particularly George's family, for their contribution to the wonderful atmosphere achieved during the Conference. We would like also to acknowledge the authors of the papers collected in the present volume, the members of the Scientific Committee for their guidance and support and the referees for their generous work. M Asorey, J Clemente-Gallardo and G Marmo The Local Organizing Committee George Sudarshan International Advisory Committee A. Ashtekhar (Pennsylvania State University, USA) L. J. Boya (Universidad de Zaragoza, Spain) I. Cirac (Max Planck Institute, Garching, Germany) G. F. Dell Antonio (Universitá di Roma La Sapienza, Italy) A. Galindo (Universidad Complutense de Madrid, Spain) S. L. Glashow (Boston University
Classical Solutions in Quantum Field Theory
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
Local Energy Velocity of Classical Fields
Drozdov, I. V.; Stahlhofen, A. A.
2007-01-01
It is proposed to apply a recently developed concept of local wave velocities to the dynamical field characteristics, especially for the canonical field energy density. It is shown that local energy velocities can be derived from the lagrangian directly. The local velocities of zero- and first- order for energy propagation has been obtained for special cases of scalar and vector fields. Some important special cases of these results are discussed.
Conformal Invariance in Classical Field Theory
Grigore, D. R.
1993-01-01
A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the action functional can be taken strictly invariant with respect to these transformations. In other words, there does not exists a "Chern-Simons" type Lagrangian for a conformally invariant Lagrangian theory.
Failure of the classical field model of Moessbauer spectroscopy
The conventional classical treatment of the field emitted by a Moessbauer nucleus predicts an enhanced counting rate in a two-detector coincidence scheme, whereas quantum electrodynamics does not. Our experiment agrees with QED
Quantum fermions and quantum field theory from classical statistics
Wetterich, C.
2012-01-01
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory for Dirac particles in an external electromagnetic field. This yields in the non-relativistic one-particle limit the Schr\\"odinger equation for a quantum particle in a potential. Interference or tunneling arise from classical probabilities.
A Tulczyjew triple for classical fields
The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of the variational calculus, we construct the Tulczyjew triple for first-order field theory. The important feature of our approach is that we do not postulate ad hoc the ingredients of the theory, but obtain them as unavoidable consequences of the variational calculus. This picture of field theory is covariant and complete, containing not only the Lagrangian formalism and Euler–Lagrange equations but also the phase space, the phase dynamics and the Hamiltonian formalism. Since the configuration space turns out to be an affine bundle, we have to use affine geometry, in particular the notion of the affine duality. In our formulation, the two maps α and β which constitute the Tulczyjew triple are morphisms of double structures of affine-vector bundles. We also discuss the Legendre transformation, i.e. the transition between the Lagrangian and the Hamiltonian formulation of the first-order field theory. (paper)
A Tulczyjew triple for classical fields
Grabowska, Katarzyna
2012-04-01
The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of the variational calculus, we construct the Tulczyjew triple for first-order field theory. The important feature of our approach is that we do not postulate ad hoc the ingredients of the theory, but obtain them as unavoidable consequences of the variational calculus. This picture of field theory is covariant and complete, containing not only the Lagrangian formalism and Euler-Lagrange equations but also the phase space, the phase dynamics and the Hamiltonian formalism. Since the configuration space turns out to be an affine bundle, we have to use affine geometry, in particular the notion of the affine duality. In our formulation, the two maps α and β which constitute the Tulczyjew triple are morphisms of double structures of affine-vector bundles. We also discuss the Legendre transformation, i.e. the transition between the Lagrangian and the Hamiltonian formulation of the first-order field theory.
Qian, Xiao-Feng; Howell, John C; Eberly, J H
2015-01-01
The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schr\\"odinger's famous remark about it [Proc. Camb. Phil. Soc. {\\bf 31}, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than ${\\cal B} = 2.54$. This is many standard deviations outside the limit ${\\cal B} = 2$ established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. {\\bf 23}, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit ${\\cal B} = 2.828...$. These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.
Classical solutions of some field theoretic models
In recent years much attention has been paid to simpler fields theories, so chosen that they possess several properties of nonabelian gauge theories. They preserve the conformal invariance of the action and one can define the topological charge for them. They possess nontrivial solutions to the equations of motion. The perturbation theory based on the fluctuations around each solution is characterized by asymptotic freedom. A model called CP sup(n-1) is presented and some models which are its natural generalizations are discussed. (M.F.W.)
Classical and quantum electrodynamics and the B(3) field
Evans, Myron W
2001-01-01
It is well known that classical electrodynamics is riddled with internal inconsistencies springing from the fact that it is a linear, Abelian theory in which the potentials are unphysical. This volume offers a self-consistent hypothesis which removes some of these problems, as well as builds a framework on which linear and nonlinear optics are treated as a non-Abelian gauge field theory based on the emergence of the fundamental magnetizing field of radiation, the B(3) field. Contents: Interaction of Electromagnetic Radiation with One Fermion; The Field Equations of Classical O (3) b Electrodyn
Lectures on Classical and Quantum Theory of Fields
Arodź, Henryk
2010-01-01
This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course.
Lectures on classical and quantum theory of fields
This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course. (orig.)
Backreaction to wormhole by classical scalar field: Will classical scalar field destroy wormhole?
Kim, Sung-Won
1999-01-01
There are two effects of extra matter fields on the Lorentzian traversable wormhole. The ``primary effect'' says that the extra matter can afford to be a part of source or whole source of the wormhole when the wormhole is being formed. Thus the matter does not affect the stability of wormhole and the wormhole is still safe. If the extra matter is extotic, it can be the whole part of the source of the wormhole. The ``auxiliary effect'' is that the extra matter plays the role of the additional ...
Dynamics of classical and quantum fields an introduction
Setlur, Girish S
2014-01-01
Dynamics of Classical and Quantum Fields: An Introduction focuses on dynamical fields in non-relativistic physics. Written by a physicist for physicists, the book is designed to help readers develop analytical skills related to classical and quantum fields at the non-relativistic level, and think about the concepts and theory through numerous problems. In-depth yet accessible, the book presents new and conventional topics in a self-contained manner that beginners would find useful. A partial list of topics covered includes: Geometrical meaning of Legendre transformation in classical mechanics Dynamical symmetries in the context of Noether's theorem The derivation of the stress energy tensor of the electromagnetic field, the expression for strain energy in elastic bodies, and the Navier Stokes equation Concepts of right and left movers in case of a Fermi gas explained Functional integration is interpreted as a limit of a sequence of ordinary integrations Path integrals for one and two quantum particles and for...
Introduction to classical and quantum Lagrangian field theory. 9
The basic principles of relativistic Lagrangian field theory are introduced, first in the classical context and later in the quantized form. Various free fields are discussed, their quantization, Lorentz invariance and the important discrete symmetries. Going on to interacting quantum fields, the invariant perturbation theory and Feynman graphs are succinctly discussed. Renormalizability and renormalization methods are covered with emphasis on the method of dimensional regularization. (author).3 refs.; 7 figs
On the variational formulation of classical Abelian gauge field theories
It is shown how one can formulate an action principle for classical Abelian gauge theories not by means of gauge potentials and currents but in terms of the gauge invariant field strengths and gauge variant stream potentias. The discussion is on a general formal level in n=s+t space-time dimensions and uses, for brevity, the language of differential forms
Classical electromagnetic field theory in the presence of magnetic sources
Chen, W J; Naón, C M; Chen, Wen-Jun; Li, Kang
2001-01-01
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a consistent Lagrangian for the theory. Then from the action principle we get both Maxwell's equation and the equation of motion of a dyon moving in the electro-magnetic field.
Classical Electromagnetic Field Theory in the Presence of Magnetic Sources
LI Kang(李康); CHEN Wen-Jun(陈文俊); NAON Carlos M.
2003-01-01
Using two new well-defined four-dimensional potential vectors, we formulate the classical Maxwell field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources.We set up a consistent Lagrangian for the theory. Then from the action principle we obtain both Maxwell's equation and the equation of motion of a dyon moving in the electromagnetic field.
Effect of classical noise on the geometric quantum phase
We consider the effect of classical noise applied to the geometric quantum phase of a spin 1/2 in a revolving magnetic field. The Berry phase shows some sensitivity to the noise because the Bloch vector cannot return to its original direction, and the variance caused by noise is proportional to the evolution time
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
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
Classical and Quantum Gauged Massless Rarita-Schwinger Fields
Adler, Stephen L
2015-01-01
We show that, in contrast to known results in the massive case, a minimally gauged massless Rarita-Schwinger field yields consistent classical and quantum theories. To simplify the algebra, we study a two component left chiral reduction of the massless theory. We formulate the classical theory in both Lagrangian and Hamiltonian form for a general non-Abelian gauging, and analyze the constraints and the Rarita-Schwinger gauge invariance of the action. An explicit wave front calculation for Abelian gauge fields shows that wave-like modes do not propagate with superluminal velocities. The quantized case is studied in covariant radiation gauge and axial gauge for the Rarita-Schwinger field, by both functional integral and Dirac bracket methods. The constraints have the form needed to apply the Faddeev-Popov method for deriving a functional integral in covariant radiation gauge. The Dirac bracket approach yields consistent Hamilton equations of motion in covariant radiation gauge, and leads to anticommutation rela...
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Kamenshchik, Alexander Y.; Manti, Serena
2012-01-01
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical ...
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Kamenshchik, A.; Manti, S.
2013-01-01
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical ...
On Covariant Poisson Brackets in Classical Field Theory
Forger, Michael; Salles, Mário O.
2015-01-01
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem - as testified by the extensive literature on "multisymplectic Poisson brackets", together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls - De Witt bracket and whose construction in a geometrical setting is now well unde...
Local gauge invariant Lagrangeans in classical field theories
We investigate the most general local gauge invariant Lagrangean in the framework of classical field theory. We rederive esentially Utiyama's result with a slight generalization. Our proof makes clear the importance of the so called current conditions, i.e. the requirement that the Noether currents are different from zero. This condition is of importance both in the general motivation for the introduction of the Yang-Mills fields and for the actual proof. Some comments are made about the basic mathematical structure of the problem - the gauge group. (author)
Motion of small bodies in classical field theory
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
Quantum Mind from a Classical Field Theory of the Brain
Zizzi, Paola
2011-01-01
We suggest that, with regard to a theory of quantum mind, brain processes can be described by a classical, dissipative, non-abelian gauge theory. In fact, such a theory has a hidden quantum nature due to its non-abelian character, which is revealed through dissipation, when the theory reduces to a quantum vacuum, where temperatures are of the order of absolute zero, and coherence of quantum states is preserved. We consider in particular the case of pure SU(2) gauge theory with a special anzatz for the gauge field, which breaks Lorentz invariance. In the ansatz, a contraction mapping plays the role of dissipation. In the limit of maximal dissipation, which corresponds to the attractive fixed point of the contraction mapping, the gauge fields reduce, up to constant factors, to the Pauli quantum gates for one-qubit states. Then tubuline-qubits can be processed in the quantum vacuum of the classical field theory of the brain, where decoherence is avoided due to the extremely low temperature. Finally, we interpret...
Lie Groupoids in Classical Field Theory I: Noether's Theorem
Costa, Bruno T; Pêgas, Luiz Henrique P
2015-01-01
In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. Here, we outline the basis of the program and, as a first step, show how to (re)formulate Noether's theorem about the connection between symmetries and conservation laws in this approach.
Models of measurement for quantum fields and for classical continuous random fields
Morgan, Peter
2006-01-01
A quantum field model for an experiment describes thermal fluctuations explicitly and quantum fluctuations implicitly, whereas a comparable continuous random field model would describe both thermal and quantum fluctuations explicitly. An ideal classical measurement does not affect the results of later measurements, in contrast to ideal quantum measurements, but we can describe the consequences of the thermal and quantum fluctuations of classically non-ideal measurement apparatuses explicitly....
Escaping the crunch: Gravitational effects in classical transitions
During eternal inflation, a landscape of vacua can be populated by the nucleation of bubbles. These bubbles inevitably collide, and collisions sometimes displace the field into a new minimum in a process known as a classical transition. In this paper, we examine some new features of classical transitions that arise when gravitational effects are included. Using the junction condition formalism, we study the conditions for energy conservation in detail, and solve explicitly for the types of allowed classical transition geometries. We show that the repulsive nature of domain walls, and the de Sitter expansion associated with a positive energy minimum, can allow for classical transitions to vacua of higher energy than that of the colliding bubbles. Transitions can be made out of negative or zero energy (terminal) vacua to a de Sitter phase, restarting eternal inflation, and populating new vacua. However, the classical transition cannot produce vacua with energy higher than the original parent vacuum, which agrees with previous results on the construction of pockets of false vacuum. We briefly comment on the possible implications of these results for various measure proposals in eternal inflation.
Controlling entanglement sudden death in cavity QED by classical driving fields
Zhang, Jian-Song; Xu, Jing-Bo; Lin, Qiang
2008-01-01
We investigate the entanglement dynamics of a quantum system consisting of two-level atoms interacting with vacuum or thermal fields with classical driving fields. We find that the entanglement of the system can be improved by adjusting the classical driving field. The influence of the classical field and the purity of the initial state on the entanglement sudden death is also studied. It is shown that the time of entanglement sudden death can be controlled by the classical driving fields. Pa...
Quasiperiodical orbits in the scalar classical lambdaphi4 field theory
New numerical and theoretical results of resonance kink-antikink (Kanti K) interactions in the classical one-dimentional space Higgs theory are presented. Earlier studies of these interactions revealed nine initial relative velocity-intervals with two-bounce Kanti K-collisions followed by the escape of kinks to infinite separations, the breathing solution was formed outside those intervals. Two-bounce Kanti K-interactions with the number of small oscillations between Kanti K-bounces up to 35 in the initial kink velocity interval 0.18 <= Vsub(infinite) <= 0.26 were found. Several examples for n-bounces Kanti K-interaction (n <= 6) are also found. The observed phenomenon can be explaned by the existence of quasi-two-periodical solutions of the nonlinear wave equation. The simple Hamiltonian with two degrees of freedom is studied. This model supplies quantitative descrtiptions of all numerical results for the field theory considered above. The considered phenomenon may be called ''autoquantization'' of a nonlinear classical scalar selfinteracting field
Classical and quantum particle dynamics in univariate background fields
Heinzl, Thomas; King, Ben
2016-01-01
We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or spacelike field dependence. For a special scenario in the classical regime we show how the radiation spectrum in the spacelike (undulator) case becomes well-approximated by the plane wave model in the high energy limit, despite the two systems being Lorentz inequivalent. In the quantum problem, there is no analogue of the WKB-exact Volkov solution. Nevertheless, WKB and uniform-WKB approaches give good approximations in all cases considered. Other approaches that reduce the underlying differential equations from second to first order are found to miss the correct physics for situations corresponding to barrier transmission and wide-angle scattering.
Geometry of Lagrangian first-order classical field theories
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied. (orig.)
