On the derivation of the Onsager relations from the Master equation

The asymptotical properties of a Markov system with discrete states are derived from the Master equation by using the quadratic approximate form of entropy.In particular, symmetry relations equivalent to the Onsager reciprocal relations are established for time reversal invariant systems.     

On Fermion Grading Symmetry for Quasi-Local Systems

We discuss fermion grading symmetry for quasi-local systems with graded commutation relations. We introduce a criterion of spontaneously symmetry breaking (SSB) for general quasi-local systems. It is formulated based on the idea that each pair of distinct phases (appeared in spontaneous symmetry breaking) should be disjoint not only for the total system but also for every complementary outside system of a local region specified by the given quasi-local structure. Under a completely model independent setting, we show the absence of SSB for fermion grading symmetry in the above sense. We obtain some structural results for equilibrium states of lattice systems. If there would exist an even KMS state for some even dynamics that is decomposed into noneven KMS states, then those noneven states inevitably violate our local thermal stability condition.     

Low-lying excited states of quantum antiferromagnets on a triangular lattice

We study low-lying states of theXY and Heisenberg antiferromagnets on a triangular lattice to clarify whether spontaneous symmetry breaking occurs atT=0 in the thermodynamic limit. Approximate forms of low-lying states are proposed, in which degrees of freedom of the sublattice magnetization and of the chirality are separated. These approximate states have a long-range order and twofold structures. It is shown that low-lying states can be accurately described with the present approximation. It has been argued that low-lying states play an important role in symmetry breaking. With the help of this approximation, we discuss the contribution of low-lying states to symmetry breaking of two types, namely creation of the spontaneous sublattice magnetization and the spontaneous chirality. Furthermore, to show evidence for the occurrence of symmetry breaking, we numerically study the low-lying states of finite systems of theXY and Heisenberg antiferromagnets. It is found that the necessary conditions for the symmetry breaking to occur are satisfied in these models.     

Black hole thermodynamics from Euclidean horizon constraints

To explain black hole thermodynamics in quantum gravity, one must introduce constraints to ensure that a black hole is actually present. I show that for a large class of black holes, such "horizon constraints" allow the use of conformal field theory techniques to compute the density of states, reproducing the Bekenstein-Hawking entropy in a nearly model-independent manner. One standard string theory approach to black hole entropy arises as a special case, lending support to the claim that the mechanism may be "universal." I argue that the relevant degrees of freedom are Goldstone-boson-like excitations arising from the weak breaking of symmetry by the constraints.     

On the absence of spontaneous symmetry breaking and of crystalline ordering in two-dimensional systems

We develop a unified approach, based on Araki's relative entropy concept, to proving absence of spontaneous breaking of continuous, internal symmetries and translation invariance in two-dimensional statistical-mechanical systems. More precisely, we show that, under rather general assumptions on the interactions, all equilibrium states of a two-dimensional system have all the symmetries, compact internal and spatial, of the dynamics, except possibly rotation invariance. (Rotation invariance remains unbroken if connected correlations decay more rapidly than the inverse square distance.) We also prove that two-dimensional systems with a non-compact internal symmetry group, like anharmonic crystals, typically do not have Gibbs states.     

Electromagnetic retarded interaction and symmetry violation of time reversal in high order stimulated radiation and absorption processes of light

It has been proved that when the retarded effect (or multiple moment effect) of radiation fields is taken into account, the high order stimulated radiation and stimulated absorption probabilities of light are not the same so that time reversal symmetry would be violated, though the Hamiltonian of electromagnetic interaction is still unchanged under time reversal. The reason to cause time reversal symmetry violation is that certain filial or partial transition processes of bound atoms are forbidden or cannot be achieved due to the law of energy conservation and the special states of atoms themselves. These restrictions would cause the symmetry violation of time reversal of other filial or partial transition processes which can be actualized really. The symmetry violation is also relative to the asymmetry of initial states of bound atoms before and after time reversal. For the electromagnetic interaction between non-bound atoms and radiation field, there is no such kind of symmetry violation of time reversal. In this way, the current formula on the parameters of stimulated radiation and absorption of light with time reversal symmetry should be revised. A more reliable foundation can be established for the theories of laser and nonlinear optics in which non-equilibrium processes are involved.     

Evaluation of an algebraic model for the vibrations of water,effects of a discrete symmetry

We evaluate the dynamics of an algebraic model Hamiltonian for the vibrational motion of the water molecule. We pay special attention to the effects of the discrete symmetry of order 2 of the model. For a comparison between the quantum dynamics and the classical dynamics it is necessary to desymmetrize such quantum states which are based on types of motion which come in symmetry related pairs. For the other states based on motion invariant under the symmetry operation