Latfield2: A c++ library for classical lattice field theory
David, Daverio; Bevis, Neil
2015-01-01
latfield2 is a C++ library designed to simplify writing parallel codes for solving partial differen- tial equations, developed for application to classical field theories in particle physics and cosmology. It is a significant rewrite of the latfield framework, moving from a slab domain decomposition to a rod decomposition, where the last two dimension of the lattice are scattered into a two dimensional process grid. Parallelism is implemented using the Message Passing Interface (MPI) standard, and hidden in the basic objects of grid-based simulations: Lattice, Site and Field. It comes with an integrated parallel fast Fourier transform, and I/O server class permitting computation to continue during the writing of large files to disk. latfield2 has been used for production runs on tens of thousands of processor elements, and is expected to be scalable to hundreds of thousands.
Geometry of Lagrangian first-order classical field theories
Echeverria-Enriquez, A. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Munoz-Lecanda, M.C. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Roman-Roy, N. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica
1996-10-01
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether`s theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied. (orig.)
Real-time quantum trajectories for classically allowed dynamics in strong laser fields
Plimak, L I
2015-01-01
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are distinctly quantum features of these trajectories, such as the complex-valued coordinates, physically relevant in the classically allowed region of phase space, and what is their origin? First, we argue that solutions of classical equations of motion can account for quantum effects. To this end, we construct an exact solution to the classical Hamilton-Jacobi equation which accounts for dynamics of the wave packet, and show that this solution is physically correct in the limit $\\hbar \\to 0$. Second, we show that imaginary components of classical trajectories are directly linked to the finite size of the initial wavepacket in momentum space. This way, if the electronic wavepacket produced by optical tunneling in strong infrared fiels is localised both in coordinate and momentum, its m...
Gauge-fields and integrated quantum-classical theory
Physical situations in which quantum systems communicate continuously to their classically described environment are not covered by contemporary quantum theory, which requires a temporary separation of quantum degrees of freedom from classical ones. A generalization would be needed to cover these situations. An incomplete proposal is advanced for combining the quantum and classical degrees of freedom into a unified objective description. It is based on the use of certain quantum-classical structures of light that arise from gauge invariance to coordinate the quantum and classical degrees of freedom. Also discussed is the question of where experimenters should look to find phenomena pertaining to the quantum-classical connection. 17 refs
Classical mutual information in mean-field spin glass models
Alba, Vincenzo; Inglis, Stephen; Pollet, Lode
2016-03-01
We investigate the classical Rényi entropy Sn and the associated mutual information In in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and analytical tools we investigate the S-K model in the n -sheet booklet. This is achieved by gluing together n independent copies of the model, and it is the main ingredient for constructing the Rényi entanglement-related quantities. We find a glassy phase at low temperatures, whereas at high temperatures the model exhibits paramagnetic behavior, consistent with the regular S-K model. The temperature of the paramagnetic-glassy transition depends nontrivially on the geometry of the booklet. At high temperatures we provide the exact solution of the model by exploiting the replica symmetry. This is the permutation symmetry among the fictitious replicas that are used to perform disorder averages (via the replica trick). In the glassy phase the replica symmetry has to be broken. Using a generalization of the Parisi solution, we provide analytical results for Sn and In and for standard thermodynamic quantities. Both Sn and In exhibit a volume law in the whole phase diagram. We characterize the behavior of the corresponding densities, Sn/N and In/N , in the thermodynamic limit. Interestingly, at the critical point the mutual information does not exhibit any crossing for different system sizes, in contrast with local spin models.
Two-Component Theory of Classical Proca Fields in Curved Spacetimes with Torsionless Affinities
Santos Júnior, S. I.; Cardoso, J. G.
2016-04-01
The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is reviewed. Subsequently the entire set of field equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the fields allowed for. It appears that no interaction couplings between such fields and electromagnetic curvatures are ultimately carried by the wave equations at issue. What results is, in effect, that the only interactions which occur in the theoretical context under consideration involve strictly Proca fields and wave functions for gravitons.
Enhancing Quantum Discord in Cavity QED by Applying Classical Driving Field
QIAN Yi; XU Jing-Bo
2012-01-01
We investigate the quantum discord dynamics in a cavity quantum electrodynamics system, which consists of two noninteracting two-level atoms driven by independent optical Gelds and classical fields, and find that the quantum discord vanishes only asymptotically although entanglement disappears suddenly during the time evolution in the absence of classical fields. It is shown that the amount of quantum discord can be increased by adjusting the classical driving fields because the increasing degree of the amount of quantum mutual information is greater than classical correlation by applying the classical driving fields. Finally, the influence of the classical driving field on the fidelity of the system is also examined.%We investigate the quantum discord dynamics in a cavity quantum electrodynamics system,which consists of two noninteracting two-level atoms driven by independent optical fields and classical fields,and find that the quantum discord vanishes only asymptotically although entanglement disappears suddenly during the time evolution in the absence of classical fields.It is shown that the amount of quantum discord can be increased by adjusting the classical driving fields because the increasing degree of the amount of quantum mutual information is greater than classical correlation by applying the classical driving fields.Finally,the influence of the classical driving field on the fidelity of the system is also examined.
Classical dynamics of a charged particle in a laser field beyond the dipole approximation
Jameson, Paul; Khvedelidze, Arsen
2008-01-01
The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the non-relativistic Hamilton-Jacobi theory. The exact parametric representation for a particle's orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wav...
Evolution of quantum field, particle content and classicality in the three stage universe
Singh, Suprit; Padmanabhan, T
2013-01-01
We study the evolution of a quantum scalar field in a toy universe which has three stages of evolution, viz., (i) an early (inflationary) de Sitter phase (ii) radiation dominated phase and (iii) late-time (cosmological constant dominated) de Sitter phase. Using Schr\\"odinger picture, the scalar field equations are solved separately for the three stages and matched at the transition points. The boundary conditions are chosen so that field modes in the early de Sitter evolves from Bunch-Davies vacuum state. We determine the (time-dependent) particle content of this quantum state for the entire evolution of the universe and describe the various features both numerically and analytically. We also describe the quantum to classical transition in terms of a {\\it classicality parameter} which tracks the particle creation and its effect on phase space correlation of the quantum field.
Real-time quantum trajectories for classically allowed dynamics in strong laser fields
Plimak, L. I.; Ivanov, Misha Yu.
2015-10-01
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here, we address a key question which arises in this context: Are distinctly quantum features of these trajectories, such as the complex-valued coordinates, physically relevant in the classically allowed region of phase space, and what is their origin? First, we argue that solutions of classical equations of motion can account for quantum effects. To this end, we construct an exact solution to the classical Hamilton-Jacobi equation which accounts for dynamics of the wave packet, and show that this solution is physically correct in the limit ?. Second, we show that imaginary components of classical trajectories are directly linked to the finite size of the initial wave packet in momentum space. This way, if the electronic wave packet produced by optical tunnelling in strong infrared fields is localised both in coordinate and momentum, its motion after tunnelling ipso facto cannot be described with purely classical trajectories - in contrast to popular models in the literature.
On covariant Poisson brackets in classical field theory
Forger, Michael [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Salles, Mário O. [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN (Brazil)
2015-10-15
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.
On covariant Poisson brackets in classical field theory
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra
On covariant Poisson brackets in classical field theory
Forger, Michael; Salles, Mário O.
2015-10-01
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on "multisymplectic Poisson brackets," together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls-De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic "multisymplectic Poisson bracket" already proposed in the 1970s can be derived from the Peierls-De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.
Classical particles with spin in electromagnetic and gravitational fields
Following a review of several problems connected with classical particles with intrinsic angular momentum are reproduced the Frenkel equations (with the condition S sup(μν)U sub(ν)=0) by means of a holonomic variational principle, and have related them to Bargann, Michel and Tededgie equations. The treatment is then generalized to the case in wich S sup(μν)U sub(ν)=0 and the resulting equation coincide in the linearized limit with those obtained by Suttorp and de Groot. Also, by using variational principles, the generalizations to Frenkel equations are obtained, as well as to those of Suttorp and de Groot when electromagnetic and gravitational interactions are considered. Finally, those equations are analysed according to a scheme proposed by Oliveira and Tiommo where the gravitational interactions are described by gravielectric and gravimagnetic fields. The analogies in these equations of motion between the gravitational and eletromagnetic interactions, in the case in which the particle has a giromagnetic factor g=1, are shown. The last results complete a previous study by wald. (Author)
A Gauge-theoretical Treatment of the Gravitational Field: Classical
Gomes, Henrique
2008-01-01
In the geometrodynamical setting of general relativity one is concerned mainly with Riemannian metrics over a manifold $M$. We show that for the space Riem$(M)$, we have a natural principal fiber bundle (PFB) structure. This construction makes the gravitational field amenable to exactly the same gauge-theoretic treatment given in [Littlejohn] where it is used to separate rotational and vibrational degrees of freedom of $n$-particle systems, both classically and quantum mechanically. Furthermore, we show how the gauge connection in this PFB setting can be seen as a realization of Mach's Principle of Relative Motion, in accordance with Barbour's et al work on timeless gravitational theories. We show Barbour's reconstruction of GR is obtained by requiring the connection to be the one induced by the deWitt metric in Riem$(M)$. As a simple application of the gauge theory, we put the ADM lagrangian in a Kaluza-Klein context, and from conservation of charge we derive an interesting condition on the three-dimensional...
In this paper, a detailed numerical comparison of the high-harmonic generation (HHG) from free electrons in intense laser fields in both classical and semi-classical frameworks has been presented. These two frameworks have been widely used in the literature. It has been found that the HHG spectra display distinct quantitative differences for high-energy electrons. In some special situations, qualitative differences appear. Even if the radiation reaction is included in the electron classical dynamics, no consistent result can be obtained. Hence it should be of critical importance to submit the present HHG theory for high-precision experimental tests, which can help us not only to justify the present theories, but also to check the QED predictions in the high-intensity regime. (paper)
Quantum averaging and resonances: two-level atom in a one-mode classical laser field
M. Amniat-Talab
2007-06-01
Full Text Available We use a nonperturbative method based on quantum averaging and an adapted from of resonant transformations to treat the resonances of the Hamiltonian of a two-level atom interacting with a one-mode classical field in Floquet formalism. We illustrate this method by extraction of effective Hamiltonians of the system in two regimes of weak and strong coupling. The results obtained in the strong-coupling regime, are valid in the whole range of the coupling constant for the one-photon zero-field resonance.
Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions
Ryan eBabbush
2013-10-01
Full Text Available Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Qin, Hong [PPPL; Burby, Joshua W [PPPL; Davidson, Ronald C [PPPL
2014-10-01
It is commonly believed that energy-momentum conservation is the result of space-time symmetry. However, for classical particle-field systems, e.g., Klimontovich-Maxwell and Klimontovich- Poisson systems, such a connection hasn't been formally established. The difficulty is due to the fact that particles and the electromagnetic fields reside on different manifolds. To establish the connection, the standard Euler-Lagrange equation needs to be generalized to a weak form. Using this technique, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived.
Limits of applicability of the classical field concept in Moessbauer spectroscopy
We show that the classical model widely employed for the field radiated by an excited Moessbauer nucleus predicts an enhanced rate of coincidences for two detectors. This contradicts our experiment. We discuss the limits of applicability of the classical field concept for various experimental conditions. (orig.)
Quantum Electrodynamics Basis of Classical-Field High-Harmonic Generation Theory
王兵兵; 高靓辉; 傅盘铭; 郭东升; R. R. Freeman
2001-01-01
From the nonperturbative quantum electrodynamics theory, we derive the Landau-Dykhne formula which represents the quantum-mechanical formulation of the three-step model. These studies provide a basis for the classical-field approaches to high-order harmonic generation and justify some assumptions used in classical-field modelling.
Quantization, Classical and Quantum Field Theory and Theta - Functions
Tyurin, Andrey N.
2002-01-01
In the abelian case (the subject of several beautiful books) fixing some combinatorial structure (so called theta structure of level k) one obtains a special basis in the space of sections of canonical polarization powers over the jacobians. These sections can be presented as holomorphic functions on the "abelian Schottky space". This fact provides various applications of these concrete analytic formulas to the integrable systems, classical mechanics and PDE's. Our practical goal is to do the...
A course in mathematical physics 1 and 2 classical dynamical systems and classical field theory
Thirring, Walter
1992-01-01
The last decade has seen a considerable renaissance in the realm of classical dynamical systems, and many things that may have appeared mathematically overly sophisticated at the time of the first appearance of this textbook have since become the everyday tools of working physicists. This new edition is intended to take this development into account. I have also tried to make the book more readable and to eradicate errors. Since the first edition already contained plenty of material for a one semester course, new material was added only when some of the original could be dropped or simplified. Even so, it was necessary to expand the chap ter with the proof of the K-A-M Theorem to make allowances for the cur rent trend in physics. This involved not only the use of more refined mathe matical tools, but also a reevaluation of the word "fundamental. " What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler's laws, which determine the radii of the ...
Motion in classical field theories and the foundations of the self-force problem
Harte, Abraham I
2014-01-01
This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and self-torque are derived using simple, non-perturbative arguments. The relevant concepts are developed gradually by considering motion in a series of increasingly complicated theories. Newtonian gravity is discussed first, then Klein-Gordon theory, electromagnetism, and finally general relativity. Linear and angular momenta as well as centers of mass are defined in each of these cases. Multipole expansions for the force and torque are then derived to all orders for arbitrarily self-interacting extended objects. These expansions are found to be structurally identical to the laws of motion satisfied by extended test bodies, except that all relevant fields are replaced by effective versions which exclude the self-fields in a particular sense. Regularization methods traditionally ...
On the Lie symmetry group for classical fields in noncommutative space
Full text: An alternative way to include effects of noncommutative geometries in field theory is based on the concept of noncommutativity among degrees of freedom of the studied system. In this context it is reasonable to consider that, in the multiparticle noncommutative quantum mechanics (NCQM), the noncommutativity among degrees of freedom to discrete system with N particles is also verified. Further, an analysis of the classical limit of the single particle NCQM leads to a deformed Newtonian mechanics where the Newton's second law is modified in order to include the noncommutative parameter θιj and, for a one-dimensional discrete system with N particles, the dynamical evolution of each particle is given by this modified Newton's second law. Hence, applying the continuous limit to this multiparticle classical system it is possible to obtain a noncommutative extension of two -dimensional field theory in a noncommutative space. In the present communication we consider a noncommutative extension of the scalar field obtained from this approach and we analyze the Lie symmetries in order to compare the Lie group of this field with the usual scalar field in the commutative space. (author)
Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
Jurić, Tajron
2016-01-01
In this work, we consider a noncommutative (NC) massless scalar field coupled to the classical nonrotational BTZ geometry. In a manner of the theories where the gravity emerges from the underlying scalar field theory, we study the effective action and the entropy derived from this noncommutative model. In particular, the entropy is calculated by making use of the two different approaches, the brick wall method and the heat kernel method designed for spaces with conical singularity. We show that the UV divergent structures of the entropy, obtained through these two different methods, agree with each other. It is also shown that the same renormalization condition that removes the infinities from the effective action can also be used to renormalize the entanglement entropy for the same system. Besides, the interesting feature of the NC model considered here is that it allows an interpretation in terms of an equivalent system comprising of a commutative massive scalar field, but in a modified geometry; that of th...
Quantum Mind from a Classical Field Theory of the Brain
Zizzi, Paola
2011-01-01
We suggest that, with regard to a theory of quantum mind, brain processes can be described by a classical, dissipative, non-abelian gauge theory. In fact, such a theory has a hidden quantum nature due to its non-abelian character, which is revealed through dissipation, when the theory reduces to a quantum vacuum, where temperatures are of the order of absolute zero, and coherence of quantum states is preserved. We consider in particular the case of pure SU(2) gauge theory with a special anzat...
Violation of the Born Rule: Implications for the Classical Electromagnetic Field
Kastner, R. E.
2016-01-01
It is shown that violation of the Born Rule leads to a breakdown of the correspondence between the quantum electromagnetic field and its classical counterpart. Specifically, the relationship of the quantum coherent state to the classical electromagnetic field turns out to imply that if the Born Rule were violated, this could result in apparent deviations from the energy conservation law applying to the field and its sources (Poynting's Theorem). The result suggests that the Born Rule is just ...
The criteria for a solution of the field equations to be a classical limit of a quantum cosmology
Jones, R M
2002-01-01
If the gravitational field is quantized, then a solution of Einstein's field equations is a valid cosmological model only if it corresponds to a classical limit of a quantum cosmology. To determine which solutions are valid requires looking at quantum cosmology in a particular way. Because we infer the geometry by measurements on matter, we can represent the amplitude for any measurement in terms of the amplitude for the matter fields, allowing us to integrate out the gravitational degrees of freedom. Combining that result with a path-integral representation for quantum cosmology leads to an integration over 4-geometries. Even when a semiclassical approximation for the propagator is valid, the amplitude for any measurement includes an integral over the gravitational degrees of freedom. The conditions for a solution of the field equations to be a classical limit of a quantum cosmology are: (1) The effect of the classical action dominates the integration, (2) the action is stationary with respect to variation o...
An analogue of the Heisenberg uncertainty relation in prequantum classical field theory
Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility of representing averages of quantum observables, including correlations of observables on subsystems of a composite system, as averages with respect to fluctuations of classical random fields. PCSFT is a classical model of wave type. For example, 'electron' is described by electronic field. In contrast to quantum mechanics (QM), this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of , for example, an electron contains the irreducible contribution of the background field vacuum fluctuations. In principle, the traditional QM-formalism can be considered as a special regularization procedure: subtraction of averages with respect to vacuum fluctuations. In this paper, we derive a classical analogue of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. The PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM.
Effect of Classical Music on Reducing Blood Pressure in Children
Saing, Saloma Klementina; Rina, Oke; Ramayati, Rafita; Rusdidjas
2009-01-01
Background High blood pre ssure remains a public health problem. High blood pressure in children and adolescent is a major risk for cardiovascular disease in adulthood which can cause high morbidity and mortality. Listening to the classical music can be used as an alternative in reducing high blood pressure. Objective To investigate the effect of classical music in reducing blood pressure in children with high normal blood pressure and or hypertension. Methods Eighty eight students of S...
k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner–Rusk Formulations
The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner–Rusk formulation on classical mechanics.
Carter subgroups of singular classical groups over finite fields
高有; 石新华
2004-01-01
Let Fq be a finite field with qelements whereq = pα. In the present paper, the authors study the existence and structure of Carter subgroups of singular symplectic group Sp (Fq), singular unitary group U ( Fq2 ) and singular orthogonal group O ( Fq ) ( n is even) over finite fields Fq.
Classical solutions in quantum field theory solitons and instantons in high energy physics
Weinberg, Erick J
2012-01-01
Classical solutions play an important role in quantum field theory, high energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on ...
Synthetic Lorentz force in classical atomic gases via Doppler effect and radiation pressure
Dubček, T; Jukić, D; Aumiler, D; Ban, T; Buljan, H
2014-01-01
We theoretically predict a novel type of synthetic Lorentz force for classical (cold) atomic gases, which is based on the Doppler effect and radiation pressure. A fairly uniform and strong force can be constructed for gases in macroscopic volumes of several cubic millimeters and more. This opens the possibility to mimic classical charged gases in magnetic fields, such as those in a tokamak, in cold atom experiments.
Classical Billiards in a Magnetic Field and a Potential
Berglund, N
1996-01-01
We study billiards in plane domains, with a perpendicular magnetic field and a potential. We give some results on periodic orbits, KAM tori and adiabatic invariants. We also prove the existence of bound states in a related scattering problem.
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Qin, Hong; Davidson, Ronald C
2015-01-01
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underly...
Kim, Il-Gwang; Ri, Chol-Man; Im, Song-Jin
2016-01-01
In our paper we derived the classical motion equation of electromagnetic field in space with Higgs field and by means of it discussed the distributions of charge and current formed when the static electrical and magnetic fields are interacting with the spherically symmetrical Higgs field, and predicted the electrical polarizability of electron.
A course in mathematical physics 2 classical field theory
Thirring, Walter
1978-01-01
In the past decade the language and methods ofmodern differential geometry have been increasingly used in theoretical physics. What seemed extravagant when this book first appeared 12 years ago, as lecture notes, is now a commonplace. This fact has strengthened my belief that today students of theoretical physics have to learn that language-and the sooner the better. Afterall, they willbe the professors ofthe twenty-first century and it would be absurd if they were to teach then the mathematics of the nineteenth century. Thus for this new edition I did not change the mathematical language. Apart from correcting some mistakes I have only added a section on gauge theories. In the last decade it has become evident that these theories describe fundamental interactions, and on the classical level their structure is suffi cientlyclear to qualify them for the minimum amount ofknowledge required by a theoretician. It is with much regret that I had to refrain from in corporating the interesting developments in Kal...
The Poisson algebra of classical Hamiltonians in field theory and the problem of its quantization
Stoyanovsky, A.
2010-01-01
We construct the commutative Poisson algebra of classical Hamiltonians in field theory. We pose the problem of quantization of this Poisson algebra. We also make some interesting computations in the known quadratic part of the quantum algebra.
The reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity
Latyshev, A V
2015-01-01
The analysis of nonlinear interaction of transversal electromagnetic field with degenerate collisionless classical and quantum plasmas is carried out. Formulas for calculation electric current in degenerate collisionless classical and quantum plasmas are deduced. It has appeared, that the nonlinearity account leads to occurrence of longitudinal electric current directed along a wave vector. This second current is orthogonal to the known transversal current, received at the classical linear analysis. Graphic comparison of density of electric current for classical degenerate Fermi plasmas and Fermi-Dirac plasmas (plasmas with any degree of degeneration of electronic gas) is carried out. Graphic comparison of density of electric current for classical and quantum degenerate plasmas is carried out. Also comparison of dependence of density of electric current of quantum degenerate plasmas from dimensionless wave number at various values of dimensionless frequency of oscillations of electromagnetic field is carried ...
Measuring a piecewise constant axion field in classical electrodynamics
Obukhov, Yuri N. [Institute for Theoretical Physics, University of Cologne, 50923 Cologne (Germany)]. E-mail: yo@thp.uni-koeln.de; Hehl, Friedrich W. [Institute for Theoretical Physics, University of Cologne, 50923 Cologne (Germany)
2005-06-27
In order to settle the problem of the 'Post constraint' in material media, we consider the propagation of a plane electromagnetic wave in a medium with a piecewise constant axion field. Although a constant axion field does not affect the wave propagation in a homogeneous medium, we show that the reflection and transmission of a wave at an interface between the two media is sensitive to the difference of the axion values. This observation can be used to determine experimentally the axion piece in matter despite the fact that a constant axion value does not contribute to the Maxwell equations.
Measuring a piecewise constant axion field in classical electrodynamics
Obukhov, Yu N; Obukhov, Yuri N.; Hehl, Friedrich W.
2005-01-01
In order to settle the problem of the "Post constraint" in material media, we consider the propagation of a plane electromagnetic wave in a medium with a piecewise constant axion field. Although a constant axion field does not affect the wave propagation in a homogeneous medium, we show that the reflection and transmission of a wave at an interface between the two media is sensitive to the difference of the axion values. This observation can be used to determine experimentally the axion piece in matter despite the fact that a constant axion value does not contribute to the Maxwell equations.
Rare region effects at classical, quantum and nonequilibrium phase transitions
Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process. (topical review)
Rare region effects at classical, quantum and nonequilibrium phase transitions
Vojta, Thomas [Department of Physics, University of Missouri-Rolla, Rolla, MO 65409 (United States)
2006-06-02
Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process. (topical review)
Is the Meissner effect explicable in terms of classical electrodynamics
The core radius r0 of a current-carrying superconducting cylinder in the intermediate state determined from experimental data disagrees with the theoretical value of r0 derived on the basis of the classical interpretation of the Meissner effect. Then the problem arises of whether this interpretation of the Meissner effect corresponds to reality. (Auth.)
Non-Noetherian symmetries for oscillators in classical mechanics and in field theory
Hojman, Sergio A.; Delajara, Jamie; Pena, Leda
1995-01-01
Infinitely many new conservation laws both for free fields as well as for test fields evolving on a given gravitational background are presented. The conserved currents are constructed using the field theoretical counterpart of a recently discovered non-Noetherian symmetry which gives rise to a new way of solving the classical small oscillations problem. Several examples are discussed.
Classical trajectory perspective of atomic ionization in strong laser fields semiclassical modeling
Liu, Jie
2014-01-01
The ionization of atoms and molecules in strong laser fields is an active field in modern physics and has versatile applications in such as attosecond physics, X-ray generation, inertial confined fusion (ICF), medical science and so on. Classical Trajectory Perspective of Atomic Ionization in Strong Laser Fields covers the basic concepts in this field and discusses many interesting topics using the semiclassical model of classical trajectory ensemble simulation, which is one of the most successful ionization models and has the advantages of a clear picture, feasible computing and accounting for many exquisite experiments quantitatively. The book also presents many applications of the model in such topics as the single ionization, double ionization, neutral atom acceleration and other timely issues in strong field physics, and delivers useful messages to readers with presenting the classical trajectory perspective on the strong field atomic ionization. The book is intended for graduate students and researchers...
Classical dynamics of a charged particle in a laser field beyond the dipole approximation
Jameson, Paul
2008-01-01
The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the non-relativistic Hamilton-Jacobi theory. The exact parametric representation for a particle's orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wave the particle's trajectory, as an explicit function of the laboratory frame's time, is given in terms of the Jacobian elliptic functions, whose modulus is proportional to the laser's intensity and depends on the polarization of radiation. It is shown that the system exposes the ``intensity duality'', correspondence between the motion in the backgrounds with various intensities. In virtue of the modular properties of the Jacobian functions, by starting with the representative ``fundamental solution'' and applying a certai...
Gamma-ray halos as a measure of intergalactic magnetic fields: a classical moment problem
Ahlers, Markus
2011-01-01
The presence of weak intergalactic magnetic fields can be studied by their effect on electro-magnetic cascades induced by multi-TeV gamma-rays in the cosmic radiation background. Small deflections of secondary electrons and positrons as the cascade develops extend the apparent size of the emission region of distant TeV gamma-ray sources. These gamma-ray halos can be resolvable in imaging atmospheric Cherenkov telescopes and serve as a measure of the intergalactic magnetic field strength and coherence length. We present a method of calculating the gamma-ray halo for isotropically emitting sources by treating magnetic deflections in the cascade as a diffusion process. With this ansatz the moments of the halo follow from a set of simple diffusion-cascade equations. The reconstruction of the angular distribution is then equivalent to a classical moment problem. We present a simple solution using Pade approximations of the moment's generating function.
Dynamics of an electron spin in strong classical and quantized electromagnetic fields
Skoromnik, Oleg
2014-07-09
The electron motion in the presence of a strong classical and quantized pulse of an electromagnetic field is studied with a special emphasis on the spin degree of freedom. It is shown that the Hamiltonian of this system can be separated into two parts with the help of canonical transformations of the field variables, namely the interaction between an electron and a single collective mode of the field and fluctuations relatively to this collective mode. The application of perturbation theory to the fluctuations allows the conditions of applicability of the single-mode approximation for the quantized external field to be formulated. Furthermore, within this approximation the electron spin evolution is investigated. In addition to fast spin oscillations at the laser frequency, a second time scale is identified due to the intensity-dependent emissions and absorptions of field quanta, that is collapse and revival dynamics. The effect is observable at the experimentally feasible intensity of 10{sup 18} Wcm{sup 2}. After this, we switch to the regime of higher intensities, when the fluctuations of the external field can be neglected. We investigate the asymmetries in the electron scattering arising due to the electron polarization and pulse duration, and constrain the optimal conditions for the asymmetry observation.
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.
Reginatto, Marcel
2013-01-01
I consider the formulation of hybrid cosmological models that consists of a classical gravitational field interacting with a quantized massive scalar field in the formalism of ensembles on configuration space. This is a viable approach that provides an alternative to semiclassical gravity. I discuss a particular, highly nonclassical solution in two approximations, minisuperspace and spherically-symmetric midisuperspace. In both cases, the coupling of the quantum scalar field and classical gravitational field leads to a cosmological model which has a quantized radius of the universe.
Classical electrodynamics of a nonlinear Dirac field free solutions
In previous papers it has been shown that adding a positive scalar self-interaction (anti psipsi)2 to the Dirac field Lagrangian provides a reasonably satisfactory model to describe the barions. In this work, the authors analyze other solutions of the same nonlinear Dirac equation, making progress in the direction of a systematic analysis. These solutions could provide the ground states for more elaborate interacting schemes of the real particles. Unfortunately the new solutions appear to have energies consistently higher than the ones analyzed in previous papers. Also, the more complicated solutions, whose energy seems to be much higher than the simplest one, leave little hope for a low minimum energy state. (Auth.)
Aspects of integrability in a classical model for non-interacting fermionic fields
Grosse-Holz, Simon; Richter, Klaus; Urbina, Juan Diego
2015-01-01
In this work we investigate the issue of integrability in a classical model for noninteracting fermionic fields. This model is constructed via classical-quantum correspondence obtained from the semiclassical treatment of the quantum system. Our main finding is that the classical system, contrary to the quantum system, is not integrablein general. Regarding this contrast it is clear that in general classical models for fermionic quantum systems have to be handled with care. Further numerical investigation of the system showed that there may be islands of stability in the phase space. We also investigated a similar model that is used in theoretical chemistry and found this one to be most probably integrable, although also here the integrability is not assured by the quantum-classical correspondence principle.
Classical and Quantum Szilard Engine under Generalized Uncertainty Principle Effect
Chen, Chih-Wei
2016-01-01
We studied the Szilard engine under the effect of generalized uncertainty principle (GUP). In the classical Szilard engine, the work done by the engine is reduced by the GUP effect via a modified ideal gas law. In the quantum Szilard engine, the correction comes from the shifted eigen energy due to the nonlinear momentum dependence. We studied its effect on both bosonic and fermionic molecules.
Exact treatment of the Jaynes-Cummings model under the action of an external classical field
We consider the usual Jaynes-Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency ω0 and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strong value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity. - Highlights: → The time-dependent JCM, in the presence of the classical field, is still one of the essential problems in the quantum optics. → A new approach is applied through a certain canonical transformation. → The classical field augments the atomic frequency ω0 and mixes the original atomic states.
Rydberg atoms in external fields as an example of open quantum systems with classical chaos
We examine the quantum spectra of hydrogen atoms in external magnetic and electric fields above the ionization threshold with respect to signatures of classical chaos characteristics of open systems. The spectra are obtained by calculating wavefunctions and photionization cross sections in the continuum region with the aid of the complex-coordinate-rotation method. We find that the photoionization cross sections exhibit strong Ericson fluctuations, a quantum feature characteristic of classically chaotic scattering, in energy-field regions where classical trajectory calculations reveal a fractal dependence of the classical ionization time on the initial conditions. We also compare the nearest-neighbour-spacing distributions of complex resonance energies with predictions of random-matrix theories and find that our results are well reproduced by a Ginibre distribution. (author)
Exact treatment of the Jaynes-Cummings model under the action of an external classical field
Abdalla, M. Sebawe; Khalil, E. M.; Obada, A. S.-F.
2011-09-01
We consider the usual Jaynes-Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency ω0 and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strong value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity.
Violation of the Born Rule: Implications for the Classical Electromagnetic Field
Kastner, R E
2016-01-01
It is shown that violation of the Born Rule leads to a breakdown of the correspondence between the quantum electromagnetic field and its classical counterpart. Specifically, the relationship of the quantum coherent state to the classical electromagnetic field turns out to imply that if the Born Rule were violated, this could result in apparent deviations from the energy conservation law applying to the field and its sources (Poynting's Theorem). The result suggests that the Born Rule is just as fundamental a law of Nature as are the conservation laws.
(Semi)classical motion in fields of Aharonov-Bohm and Aharonov-Casher
Azimov, Ya. I.; Ryndin, R. M.
1997-01-01
Particle motion in the fields of Aharonov-Bohm and Aharonov-Casher is considered in framework of the classical theory to reveal conditions admitting duality of the two configurations. Important role of orientation of the magnetic dipole moment is demonstrated. Duality becomes totally destroyed by addition of electric dipole and/or higher multipole moments. Correspondence between quantum and classical considerations is also discussed.
A Semi-classical Upper Limit For Magnetic Fields Strength And the Case of Magnetars
Shafig, Amir A E
2015-01-01
In the pass from classical to modern physics, the idea of supposing some quantities having distinct or bounded values and keeping the rest continuous has been useful in treating many problems. In this paper, we suppose an upper limit for velocity of the classical particles and show applying this assumption to electromagnetism leads us to a maximum strength for magnetic fields which reveals an acceptable coincidence with the highest strengths in the cosmos, observed in magnetars.
Jiansong Zhang; Aixi Chen
2011-01-01
We investigate the entanglement dynamics of a quantum system consisting of two two-level atoms in a cavity with classical driving fields in the presence of white noise. The cavity is initially prepared in the vacuum state. Generally, the entanglement of two atoms decreases with the intensity of the thermal fields and the coupling strength of the two-level atoms to the thermal fields. However, we find that the entanglement of the quantum system can be enhanced by adjusting the frequency and the strength of the classical driving fields in the presence of white noise.%@@ We investigate the entanglement dynamics of a quantum system consisting of two two-level atoms in a cavity with classical driving fields in the presence of white noise.The cavity is initially prepared in the vacuum state.Generally, the entanglement of two atoms decreases with the intensity of the thermal fields and the coupling 8trength of the two-level atoms to the thermal fields.However, we find that the entanglement of the quantum system can be enhanced by adjusting the frequency and the strength of the classical driving fields in the presence of white noise.
Classical trajectory perspective of atomic ionization in strong laser fields. Semiclassical modeling
Dealing with timely and interesting issues in strong laser physics. Illustrates complex strong field atomic ionization with the simple semiclassical model of classical trajectory perspective for the first time. Provides a theoretical model that can be used to account for recent experiments. The ionization of atoms and molecules in strong laser fields is an active field in modern physics and has versatile applications in such as attosecond physics, X-ray generation, inertial confined fusion (ICF), medical science and so on. Classical Trajectory Perspective of Atomic Ionization in Strong Laser Fields covers the basic concepts in this field and discusses many interesting topics using the semiclassical model of classical trajectory ensemble simulation, which is one of the most successful ionization models and has the advantages of a clear picture, feasible computing and accounting for many exquisite experiments quantitatively. The book also presents many applications of the model in such topics as the single ionization, double ionization, neutral atom acceleration and other timely issues in strong field physics, and delivers useful messages to readers with presenting the classical trajectory perspective on the strong field atomic ionization. The book is intended for graduate students and researchers in the field of laser physics, atom molecule physics and theoretical physics. Dr. Jie Liu is a professor of Institute of Applied Physics and Computational Mathematics, China and Peking University.
Zampeli, Adamantia; Pailas, Theodoros; Terzis, Petros A.; Christodoulakis, T.
2016-05-01
In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries on the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.
Mahajan, Gaurang
2007-01-01
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is straightforward, several conceptual issues arise in such a study. We present a general formalism to address some of the conceptual issues like the emergence of classicality, definition of particle content, back reaction etc. In particular, we parametrize the wave function in terms of a complex number (which we call excitation parameter) and express all physically relevant quantities in terms it. Many of the notions -- like those of particle number density, effective Lagrangian etc., which are usually defined using asymptotic in-out states -- are generalized as time-dependent concepts and we show that these generalized definitions lead to useful and reasonable results. Having developed the general formalism we apply it to several examples. Exact analytic expressions are found ...
Molecular dynamics simulations using a combined quantum/classical force field have been carried out to investigate the properties of hydrogen peroxide in aqueous solution. Radial distribution functions exhibit close similarities with those obtained for the OH radical. They show that H2O2 is a better proton donor than H2O but a weaker proton acceptor. Solvent effects modify the O-H bonds, which are weakened and elongated by 0.02 A. The HOOH dihedral angle decreases by 11 deg. and the dipole moment increases by 0.8 D. The O-O bond length and bond order do not change much. Fluctuations of the frontier orbital energies are analyzed in detail as a function of both, the HOOH geometry and the solvent configuration. Hydrogen-bonds with solvent molecules appear to have an opposite influence depending on their donor/acceptor character. Interconversion between energy minima always proceeds through a transoid transition state
Jurić, Tajron; Samsarov, Andjelo
2016-05-01
In this work, we consider a noncommutative (NC) massless scalar field coupled to the classical nonrotational BTZ geometry. In a manner of the theories where the gravity emerges from the underlying scalar field theory, we study the effective action and the entropy derived from this noncommutative model. In particular, the entropy is calculated by making use of the two different approaches, the brick-wall method and the heat kernel method designed for spaces with conical singularity. We show that the UV divergent structures of the entropy obtained through these two different methods agree with each other. It is also shown that the same renormalization condition that removes the infinities from the effective action can also be used to renormalize the entanglement entropy for the same system. Besides, the interesting feature of the NC model considered here is that it allows an interpretation in terms of an equivalent system comprising a commutative massive scalar field but in a modified geometry: that of the rotational BTZ black hole, the result that hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole.
Influence of the External Classical Field on the Entanglement of a Two-Level Atom
Khalil, E. M.
2013-04-01
The atomic and the field entropies of a two-level atom, which is additionally driven by an external classical field are investigated. Under a certain canonical transformation for the excited and ground states the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture exact solutions for the time-dependent dynamical operators are obtained. The entanglement between atom-field system is studied by using the atomic and the field entropies. Also we use the concurrence to detect the sudden death phenomenon and the relationship between entropies and the concurrence of the entanglement are discussed. It is shown that the amount of entanglement, the atomic and the field entropies of the subsystem can be improved by controlling the external classical field.
Classical Electromagnetic Fields from Quantum Sources in Heavy-Ion Collisions
Holliday, Robert
2016-01-01
Electromagnetic fields are generated in high energy nuclear collisions by spectator valence protons. These fields are traditionally computed by integrating the Maxwell equations with point sources. One might expect that such an approach is valid at distances much larger than the proton size and thus such a classical approach should work well for almost the entire interaction region in the case of heavy nuclei. We argue that, in fact, the contrary is true: due to the quantum diffusion of the proton wave function, the classical approximation breaks down at distances of the order of the system size. As a result, the electromagnetic field (in vacuum) is present in the interaction region in the form of a traveling wave for much longer time than it was previously anticipated. Additionally, the quantum treatment of the sources removes the short-distance divergence of the field, making it possible to compute the maximal field strength achievable at a given collision energy.
Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation
Scheck, Florian
2012-01-01
The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...
Quantum-classical correspondence of a field induced KAM-type transition: A QTM approach
P K Chattaraj; S Sengupta; S Giri
2008-01-01
A transition from regular to chaotic behaviour in the dynamics of a classical Henon-Heiles oscillator in the presence of an external field is shown to have a similar quantum signature when studied using the pertaining phase portraits and the associated Kolmogorov-Sinai-Lyapunov entropies obtained through the corresponding Bohmian trajectories.
In this paper, classical particle transport processes in field-reversed configuration plasma is investigated by particle-tracking calculations. The end-loss rate is found to increase with ion temperature, and the temperature dependence is much stronger than that of the Bohm scaling and the empirical scaling. (author)
The trace of the fermion heat kernel in a constant field as a classical problem
The heat kernel of Dirac fermions in a constant gauge field is calculated using the supersymmetric sigma-model. It is shown that not only the index and the anomaly, but also the other characteristics of the Dirac operator are expressed through characteristic polynomials. The trace of the heat kernel can be found by solving a problem in classical mechanics. (orig.)
Apparent Paradoxes in Classical Electrodynamics: A Fluid Medium in an Electromagnetic Field
Kholmetskii, A. L.; Yarman, T.
2008-01-01
In this paper we analyse a number of teaching paradoxes of classical electrodynamics, dealing with the relativistic transformation of energy and momentum for a fluid medium in an external electromagnetic field. In particular, we consider a moving parallel plate charged capacitor, where the electric attraction of its plates is balanced by the…
Classical and thermodynamical aspects of black holes with conformally coupled scalar field hair
Winstanley, Elizabeth(Consortium for Fundamental Physics, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, United Kingdom)
2004-01-01
We discuss the existence, stability and classical thermodynamics of four-dimensional, spherically symmetric black hole solutions of the Einstein equations with a conformally coupled scalar field. We review the solutions existing in the literature with zero, positive and negative cosmological constant. We also outline new results on the thermodynamics of these black holes when the cosmological constant is non-zero.
Generation of non-classical optical fields by a beam splitter with second-order nonlinearity
Prakash, Hari
2016-01-01
We propose quantum-mechanical model of a beam splitter with second-order nonlinearity and show that non-classical features such as squeezing and sub-Poissonian photon statistics of optical fields can be generated in output fundamental and second harmonic modes when we mix coherent light beams via such a nonlinear beam splitter.
Field-testing of the ICHD-3 beta diagnostic criteria for classical trigeminal neuralgia
Maarbjerg, Stine; Sørensen, Morten Togo; Gozalov, Aydin; Bendtsen, Lars; Olesen, Jes
2015-01-01
INTRODUCTION: We aimed to field-test the beta version of the third edition of the International Classification of Headache Disorders (ICHD-3 beta) diagnostic criteria for classical trigeminal neuralgia (TN). The proposed beta draft of the 11th version of the International Classification of Diseases...
Classical Yang- Baxter Equation and Low Dimensional Triangular Lie Bialgebras Over Arbitrary Field
Zhang, Shouchuan
2006-01-01
Let $ L $ be a Lie algebra over arbitrary field $ k $ with dim $ L $ =3 and dim $ L' $ =2. All solutions of constant classical Yang- Baxter equation (CYBE) in Lie algebra $ L $ are obtained and the necessary conditions which $ (L,[\\ ],\\Delta_{r}, r) $ is a coboundary (or triangular) Lie bialgebra are given.
The Master Ward Identity and generalized Schwinger-Dyson Equation in classical field theory
In the framework of perturbative quantum field theory a new, universal renormalization condition (called Master Ward Identity) was recently proposed by one of us (M.D.) in a joint paper with F.-M. Boas. The main aim of the present paper is to get a better understanding of the Master Ward Identity by analyzing its meaning in classical field theory. It turns out that it is the most general identity for classical local fields which follows from the field equations. It is equivalent to a generalization of the Schwinger-Dyson Equation and is closely related to the Quantum Action Principle of Lowenstein and Lam. The validity of the Master Ward Identity makes possible a local construction of quantum gauge theories. (orig.)
Effective State Metamorphosis in Semi-Classical Loop Quantum Cosmology
Singh, P
2005-01-01
Modification to the behavior of geometrical density at short scales is a key result of loop quantum cosmology, responsible for an interesting phenomenology in the very early universe. We demonstrate the way a perfect fluid with arbitrary equation of state incorporates this change in its effective dynamics in the loop modified phase. We show that irrespective of the choice of matter component, stress-energy conservation law generically implies that classical equation of state metamorphoses itself to an effective negative equation of state below a critical scale determined by the theory.
On the classical limit of self-interacting quantum field Hamiltonians with cutoffs
AMMARI, Zied; Zerzeri, Maher
2012-01-01
We study, using Hepp's method, the propagation of coherent states for a general class of self interacting bosonic quantum field theories with spatial cutoffs. This includes models with non-polynomial interactions in the field variables. We show indeed that the time evolution of coherent states, in the classical limit, is well approximated by time-dependent affine Bogoliubov unitary transformations. Our analysis relies on a non-polynomial Wick quantization and a specific hypercontractive estim...
Kuwahara, Y; Nakamura, Y; Yamanaka, Y
2013-01-01
The $2 \\times 2$-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom [Phys. Rev. Lett. 110, 174301 (2013)]. We show that the Galley's Hamilto...
Chuen-An Tang
2014-01-01
Full Text Available The purposes of this study are to test reliabilities and validities of classics-reading curriculum (CRC scale, classics-reading promotion (CRP scale, and classics-reading effect (CRE scale and to examine the relationships between CRC, CRP, and CRE in elementary schools through applying CORPS framework. The pilot sample and formal sample contain 141 and 500 participants from elementary school faculties and classics-reading volunteers in the north, central, south, and east regions of Taiwan. The findings indicate that Cronbach α coefficients of curriculum cognition (CC, curriculum teaching (CT, inside-school promotion (IP, outside-school promotion (EP, learning effect (LE, and class management effect (CME subscales are .88, .85, .93, .91, .91, .94, respectively, through exploratory factor analysis and they have good internal reliabilities and construct validities, respectively, through confirmatory factor analysis. Moreover, CC, CT, IP, and EP have positive influences on LE (standardized coefficients .34, .25, .14, and .22 and on CME (standardized coefficients .41, .14, .14, and .20, respectively. CC, CT, IP, and EP can explain 69% of LE and 61% of CME. The model is supported by the data. Lastly, this study proposes some suggestions regarding the classics-reading education for elementary schools.
The classical wormhole solution and wormhole wavefunction with a nonlinear Born-Infeld scalar field
Lu, H. Q.; Shen, L. M.; Ji, P. (Ping); Ji, G. F.; Sun, N. J.
2002-01-01
On this paper we consider the classical wormhole solution of the Born-Infeld scalar field. The corresponding classical wormhole solution can be obtained analytically for both very small and large $\\dot{\\phi}$. At the extreme limits of small $\\dot{\\phi}$ the wormhole solution has the same format as one obtained by Giddings and Strominger[10]. At the extreme limits of large $\\dot{\\phi}$ the wormhole solution is a new one. The wormhole wavefunctions can also be obtained for both very small and l...
Numerical study of chiral plasma instability within the classical statistical field theory approach
Buividovich, P. V.; Ulybyshev, M. V.
2016-07-01
We report on a numerical study of real-time dynamics of electromagnetically interacting chirally imbalanced lattice Dirac fermions within the classical statistical field theory approach. Namely, we perform exact simulations of the real-time quantum evolution of fermionic fields coupled to classical electromagnetic fields, which are in turn coupled to the vacuum expectation value of the fermionic electric current. We use Wilson-Dirac Hamiltonian for fermions, and noncompact action for the gauge field. In general, we observe that the backreaction of fermions on the electromagnetic field prevents the system from acquiring chirality imbalance. In the case of chirality pumping in parallel electric and magnetic fields, the electric field is screened by the produced on-shell fermions and the accumulation of chirality is hence stopped. In the case of evolution with initially present chirality imbalance, axial charge tends to transform to helicity of the electromagnetic field. By performing simulations on large lattices we show that in most cases this decay process is accompanied by the inverse cascade phenomenon, which transfers energy from short-wavelength to long-wavelength electromagnetic fields. In some simulations, however, we observe a very clear signature of inverse cascade for the helical magnetic fields that is not accompanied by the axial charge decay. This suggests that the relation between the inverse cascade and axial charge decay is not as straightforward as predicted by the simplest form of anomalous Maxwell equations.
Classical dynamics of a charged particle in a laser field beyond the dipole approximation
Jameson, Paul; Khvedelidze, Arsen
2008-05-01
The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the nonrelativistic Hamilton-Jacobi theory. The exact parametric representation for a particle’s orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wave the particle’s trajectory, as an explicit function of the laboratory frame’s time, is given in terms of the Jacobian elliptic functions, whose modulus is proportional to the laser’s intensity and depends on the polarization of radiation. It is shown that the system exposes the intensity duality, correspondence between the motion in the backgrounds with various intensities. In virtue of the modular properties of the Jacobian functions, by starting with the representative “fundamental solution” and applying a certain modular transformation one can obtain the particle’s orbit in the monochromatic plane wave background with arbitrarily prescribed characteristics.
Estimating galaxy cluster magnetic fields by the classical and hadronic minimum energy criterion
Pfrommer, C
2004-01-01
We wish to estimate magnetic field strengths of radio emitting galaxy clusters by minimising the non-thermal energy density contained in cosmic ray electrons (CRe), protons (CRp), and magnetic fields. The classical minimum energy estimate can be constructed independently of the origin of the radio synchrotron emitting CRe yielding thus an absolute minimum of the non-thermal energy density. Provided the observed synchrotron emission is generated by a CRe population originating from hadronic interactions of CRp with the ambient thermal gas of the intra-cluster medium, the parameter space of the classical scenario can be tightened by means of the hadronic minimum energy criterion. For both approaches, we derive the theoretically expected tolerance regions for the inferred minimum energy densities. Application to the radio halo of the Coma cluster and the radio mini-halo of the Perseus cluster yields equipartition between cosmic rays and magnetic fields within the expected tolerance regions. In the hadronic scena...
Back-Reaction of Classical Fields on Black Hole Area Law
Huang, Wung-Hong
2015-01-01
We study the back-reaction of classical Maxwell field and massive scalar field on the BTZ black hole entropy. The exact values of the modification which correct the black hole area law are found. We discuss the similar properties between the scalar and Maxwell field which is investigated in both of Coulomb gauge and Lorentz gauge. The dependences of mass and mode number on the black hole entropy are illustrated. We also study the back-reaction by D branes, which is described by DBI action, and explicitly check that the classical solution which gives the black hole entropy precisely corrects the black hole area law. Our results extend the calculations of the generalized gravitational entropy proposed in recent by Lewkowycz and Maldacena [1].
Spatial Wilson loops in the classical field of high-energy heavy-ion collisions
Petreska, Elena
2013-01-01
It has been previously shown numerically that the expectation value of the magnetic Wilson loop at the initial time of a heavy-ion collision exhibits area law scaling. This was obtained for a classical non-Abelian gauge field in the forward light cone and for loops of area $A\\gsim 2/Q_s^2$. Here, we present an analytic calculation of the spatial Wilson loop evaluated in the classical field of a collision within perturbation theory. We show that the leading diagram corresponds to two sources, for both projectile and target, whose field is evaluated at second order in the gauge potential. We find that in ``naive'' perturbation theory without screening the magnetic flux through a loop is proportional to the square of its area.
Dodonov, V V
2016-01-01
An exact infinite set of coupled ordinary differential equations, describing the evolution of the modes of the classical electromagnetic field inside an ideal cavity, containing a thin slab with the time-dependent conductivity $\\sigma(t)$ and dielectric permittivity $\\varepsilon(t)$, is derived for the dispersion-less media. This problem is analyzed in connection with the attempts to simulate the so called Dynamical Casimir Effect in three-dimensional electromagnetic cavities, containing a thin semiconductor slab, periodically illuminated by strong laser pulses. Therefore it is assumed that functions $\\sigma(t)$ and $\\delta\\varepsilon(t)=\\varepsilon(t)-\\varepsilon(0)$ are different from zero during short time intervals (pulses) only. The main goal is to find the conditions, under which the initial nonzero classical field could be amplified after a single pulse (or a series of pulses). Approximate solutions to the dynamical equations are obtained in the cases of "small" and "big" maximal values of the function...
We review a recently introduced unified approach to the analytical quantification of correlations in Gaussian states of bosonic scalar fields by means of Rényi-2 entropy. This allows us to obtain handy formulae for classical, quantum, total correlations, as well as bipartite and multipartite entanglement. We apply our techniques to the study of correlations between two modes of a scalar field as described by observers in different states of motion. When one or both observers are in uniform acceleration, the quantum and classical correlations are degraded differently by the Unruh effect, depending on which mode is detected. Residual quantum correlations, in the form of quantum discord without entanglement, may survive in the limit of an infinitely accelerated observer Rob, provided they are revealed in a measurement performed by the inertial Alice. (paper)
A double-slit experiment for non-classical interference effects in decision making.
La Mura, Pierfrancesco
2014-01-01
We discuss the possible nature and role of non-physical entanglement, and the classical vs. non-classical interface, in models of human decision-making. We also introduce an experimental setting designed after the double-slit experiment in physics, and discuss how it could be used to discriminate between classical and non-classical interference effects in human decisions. PMID:24259289
AMMARI, Zied; Falconi, Marco
2016-01-01
In the mid Sixties Edward Nelson proved the existence of a consistent quantum field theory that describes the Yukawa-like interaction of a non-relativistic nucleon field with a relativistic meson field. Since then it is thought, despite the renormalization procedure involved in the construction, that the quantum dynamics should be governed in the classical limit by a Schr\\"odinger-Klein-Gordon system with Yukawa coupling. In the present paper we prove this fact in the form of a Bohr correspon...
Kuwahara, Y.; Nakamura, Y.; Yamanaka, Y.
2013-12-01
The 2×2-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom [1]. We show that the Galley's Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD.
Kuwahara, Y., E-mail: a.kuwahara1224@asagi.waseda.jp; Nakamura, Y., E-mail: nakamura@aoni.waseda.jp; Yamanaka, Y., E-mail: yamanaka@waseda.jp
2013-12-09
The 2×2-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom. We show that the Galley's Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD.
Current-carrying plasma and the magnetic field ambiguity in classical MHD theory
An ambiguity in the classical theoretical framework used for computing magnetohydrostatic equilibrium is pointed out and analyzed. This inconsistency implies that some proposed solutions of the magnetohydrodynamic (MHD) equations may not represent actual magnetic fields of plasma currents in the geometry considered. The root of the inconsistency is that the magnetostatic field equation and the magnetohydrostatic equations are not invariant under the same transformations. There are two types of problems where inconsistencies have arisen in the literature: (a) unphysical magnetic fields are postulated inside a plasma current; and (b) vacuum magnetic fields are postulated that are not gradient fields. In both cases, magnetic fields are obtained which cannot be created in the laboratory. This inconsistency is traced back to a mishandling of the mathematical structure of the magnetic field equation. The magnetic field rvec B is a vector potential for the current density distribution rvec j, just as rvec A is a vector potential for rvec B. Nevertheless, whereas a gauge transformation on rvec A is unobservable (gauge invariant), the analogous gauge transformation in the rvec B vector (gradient field transformation) is indeed observable and changes the Lorentz force. Following Alfven, the authors characterize plasmas mathematically through the field lines of the current density distribution vector. Classical MHD theory, by contrast, is concerned strictly with magnetic field lines. They show here how this magnetic field approach can lead to inconsistencies when applied to plasmas. A resolution of entrenched ambiguities is made possible by using the current fiber description to derive a corrected Grad-Shafranov plasma equilibrium equation
Khrennikov, Andrei
2016-01-01
The scientific methodology based on two descriptive levels, ontic (reality as it is ) and epistemic (observational), is briefly presented. Following Schr\\"odinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be inaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity - the quantum state ("wave function"). The correspondence PCSFT to QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and th...
Xiao, Jie; Guo, Zhaoli; Cai, Chao
2013-10-01
Outside the classical receptive field (CRF), there exists a broad non-classical receptive field (NCRF). The response of the central neuron is affected not only by the stimulus inside the CRF, but also modulated by the stimulus surrounding it. The contextual modulation is mediated by horizontal connections across the visual cortex. In this paper, a contour detection method inspired by the visual mechanism in the primary visual cortex (V1) is proposed. The method is divided in three steps. Firstly, the response of every single visual neuron in V1 is computed by local energy. Secondly, the facilitation and suppression (the contextual influence) on a neuron through horizontal interactions are obtained by constructing a two neighbor modulating functions. Finally, the total output response of one neuron to complex visual stimuli is acquired by combing the influence of local visual context on the neuron and energy response by itself. We tested it on natural image and encouraging results were acquired.
A. Sadeghi
2007-03-01
Full Text Available Using both mean field renormalization group (MFRG and Surface-Bulk MFRG (SBMFRG, we study the critical behavior of the classical Heisenberg and XY models on a simple cubic lattice. Critical temperatures as well as critical exponents, characteristic the universality classes of these two models were calculated, analytically for1, 2, 3 and 4 spin clusters. The results are in good agreement with higher accurate methods such as Monte Carlo and High- temperature series.
Classical Monte-Carlo simulation for Rydberg states ionization in strong field
Carrat, Vincent; Magnuson, Eric; Gallagher, Thomas
2016-05-01
The resilience of Rydberg states against ionization has fascinated physicists for a long time. One might expect that the loosely bound electron would be ionized by modest electromagnetic field. However, experiments show that a notable fraction of neutral atoms survive in Rydberg states when exposed to strong microwave or laser fields. Energy transfer between the field and the photoelectron occurs when the electron is close to the ionic core and depends on the phase of the field. Since those states have orbital times that can be larger than the field pulse duration, these energy exchanges will only occur a few times. While we can experimentally control the initial time when we create the Rydberg states and as a consequence the initial energy transfer from the field, our classical calculation suggests that the phase when the electron is returning to the ionic core on the next orbit is chaotic. Statistically the electron only has a 50% chance to gain energy which may lead to ionization. Additionally the population tends to accumulate in very high n states where ionization is less likely due to fewer rescattering events. Though incomplete, this classical Monte-Carlo simulation provides useful insights for understanding the experimental observations. This work has been entirely performed at University of Virginia and is supported by the U. S. Department of Energy, Office of Basic energy Sciences.
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.
2014-04-01
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
One-dimensional classical diffusion in a random force field with weakly concentrated absorbers
Texier, Christophe; Hagendorf, Christian
2009-01-01
A one-dimensional model of classical diffusion in a random force field with a weak concentration $\\rho$ of absorbers is studied. The force field is taken as a Gaussian white noise with $\\mean{\\phi(x)}=0$ and $\\mean{\\phi(x)\\phi(x')}=g \\delta(x-x')$. Our analysis relies on the relation between the Fokker-Planck operator and a quantum Hamiltonian in which absorption leads to breaking of supersymmetry. Using a Lifshits argument, it is shown that the average return probability is a power law $\\sme...
Finite size effect on classical ideal gas revisited
Ghosh, P.; Ghosh, S.; Mitra, J.; Bera, N.
2015-09-01
Finite size effects on classical ideal gas are revisited. The micro-canonical partition function for a collection of ideal particles confined in a box is evaluated using Euler-Maclaurin’s as well as Poisson's summation formula. In Poisson's summation formula there are some exponential terms which are absent in Euler-Maclaurin’s formula. In the thermodynamic limit the exponential correction is negligibly small but in the macro/nano dimensions and at low temperatures they may have a great significance. The consequences of finite size effects have been illustrated by redoing the calculations in one and three dimensions keeping the exponential corrections. Global and local thermodynamic properties, diffusion driven by the finite size effect, and effect on speed of sound have been discussed. Thermo-size effects, similar to thermoelectric effects, have been described in detail and may be a theoretical basis with which to design nano-scaled devices. This paper can also be very helpful for undergraduate and graduate students in physics and chemistry as an instructive exercise for a good course in statistical mechanics.
Effective state metamorphosis in semi-classical loop quantum cosmology
Modification to the behaviour of geometrical density at short scales is a key result of loop quantum cosmology, responsible for an interesting phenomenology in the very early universe. We demonstrate the way matter with arbitrary scale factor dependence in Hamiltonian incorporates this change in its effective dynamics in the loop-modified phase. For generic matter, the equation of state starts varying near a critical scale factor, becomes negative below it and violates the strong energy condition. This opens a new avenue to generalize various phenomenological applications in loop quantum cosmology. We show that different ways to define energy density may yield radically different results, especially for the case corresponding to classical dust. We also discuss implications for frequency dispersion induced by modification to geometric density at small scales
Production of partons in the presence of classical fields in ultrarelativistic heavy-ion collisions
In this work the production of quarks, antiquarks and of gluonic fluctuations is studied in the presence of classical bosonic field. A comparison of the production of anti-quark pairs with the creation of pairs of gluonic quantum fluctuations based on perturbative calculations will be presented here. This analysis is valid for quantum particles with a large momentum compared to the magnitude of the classical vector potential multiplied by the coupling constant. The model contains 3 parameters: the initial magnitude of the gauge field, the coupling constant and the time scale on which the field decays. It appears that none of the species (quark-antiquark pairs, gluonic fluctuation pairs, bosons and fermion-anti fermions) can be neglected from the beginning. A corresponding calculation requires a non-perturbative description of at least the soft fermions. In this thesis the exact expression for fields varying arbitrarily in time is derived. After the full solution has been obtained, various approximation schemes are proposed for different domains, in order to find out into which the situation under consideration falls. There are approximations in the ultraviolet (perturbative), the infrared, and the Abelian (commutative) regime. The exact expression and the lowest orders of the different approximation schemes are evaluated in the presence of the model field with the same parameters as before. (A.C.)
We investigate a two-level atom interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence and find that a stationary quantum discord can arise in the interaction of the atom and cavity field as the time turns to infinity. We also find that the stationary quantum discord can be increased by applying a classical driving field. Furthermore, we explore the quantum discord dynamics of two identical non-interacting two-level atoms independently interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence. Results show that the quantum discord between two atoms is more robust than entanglement under phase decoherence and the classical driving field can help to improve the amount of quantum discord of the two atoms. (general)
In this paper, we investigate the effects of a classical gravitational field on the dynamical behaviour of the nonlinear atom-field interaction within the framework of the f-deformed Jaynes-Cummings model. For this purpose, we first introduce a set of new atomic operators obeying an f-deformed su(2) algebraic structure to derive an effective Hamiltonian for the system under consideration. Then by solving the Schroedinger equation in the interaction picture and considering certain initial quantum states for the atomic and radiation subsystems, we analyse the influence of gravity on the temporal evolution of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and deformed quadrature squeezing of the radiation field.
Negative effective mass of wave-driven classical particles in dielectric media
For a classical particle undergoing nonlinear interaction with a wave in dielectric medium, a perturbation theory is developed, showing that the particle motion can be described in terms of an effective parallel mass which can become negative. A relativistic particle interacting with a circularly polarized wave and a static magnetic field is studied as an example. For the three stationary orbits corresponding to the same velocity parallel to the magnetic field, the conditions are found under which all these equilibria are centerlike, or neutrally stable. It is shown that a negative parallel mass is realized in the vicinity of the intermediate-energy equilibrium and can lead to a plasma collective instability.
A New Semi-Symmetric Uniﬁed Field Theory of the Classical Fields of Gravity and Electromagnetism
Suhendro I.
2007-10-01
Full Text Available We attempt to present a classical theoretical framework in which the gravitational and electromagnetic fields are unified as intrinsic geometric objects in the space-time manifold. For this purpose, we first present the preliminary geometric considerations dealing with the metric differential geometry of Cartan connections. The unified field theory is then developed as an extension of the general theory of relativity based on a semi- symmetric Cartan connection which is meant to be as close as possible structurally to the symmetric connection of the Einstein-Riemann space-time.
Latyshev, A V
2015-01-01
From Vlasov kinetic equation for collisionless plasmas distribution function in square-law approximation on size of electromagnetic field is received. Formulas for calculation electric current at any temperature (any degree of degeneration of electronic gas) are deduced. The case of small values of the wave numbers is considered. It is shown, that the nonlinearity account leads to occurrence the longitudinal electric current directed along a wave vector. This longitudinal current orthogonal to known transversal classical current, received at the linear analysis. From the kinetic equation with Wigner integral for collisionless quantum plasma distribution function is received in square-law on vector potential approximation. Formulas for calculation electric current at any temperature are deduced. The case of small values of wave number is considered. It is shown, that size of a longitudinal current at small values of wave number and for classical plasma and for quantum plasma coincide. Graphic comparison of dim...
Zarei, Mohammad Hossein
2016-01-01
Although creating a unified theory in Elementary Particles Physics is still an open problem, there are a lot of attempts for unifying other fields of physics. Following such unifications, we regard a two dimensional (2D) classical $\\Phi^{4}$ field theory model to study several field theories with different symmetries in various dimensions. While the completeness of this model has been already proved by a mapping between statistical mechanics and quantum information theory, here, we take into account a fundamental systematic approach with purely mathematical basis to re-derive such completeness in a general manner. Due to simplicity and generality, we believe that our method leads to a general approach which can be understood by other physical communities as well as quantum information theorists. Furthermore, our proof of the completeness is not only a proof-of-principle, but also an interesting algorithmic proof. We consider a discrete version of a general field theory as an arbitrary polynomial function of f...
The influence of phase damping on a two-level atom in the presence of the classical laser field
Sebawe Abdalla, M.; Obada, A.-S. F.; Khalil, E. M.; Ali, S. I.
2013-11-01
In this paper we consider the influence of phase damping on the Jaynes-Cummings model (JCM) in the presence of the classical laser field. It is shown that for the temporal evolution of the atomic inversion a detuning parameter plays a role in delaying the effect of the damping. Our consideration is also extended to discuss the atomic Wehrl entropy and entropy squeezing. For the case of the marginal distribution, it is noted that the damping factor plays a considerable role in reducing the number of the fluctuations in the function behavior. On the other hand the damping factor removes the phenomenon of squeezing from both quadratures of the entropy squeezing.
A Clifford Algebra Approach to the Classical Problem of a Charge in a Magnetic Monopole Field
Vaz, Jayme
2013-05-01
The motion of an electric charge in the field of a magnetic monopole is described by means of a Lagrangian model written in terms of the Clifford algebra of the physical space. The equations of motion are written in terms of a radial equation (involving r=| r|, where r( t) is the charge trajectory) and a rotor equation (written in terms of an unitary operator spinor R). The solution corresponding to the charge trajectory in the field of a magnetic monopole is given in parametric form. The model can be generalized in order to describe the motion of a charge in the field of a magnetic monopole and other additional central forces, and as an example, we discuss the classical ones involving linear and inverse square interactions.
Full text: We consider a classical particle minimally coupled to an external electromagnetic field, in both non-relativistic and relativistic regimes. The coupling is constructed via the electromagnetic potential which is assumed to satisfy the classical Maxwell equations. We review Noether's theorem at classical level associating infinitesimal symmetries to conserved quantities. The fundamental space-time symmetries are investigated considering a non-relativistic action, a relativistic action in a particular reference frame and an explicitly Lorentz invariant Lagrangian. We work out in detail the corresponding conserved quantities for each case. The well-known Noether's theorem establishes a connection between continuous infinitesimal symmetries of the action and conserved quantities - given a particular action, for each infinitesimal symmetry there exists an explicit conserved quantity. In particular, a single particle subjected to an external electromagnetic field gives rise to an action which may enjoy space-time symmetries. For the non-relativistic particle, we analyze translations in space and time and spatial rotations, calculating the conserved quantities - linear momentum, energy and angular momentum. The relativistic particle enjoys space-time Lorentz symmetry. Thus we check the six symmetries of the homogeneous Lorentz group, corresponding to three spatial rotations and three boosts, and the four space-time translations extending to the non-homogeneous Lorentz group (Poincare group). We consider two distinct actions describing the relativistic particle minimally coupled to an external electromagnetic field - the first one describes the particle in a particular frame of reference enforcing the relativistic generalization of Newton's second law with the Lorentz force while the second one is obtained from a Lorentz scalar Lagrangian. In all cases the conserved quantities are explicitly calculated via Noether's theorem. (author)
Li, Jianxiong; Thumm, Uwe
2016-05-01
During the IR-streaked XUV photoemission from nanoparticles, the net IR electric field varies over the spatial extension of the target, an effect that for metallic particles is further enhanced by strong induced plasmonic polarization. This spatial dependence prevents the convenient use of ``Volkov states'' [solutions of the time-dependent Schrödinger equation for a free electron in a spatially homogeneous (cw) electromagnetic field] as approximate final states in quantum-mechanical photoemission calculations. To obtain the wave function of a free electron in a spatially inhomogeneous electromagnetic field, we propose a semi-classical approach based on time-dependent WKB theory. Generalizing ordinary Volkov states, this method provides a simple expression for modeling the final photoelectron state. We employ such generalized Volkov states to calculate the streaked photoelectron spectra from gold nanospheres and assess their accurary. Supported by the NSD-EPSCoR program, NSF, and the USDoE.
Kamboj, Aman; Patel, Chhabi L.; Chaturvedi, V.K.; Saini, Mohini; Praveen K. Gupta
2014-01-01
We report the complete genome sequence of an Indian field isolate of classical swine fever virus (CSFV) belonging to predominant subgenotype 1.1 prevalent in India. This report will help in understanding the molecular diversity of CSFV strains circulating worldwide and to select and develop a suitable vaccine candidate for classical swine fever (CSF) control in India.
Garcia-Adeva, A. J.; Huber, D. L.
2001-01-01
A microscopic derivation of the classical Generalized Constant Coupling (GCC) model for geometrically frustrated magnets is presented. Starting from the classical Heisenberg Hamiltonian, the partition function for clusters with p = 2, 3, 4 ,...spins in the presence of the inhomogeneous symmetry breaking fields (SBF) created by spins outside the unit is calculated. The effective fields characterizing the interaction between units naturally arise as averages over the SBF. These effective fields...
Effects of complex parameters on classical trajectories of Hamiltonian systems
Asiri Nanayakkara; Thilagarajah Mathanaranjan
2014-06-01
Anderson et al have shown that for complex energies, the classical trajectories of real quartic potentials are closed and periodic only on a discrete set of eigencurves. Moreover, recently it was revealed that when time is complex $t(t = t_r e^{i_})$, certain real Hermitian systems possess close periodic trajectories only for a discrete set of values of . On the other hand, it is generally true that even for real energies, classical trajectories of non-PT symmetric Hamiltonians with complex parameters are mostly non-periodic and open. In this paper, we show that for given real energy, the classical trajectories of complex quartic Hamiltonians $H = p^2 + ax^4 + bx^k$ (where is real, is complex and = 1 or 2) are closed and periodic only for a discrete set of parameter curves in the complex -plane. It was further found that given complex parameter , the classical trajectories are periodic for a discrete set of real energies (i.e., classical energy gets discretized or quantized by imposing the condition that trajectories are periodic and closed). Moreover, we show that for real and positive energies (continuous), the classical trajectories of complex Hamiltonian $H = p^2 + x^4$, ($= _r$ e$^{i}$) are periodic when $ = 4 \\tan^{−1}$[($n/(2m + n)$)] for $\\forall n$ and $m \\mathbb{Z}$.
Exact solution of the classical mechanical quadratic Zeeman effect
Sambhu N Datta; Anshu Pandey
2007-06-01
We address the curious problem of quadratic Zeeman effect at the classical mechanical level. The problem has been very well understood for decades, but an analytical solution of the equations of motion is still to be found. This state of affairs persists because the simultaneous presence of the Coulombic and quadratic terms lowers the dynamical symmetry. Energy and orbital angular momentum are still constants of motion. We find the exact solutions by introducing the concept of an image ellipse. The quadratic effect leads to a dilation of space–time, and a one-to-one correspondence is observed for pairs of physical quantities like energy and angular momentum, and the maximum and minimum distances from the Coulomb center for the Zeeman orbit and the corresponding pairs for the image ellipse. Thus, instead of finding additional conserved quantities, we find constants of motion for an additional dynamics, namely, the image problem. The trajectory is open, in agreement with Bertrand's theorem, but necessarily bound. A stable unbound trajectory does not exist for real values of energy and angular momentum. The radial distance, the angle covered in the plane of the orbit, and the time are uniquely determined by introducing further the concept of an image circle. While the radial distance is defined in a closed form as a transcendental function of the image-circular angle, the corresponding orbit angle and time variables are found in the form of two convergent series expansions. The latter two variables are especially contracted, thereby leading to a precession of the open cycles around the Coulomb center. It is expected that the space–time dilation effect observed here would somehow influence the solution of the quantum mechanical problem at the non-relativistic level.
Relativistic and nonrelativistic classical field theory on fivedimensional space-time
This paper is a sequel to earlier ones in which, on the one hand, classical field theories were described on a curved Newtonian space-time, and on the other hand, the Newtonian gravitation theory was formulated on a fivedimensional space-time with a metric of signature and a covariantly constant vector field. Here we show that Lagrangians for matter fields are easily formulated on this extended space-time from simple invariance arguments and that stress-energy tensors can be derived from them in the usual manner so that four-dimensional space-time expressions are obtained that are consistent in the relativistic as well as in the Newtonian case. In the former the theory is equivalent to General Relativity. When the magnitude of the distinguished vector field vanishes equations for the (covariant) Newtonian limit follow. We demonstrate this here explicity in the case of the Klein-Gordon/Schroedinger and the Dirac field and its covariant nonrelativistic analogue, the Levy-Leblond field. Especially in the latter example the covariant Newtonian theory simplifies dramatically in this fivedimensional form
Axiomatics of classical electrodynamics and its relation to gauge field theory
Gronwald, F; Nitsch, J; Gronwald, Frank; Hehl, Friedrich W.
2005-01-01
We give a concise axiomatic introduction into the fundamental structure of classical electrodynamics: It is based on electric charge conservation, the Lorentz force, magnetic flux conservation, and the existence of local and linear constitutive relations. The {\\it inhomogeneous} Maxwell equations, expressed in terms of $D^i$ and $H_i$, turn out to be a consequence of electric charge conservation, whereas the {\\it homogeneous} Maxwell equations, expressed in terms of $E_i$ and $B^i$, are derived from magnetic flux conservation and special relativity theory. The excitations $D^i$ and $H_i$, by means of constitutive relations, are linked to the field strengths $E_i$ and $B^i$. Eventually, we point out how this axiomatic approach is related to the framework of gauge field theory.
Classical and quantum theory of the massive spin-two field
Koenigstein, Adrian; Giacosa, Francesco; Rischke, Dirk H.
2016-05-01
In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark-antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers JPC =2-+ is, to our knowledge, given here for the first time.
Classical and quantum theory of the massive spin-two field
Koenigstein, Adrian; Rischke, Dirk H
2015-01-01
In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincar\\'{e} group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark-antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers $J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.
Markovian evolution of classical and quantum correlations in transverse-field XY model
Pal, A. K.; Bose, I.
2012-08-01
The transverse-field XY model in one dimension is a well-known spin model for which the ground state properties and excitation spectrum are known exactly. The model has an interesting phase diagram describing quantum phase transitions (QPTs) belonging to two different universality classes. These are the transverse-field Ising model and the XX model universality classes with both the models being special cases of the transverse-field XY model. In recent years, quantities related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity have been shown to provide signatures of QPTs. Another interesting issue is that of decoherence to which a quantum system is subjected due to its interaction, represented by a quantum channel, with an environment. In this paper, we determine the dynamics of different types of correlations present in a quantum system, namely, the mutual information I( ρ AB ), the classical correlations C( ρ AB ) and the quantum correlations Q( ρ AB ), as measured by the quantum discord, in a two-qubit state. The density matrix of this state is given by the nearest-neighbour reduced density matrix obtained from the ground state of the transverse-field XY model in 1d. We assume Markovian dynamics for the time-evolution due to system-environment interactions. The quantum channels considered include the bit-flip, bit-phase-flip and phase-flip channels. Two different types of dynamics are identified for the channels in one of which the quantum correlations are greater in magnitude than the classical correlations in a finite time interval. The origins of the different types of dynamics are further explained. For the different channels, appropriate quantities associated with the dynamics of the correlations are identified which provide signatures of QPTs. We also report results for further-neighbour two-qubit states and finite temperatures.
A classical picture of anomalous effects in a Tokamak
Hirano, K.
1984-01-01
Atomic collisions between plasma ions and a very small amount of neutral particles remaining in a hot plasma plays a very important role for plasma transports and may be an origin of anomalous effects observed in a Tokamak such as the diffusion coefficient independent of the field strength, a rapid plasma density increase during gas puffing and current penetration with anomalously high speed in the start-up phase. The Ohm's law derived by Cowling is used for the analysis.
Polarization effects in molecular mechanical force fields
Cieplak, Piotr [Burnham Institute for Medical Research, 10901 North Torrey Pines Road, La Jolla, CA 92120 (United States); Dupradeau, Francois-Yves [UMR CNRS 6219-Faculte de Pharmacie, Universite de Picardie Jules Verne, 1 rue des Louvels, F-80037 Amiens (France); Duan, Yong [Genome Center and Department of Applied Science, University of California, Davis, One Shields Avenue, Davis, CA 95616 (United States); Wang Junmei, E-mail: pcieplak@burnham.or [Department of Pharmacology, University of Texas Southwestern Medical Center, 6001 Forest Park Boulevard, ND9.136, Dallas, TX 75390-9050 (United States)
2009-08-19
The focus here is on incorporating electronic polarization into classical molecular mechanical force fields used for macromolecular simulations. First, we briefly examine currently used molecular mechanical force fields and the current status of intermolecular forces as viewed by quantum mechanical approaches. Next, we demonstrate how some components of quantum mechanical energy are effectively incorporated into classical molecular mechanical force fields. Finally, we assess the modeling methods of one such energy component-polarization energy-and present an overview of polarizable force fields and their current applications. Incorporating polarization effects into current force fields paves the way to developing potentially more accurate, though more complex, parameterizations that can be used for more realistic molecular simulations. (topical review)
Polarization effects in molecular mechanical force fields.
Cieplak, Piotr; Dupradeau, François-Yves; Duan, Yong; Wang, Junmei
2009-08-19
The focus here is on incorporating electronic polarization into classical molecular mechanical force fields used for macromolecular simulations. First, we briefly examine currently used molecular mechanical force fields and the current status of intermolecular forces as viewed by quantum mechanical approaches. Next, we demonstrate how some components of quantum mechanical energy are effectively incorporated into classical molecular mechanical force fields. Finally, we assess the modeling methods of one such energy component-polarization energy-and present an overview of polarizable force fields and their current applications. Incorporating polarization effects into current force fields paves the way to developing potentially more accurate, though more complex, parameterizations that can be used for more realistic molecular simulations. PMID:21828594
A systematic method is developed to study the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton's second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.
Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low utraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term which is quadratic in the fields, and physical predictions can be read straight from the effective Lagrangean. Methods will be discussed how to compute an effective low energy action from a given fundamental action, either analytically or numerically, or by a combination of both methods. Basically, the idea is to integrate out the high frequency components of fields. This requires the choice of a 'blockspin', i.e. the specification af a low frequency field as a function of the fundamental fields. These blockspins will be fields of the effective field theory. The blockspin need not be a field of the same type as one of the fundamental fields, and it may be composite. Special features of blockspin in nonabelian gauge theories will be discussed in some detail. In analytical work and in multigrid updating schemes one needs interpolation kernels A from coarse to fine grid in addition to the averaging kernels C which determines the blockspin. A neural net strategy for finding optimal kernels is presented. Numerical methods are applicable to obtain actions of effective theories on lattices of finite volume. The special case of a 'lattice' with a single site (the constraint effective potential) is of particular interest. In a higgs model, the effective action reduces in this case to the free energy, considered as a function of a gauge covariant magnetization. Its shape determines the phase structure of the theory. Its loop expansion with and without gauge fields can be used to determine finite size corrections to numerical data. (orig.)
Cosmological Consequences of Classical Flavor-Space Locked Gauge Field Radiation
Bielefeld, Jannis
2015-01-01
We propose a classical SU(2) gauge field in a flavor-space locked configuration as a species of radiation in the early universe, and show that it would have a significant imprint on a primordial stochastic gravitational wave spectrum. In the flavor-space locked configuration, the electric and magnetic fields of each flavor are parallel and mutually orthogonal to other flavors, with isotropic and homogeneous stress-energy. Due to the non-Abelian coupling, the gauge field breaks the symmetry between left- and right-circularly polarized gravitational waves. This broken chiral symmetry results in a unique signal: non-zero cross correlation of the cosmic microwave background temperature and polarization, $TB$ and $EB$, both of which should be zero in the standard, chiral symmetric case. We forecast the ability of current and future CMB experiments to constrain this model. Furthermore, a wide range of behavior is shown to emerge, depending on the gauge field coupling, abundance, and allocation into electric and mag...
Parametric Instability of Classical Yang-Mills Fields under Color Magnetic Background
Tsutsui, Shoichiro; Kunihiro, Teiji; Ohnishi, Akira
2014-01-01
We investigate instabilities of classical Yang-Mills fields in a time-dependent spatially homogeneous color magnetic background field in a non-expanding geometry for elucidating the earliest stage dynamics of ultra-relativistic heavy-ion collisions. The background gauge field configuration considered in this article is spatially homogeneous and temporally periodic, and is alluded by Berges-Scheffler-Schlichting-Sexty (BSSS). We discuss the whole structure of instability bands of fluctuations around the BSSS background gauge field on the basis of Floquet theory, which enables us to discuss the stability in a systematic way. We find various instability bands on the $(p_z, p_T)$-plane. These instability bands are caused by parametric resonance despite the fact that the momentum dependence of the growth rate for $|\\mathbf{p}| \\leq \\sqrt{B}$ is similar to a Nielsen-Olesen instability. Moreover, some of instability bands are found to emerge not only in the low momentum but also in the high momentum region; typicall...
Classical and quantum effects in noble metal and graphene plasmonics
Mortensen, N. Asger
2015-01-01
Plasmonics — the interaction of light with free electrons in metals — is commonly understood within classical electrodynamics using local-response constitutive laws (such as Ohm's law). However, the tight localization of plasmons to small volumes is revealing intriguing new physics...
Fukushima, Kimichika
2014-01-01
This article reports an explicit function of confining classical Yang-Mills vector potentials as well as quantum fluctuations around the classical field. The classical vector potential, which is composed of a confining localized function and an unlocalized function, satisfies the classical Yang-Mills equation. The confining localized function contributes to the Wilson loop, while the unlocalized function has no contribution to this loop. The confining linear potential between a pair of a heavy fermion particle and an antiparticle is due to the Lie algebra and the form of the confining localized function, which have opposite signs at positions of the particle and antiparticles along the Wilson loop in the time direction. Some classical confining parts of vector potentials also have the opposite sign for the inversion of coordinate of the axis perpendicular to the axis between two particles. The localized functions of vector potentials are squeezed around the axis connecting two particles, and the string tensio...
What can we learn from the classical theory of Yang-Mills and Dirac fields
Minimally coupled classical Yang-Mills and Dirac fields in the Minkowski space-time and in spatially bounded domains are investigated. The extended phase space, defined as the space of the Cauchy data admitting solutions of the evolution equations, is identified. The structure of the gauge symmetry group, defined as the group of all gauge transformations acting in the extended phase space is analysed. In the Minkowski space-time the Lie algebra of infinitesimal gauge symmetries has an ideal giving rise to the constraints. The quotient algebra, isomorphic to the structure algebra, labels the conserved colour charges. In the case of spatially bounded domains, each set of the boundary data gives rise to an extended phase space in which the evolution is Hamiltonian. The problem of a physical interpretation of the boundary data is discussed. (author)
Gauge bridges in classical field theory; Eichbruecken in der klassischen Feldtheorie
Jakobs, S.
2009-03-15
In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called 'gauge bridges'are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)
José Geraldo Pereira da Cruz
2010-06-01
Full Text Available In the wild, animals are exposed to an ever-changing array of sensory stimuli. The captive environment, by contrast, is generally much more impoverished in terms of the cues it offers the animals housed within. In a bid to remedy this, and promote better welfare, mice (Mus musculus were exposed to two conditions: no auditory stimulation, and stimulation with classical music. In all experiments, a battery of behavior tests was used. The results demonstrated significantly decreased immobility in the forced swim, increased enclosed arm entries in the plus-maze, and decreased immobility in the open-field, in animals that had been pre-exposed to music 24h earlier, suggesting that changes in mouse motor activity were caused by classical music. This study led to the conclusion that environmental enrichment may have profound effects on the behavior of mice in behavioral tests, and that classical music can be a relatively simple method of contributing to the well-being of captive mice, but it can affect the results of experiments such as forced swimming.
On the Classical String Solutions and String/Field Theory Duality
Aleksandrova, D.; Bozhilov, P.
2003-01-01
We classify almost all classical string configurations, considered in the framework of the semi-classical limit of the string/gauge theory duality. Then, we describe a procedure for obtaining the conserved quantities and the exact classical string solutions in general string theory backgrounds, when the string embedding coordinates depend non-linearly on the worldsheet time parameter.
Markovian evolution of classical and quantum correlations in transverse-field XY model
Pal, Amit Kumar
2011-01-01
The transverse-field XY model in one dimension is a well-known spin model for which the ground state properties and excitation spectrum are known exactly. The model has an interesting phase diagram describing quantum phase transitions (QPTs) belonging to two different universality classes. These are the transverse-field Ising model and the XX model universality classes with both the models being special cases of the transverse-field XY model. In recent years, quantities related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity have been shown to provide signatures of QPTs. Another interesting issue is that of decoherence to which a quantum system is subjected due to its interaction, represented by a quantum channel, with an environment. In this paper, we determine the dynamics of different types of correlations present in a quantum system, namely, the mutual information $I(\\rho_{AB})$, the classical correlations $C(\\rho_{AB})$ and the quantum correlations $Q(\\rho_{...
Magnetic fields and accretion flows on the classical T Tauri star V2129 Oph
Donati, JF; Gregory, SG; Petit, P; Bouvier, J; Dougados, C; Ménard, F; Cameron, AC; Harries, TJ; Jeffers, SV; Paletou, F
2007-01-01
From observations collected with the ESPaDOnS spectropolarimeter, we report the discovery of magnetic fields at the surface of the mildly accreting classical T Tauri star V2129 Oph. Zeeman signatures are detected, both in photospheric lines and in the emission lines formed at the base of the accretion funnels linking the disc to the protostar, and monitored over the whole rotation cycle of V2129 Oph. We observe that rotational modulation dominates the temporal variations of both unpolarized and circularly polarized line profiles. We reconstruct the large-scale magnetic topology at the surface of V2129 Oph from both sets of Zeeman signatures simultaneously. We find it to be rather complex, with a dominant octupolar component and a weak dipole of strengths 1.2 and 0.35 kG, respectively, both slightly tilted with respect to the rotation axis. The large-scale field is anchored in a pair of 2-kG unipolar radial field spots located at high latitudes and coinciding with cool dark polar spots at photospheric level. T...
Bruneton, Jean-Philippe
2006-01-01
Field theories whose full action is Lorentz invariant (or diffeomorphism invariant) can exhibit superluminal behaviors through the breaking of local Lorentz invariance. Quantum induced superluminal velocities are well-known examples of this effect. The issue of the causal behavior of such propagations is somewhat controversial in the literature and we intend to clarify it. We provide a careful analysis of the meaning of causality in classical relativistic field theories, and we stress the rol...
Effective quantum field theories in general spacetimes
Raab, Andreas
2008-01-01
We introduce regular charts as physical reference frames in spacetime, and we show that general spacetimes can always be fully captured by regular charts. Effective quantum field theories (QFTs) can be conveniently defined in regular reference frames, and the definition is independent of specific background metric and independent of specific regular reference frame. As a consequence, coupling to classical gravity is possible in effective QFTs without getting back-reaction effects. Moreover, w...
Casimir effects for classical and quantum liquids in slab geometry: A brief review
We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over 4He liquid around the λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries
Yoo, Jejoong; Wilson, James; Aksimentiev, Aleksei
2016-10-01
Calcium ions (Ca(2+) ) play key roles in various fundamental biological processes such as cell signaling and brain function. Molecular dynamics (MD) simulations have been used to study such interactions, however, the accuracy of the Ca(2+) models provided by the standard MD force fields has not been rigorously tested. Here, we assess the performance of the Ca(2+) models from the most popular classical force fields AMBER and CHARMM by computing the osmotic pressure of model compounds and the free energy of DNA-DNA interactions. In the simulations performed using the two standard models, Ca(2+) ions are seen to form artificial clusters with chloride, acetate, and phosphate species; the osmotic pressure of CaAc2 and CaCl2 solutions is a small fraction of the experimental values for both force fields. Using the standard parameterization of Ca(2+) ions in the simulations of Ca(2+) -mediated DNA-DNA interactions leads to qualitatively wrong outcomes: both AMBER and CHARMM simulations suggest strong inter-DNA attraction whereas, in experiment, DNA molecules repel one another. The artificial attraction of Ca(2+) to DNA phosphate is strong enough to affect the direction of the electric field-driven translocation of DNA through a solid-state nanopore. To address these shortcomings of the standard Ca(2+) model, we introduce a custom model of a hydrated Ca(2+) ion and show that using our model brings the results of the above MD simulations in quantitative agreement with experiment. Our improved model of Ca(2+) can be readily applied to MD simulations of various biomolecular systems, including nucleic acids, proteins and lipid bilayer membranes. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 752-763, 2016. PMID:27144470
Liao, Qing-Hong; Zhang, Qi; Xu, Juan; Yan, Qiu-Rong; Liu, Ye; Chen, An
2016-06-01
We have studied the dynamics and transfer of the entanglement of the two identical atoms simultaneously interacting with vacuum field by employing the dressed-state representation. The two atoms are driven by classical fields. The influence of the initial entanglement degree of two atoms, the coupling strength between the atom and the classical field and the detuning between the atomic transition frequency and the frequency of classical field on the entanglement and atomic linear entropy is discussed. The initial entanglement of the two atoms can be transferred into the entanglement between the atom and cavity field when the dissipation is neglected. The maximally entangled state between the atoms and cavity field can be obtained under some certain conditions. The time of disentanglement of two atoms can be controlled and manipulated by adjusting the detuning and classical driving fields. Moreover, the larger the cavity decay rate is, the more quickly the entanglement of the two atoms decays. Supported by National Natural Science Foundation of China under Grant Nos. 11247213, 61368002, 11304010, 11264030, 61168001, China Postdoctoral Science Foundation under Grant No. 2013M531558, Jiangxi Postdoctoral Research Project under Grant No. 2013KY33, the Natural Science Foundation of Jiangxi Province under Grant No. 20142BAB217001, the Foundation for Young Scientists of Jiangxi Province (Jinggang Star) under Grant No. 20122BCB23002, the Research Foundation of the Education Department of Jiangxi Province under Grant Nos. GJJ13051, GJJ13057, and the Graduate Innovation Special Fund of Nanchang University under Grant No. cx2015137
Non-Markovian effect on the classical and quantum correlations
We evaluate the dynamics of quantum and classical correlations in the presence of non-Markovian noises. By considering an entangled pair of spins in the noise environment described by Ornstein-Uhlenbeck processes, we show that the quantum discord of some states is completely unaffected by independent Ornstein-Uhlenbeck noises for long intervals of time, and that the inevitable onset of the sudden decrease of the quantum discord can be substantially delayed by the decrease of the noise bandwidth γ, where γ-1 = τc defines the environment's finite correlation time of the noise. (authors)
Numerical calculation of classical and non-classical electrostatic potentials
Christensen, D; Neyenhuis, B; Christensen, Dan; Durfee, Dallin S.; Neyenhuis, Brian
2006-01-01
We present a numerical exercise in which classical and non-classical electrostatic potentials were calculated. The non-classical fields take into account effects due to a possible non-zero photon rest mass. We show that in the limit of small photon rest mass, both the classical and non-classical potential can be found by solving Poisson's equation twice, using the first calculation as a source term in the second calculation. Our results support the assumptions in a recent proposal to use ion interferometry to search for a non-zero photon rest mass.
Aparna Saha; Bidhan Chandra Bag; Pranab Sarkar
2007-03-01
We present a numerical investigation of the tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier which is coupled to a non-integrable classical system and study the interplay between classical chaos and barrier fluctuation in the tunneling dynamics. We found that the coupling of the quantum system with the classical subsystem decreases the tunneling rate irrespective of whether the classical subsystem is regular or chaotic and also irrespective of the fact that whether the barrier fluctuates or not. Presence of classical chaos always enhances the tunneling rate constant. The effect of barrier fluctuation on the tunneling rate in a mixed quantum-classical system is to suppress the tunneling rate. In contrast to the case of regular subsystem, the suppression arising due to barrier fluctuation is more visible when the subsystem is chaotic.
Phenomenological aspects of radiation by relativistic electrons in external field, in matter or the vicinity of matter are reviewed, among which: infrared divergence, coherence length effects, shadowing, crystal-assisted radiation, quantum recoil and spin effects, electron side-slipping, photon impact parameter and tunneling in the radiation process
A general discussion of the mean field dynamics of finite nuclei prepared under extreme conditions of temperature and pressure are presented. The prediction of semi-classical approximation is compared with complete quantum simulations. Many features of the dynamics are carefully studied such as the collective expansion, the evaporation process, the different time-scale... This study points out many quantitative differences between quantum and semi-classical approaches. Part of the differences are related to numerical features inherent in semi-classical simulations but most of them are a direct consequence of the non treatment of nuclei as quantal objects. In particular, it is shown that because of a too strong damping in semi-classical approaches the expansion of hot nuclei is quenched and the speed of the collective motion reduced. (author)
Classical statistical thermodynamics of a gas of charged particles in magnetic field
I.M.Dubrovskii
2006-01-01
Full Text Available We will demonstrate that the paradox of classical statistical thermodynamics for a gas of charged particles in a magnetic field (GMF has not yet been explained. The paradox lies in the statement that the average magnetic moment of a gas is zero, whereas the time-average magnetic moment of each particle is always negative. We consider a gas of charged particles moving in a plane perpendicular to a uniform magnetic field. The density of distribution of the ensemble describing statistical properties of the GMF is derived starting from the basics, with due regard for the specific character of dynamics of the charged particles in the magnetic field. It is emphasized that neither the imposition of a potential barrier restricting the existence region of the GMF, nor the introduction of a background neutralizing charge occupying a finite area, is a necessary condition for the stationary equilibrium state of the GMF to exist. We show that the reason for this fact is that the density of distribution of the ensemble is dependent, besides the Hamiltonian, on another positive definite integral of motion that is a linear combination of the Hamiltonian and the angular momentum of the GMF. Basic thermodynamic relations are deduced in terms of the new density of distribution, and it is demonstrated that the GMF has a magnetic moment whose magnitude and sign are determined by the external potential field. Particularly, the GMF is diamagnetic in the absence of the neutralizing background charge. Thus, the statement of the Bohr-van Leeuwen theorem, deduced using the ordinary Gibbs density of distribution depending on the Hamiltonian only, is wrong. It is noted that a great deal of works on the theory of electronic phenomena in magnetic field are based either on the same wrong density of distribution or on the formula for average occupation numbers depending on the energy of states, which follows from this density of distribution within quantum theory. These
Classical Oe Stars in the Field of the Small Magellanic Cloud
Golden-Marx, Jesse B; Lamb, J B; Graus, Andrew S; White, Aaron S
2016-01-01
We present $29\\pm1$ classical Oe stars from RIOTS4, a spatially complete, spectroscopic survey of Small Magellanic Cloud (SMC) field OB stars. The two earliest are O6e stars, and four are earlier than any Milky Way (MW) Oe stars. We also find ten Ope stars, showing He~\\textsc{i} infill and/or emission; five appear to be at least as hot as $\\sim$O7.5e stars. The hottest, star 77616, shows He~\\textsc{ii} disk emission, suggesting that even the hottest O stars can form decretion disks, and offers observational support for theoretical predictions that the hottest, fastest rotators can generate He$^+$-ionizing atmospheres. Our data also demonstrate that Ope stars correspond to Oe stars earlier than O7.5e with strong disk emission. We find that in the SMC, Oe stars extend to earlier spectral types than in the MW, and our SMC Oe/O frequency, $0.26\\pm0.04$, is much greater than the MW value, $0.03\\pm0.01$. These results are consistent with angular momentum transport by stronger winds suppressing decretion disk format...
Torrielli, Alessandro
2016-08-01
We review some essential aspects of classically integrable systems. The detailed outline of the sections consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schrödinger model, principal chiral field); 4. Features of classical r-matrices: Belavin–Drinfeld theorems, analyticity properties, and lift of the classical structures to quantum groups; 5. Classical inverse scattering method to solve integrable differential equations: soliton solutions, spectral properties and the Gel’fand–Levitan–Marchenko equation, with examples (KdV equation, Sine-Gordon model). Prepared for the Durham Young Researchers Integrability School, organised by the GATIS network. This is part of a collection of lecture notes.
Construction of classical and quantum integrable field models unravelling hidden possibilities
Anjan Kundu
2015-11-01
Reviewing briefly the concept of classical and quantum integrable systems, we propose an alternative Lax operator approach, leading to quasi-higher-dimensional integrable model, unravelling some hidden dimensions in integrable systems. As an example, we construct a novel integrable quasi-two-dimensional NLS equation at the classical and the quantum levels with intriguing application in rogue wave modelling.
Bogenschutz, Michael P
2013-03-01
Recent developments in the study of classic hallucinogens, combined with a re-appraisal of the older literature, have led to a renewal of interest in possible therapeutic applications for these drugs, notably their application in the treatment of addictions. This article will first provide a brief review of the research literature providing direct and indirect support for the possible therapeutic effects of classic hallucinogens such as psilocybin and lysergic acid diethylamide (LSD) in the treatment of addictions. Having provided a rationale for clinical investigation in this area, we discuss design issues in clinical trials using classic hallucinogens, some of which are unique to this class of drug. We then discuss the current status of this field of research and design considerations in future randomized trials. PMID:23627783
Modeling quantization effects in field effect transistors
Numerical simulation in the field of semiconductor device development advanced to a valuable, cost-effective and flexible facility. The most widely used simulators are based on classical models, as they need to satisfy time and memory constraints. To improve the performance of field effect transistors such as MOSFETs and HEMTs these devices are continuously scaled down in their dimensions. Consequently the characteristics of such devices are getting more and more determined by quantum mechanical effects arising from strong transversal fields in the channel. In this work an approach based on a two-dimensional electron gas is used to describe the confinement of the carriers. Quantization is considered in one direction only. For the derivation of a one-dimensional Schroedinger equation in the effective mass framework a non-parabolic correction for the energy dispersion due to Kane is included. For each subband a non-parabolic dispersion relation characterized by subband masses and subband non-parabolicity coefficients is introduced and the parameters are calculated via perturbation theory. The method described in this work has been implemented in a software tool that performs a self-consistent solution of Schroedinger- and Poisson-equation for a one-dimensional cut through a MOS structure or heterostructure. The calculation of the carrier densities is performed assuming Fermi-Dirac statistics. In the case of a MOS structure a metal or a polysilicon gate is considered and an arbitrary gate bulk voltage can be applied. This allows investigating quantum mechanical effects in capacity calculations, to compare the simulated data with measured CV curves and to evaluate the results obtained with a quantum mechanical correction for the classical electron density. The behavior of the defined subband parameters is compared to the value of the mass and the non-parabolicity coefficient from the model due to Kane. Finally the presented characterization of the subbands is applied
Notes on Collective Field Theory of Large N Vector Models as Classical Mechanics on the Siegel Disc
Agarwal, A
2004-01-01
We use deformation quantization to construct the large N limits of Bosonic vector models as classical dynamical systems on the Siegel disc and study the relation of this formulation to standard results of collective field theory. Special emphasis is paid to relating the collective potential of the large N theory to a particular cocycle of the symplectic group.
SHAO Xiao-Qiang; ZHANG Shou
2008-01-01
We propose a scheme for one-step generation of cluster states with atoms sent through a thermal cavity with strong classical driving field, based on the resonant atom-cavity interaction so that the operating time is sharply short, which is important in the view of decoherence.
Casimir effects for classical and quantum liquids in slab geometry: A brief review
Biswas, Shyamal, E-mail: sbsp@uohyd.ac.in [School of Physics, University of Hyderabad, C.R. Rao Road, Gachibowli, Hyderabad-500046 (India)
2015-05-15
We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over {sup 4}He liquid around the λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries.
We theoretically investigate high-order harmonic generation by employing strong-field approximation (SFA) and present a new approach to the extension of the high-order harmonic cutoff frequency via an exploration of the dependence of high-order harmonic generation on the waveform of laser fields. The dependence is investigated via detailed analysis of the classical trajectories of the ionized electron moving in the continuum in the velocity—position plane. The classical trajectory consists of three sections (Acceleration Away, Deceleration Away, and Acceleration Back), and their relationship with the electron recollision energy is investigated. The analysis of classical trajectories indicates that, besides the final (Acceleration Back) section, the electron recollision energy also relies on the previous two sections. We simultaneously optimize the waveform in all three sections to increase the electron recollision energy, and an extension of the cutoff frequency up to Ip + 20.26Up is presented with a theoretically synthesized waveform of the laser field
WU Ning; ZHANG Da-Hua
2007-01-01
A systematic method is developed to study the classical motion of a mass point in gravitational gauge field.First,by using Mathematica,a spherical symmetric solution of the field equation of gravitational gauge field is obtained,which is just the traditional Schwarzschild solution.Combining the principle of gauge covariance and Newton's second law of motion,the equation of motion of a mass point in gravitational field is deduced.Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field,we can discuss classical tests of gauge theory of gravity,including the deflection of light by the sun,the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun.It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.
Local equilibria and state transfer of charged classical particles on a helix in an electric field
Plettenberg, J; Zampetaki, A V; Schmelcher, P
2016-01-01
We explore the effects of a homogeneous external electric field on the static properties and dynamical behavior of two charged particles confined to a helix. In contrast to the field-free setup which provides a separation of the center-of-mass and relative motion, the existence of an external force perpendicular to the helix axis couples the center-of-mass to the relative degree of freedom leading to equilibria with a localized center of mass. By tuning the external field various fixed points are created and/or annihilated through different bifurcation scenarios. We provide a detailed analysis of these bifurcations based on which we demonstrate a robust state transfer between essentially arbitrary equilibrium configurations of the two charges that can be induced by making the external force time-dependent.
We study the thermoelectric power under classically large magnetic field (TPM) in ultrathin films (UFs), quantum wires (QWs) of non-linear optical materials on the basis of a newly formulated electron dispersion law considering the anisotropies of the effective electron masses, the spin-orbit splitting constants and the presence of the crystal field splitting within the framework of k.p formalism. The results of quantum confined III-V compounds form the special cases of our generalized analysis. The TPM has also been studied for quantum confined II-VI, stressed materials, bismuth and carbon nanotubes (CNs) on the basis of respective dispersion relations. It is found taking quantum confined CdGeAs2, InAs, InSb, CdS, stressed n-InSb and Bi that the TPM increases with increasing film thickness and decreasing electron statistics exhibiting quantized nature for all types of quantum confinement. The TPM in CNs exhibits oscillatory dependence with increasing carrier concentration and the signature of the entirely different types of quantum systems are evident from the plots. Besides, under certain special conditions, all the results for all the materials gets simplified to the well-known expression of the TPM for non-degenerate materials having parabolic energy bands, leading to the compatibility test.
Petrov, Alexey A
2016-01-01
This book is a broad-based text intended to help the growing student body interested in topics such as gravitational effective theories, supersymmetric effective theories, applications of effective theory techniques to problems in condensed matter physics (superconductivity) and quantum chromodynamics (such as soft-collinear effective theory). It begins with a review of the use of symmetries to identify the relevant degrees of freedom in a problem, and then presents a variety of methods that can be used to solve physical problems. A detailed discussion of canonical examples of effective field theories with increasing complexity is then conducted. Special cases such as supersymmetry and lattice EFT are discussed, as well as recently-found applications to problems in gravitation and cosmology. An appendix includes various factoids from group theory and other topics that are used throughout the text, in an attempt to make the book self-contained.
Optimization of classical nonpolarizable force fields for OH(-) and H3O(.).
Bonthuis, Douwe Jan; Mamatkulov, Shavkat I; Netz, Roland R
2016-03-14
We optimize force fields for H3O(+) and OH(-) that reproduce the experimental solvation free energies and the activities of H3O(+) Cl(-) and Na(+) OH(-) solutions up to concentrations of 1.5 mol/l. The force fields are optimized with respect to the partial charge on the hydrogen atoms and the Lennard-Jones parameters of the oxygen atoms. Remarkably, the partial charge on the hydrogen atom of the optimized H3O(+) force field is 0.8 ± 0.1|e|-significantly higher than the value typically used for nonpolarizable water models and H3O(+) force fields. In contrast, the optimal partial charge on the hydrogen atom of OH(-) turns out to be zero. Standard combination rules can be used for H3O(+) Cl(-) solutions, while for Na(+) OH(-) solutions, we need to significantly increase the effective anion-cation Lennard-Jones radius. While highlighting the importance of intramolecular electrostatics, our results show that it is possible to generate thermodynamically consistent force fields without using atomic polarizability. PMID:26979693
Effective quantum field theories
Certain dimensional parameters play a crucial role in the understanding of weak and strong interactions based on SU(2) x U(1) and SU(3) symmetry group theories and of grand unified theories (GUT's) based on SU(5). These parameters are the confinement scale of quantum chromodynamics and the breaking scales of SU(2) x U(1) and SU(5). The concepts of effective quantum field theories and renormalisability are discussed with reference to the economics and ethics of research. (U.K.)
Useful Pedagogical Applications of the Classical Hall Effect
Houari, Ahmed
2007-01-01
One of the most known phenomena in physics is the Hall effect. This is mainly due to its simplicity and to the wide range of its theoretical and practical applications. To complete the pedagogical utility of the Hall effect in physics teaching, I will apply it here to determine the Faraday constant as a fundamental physical number and the number…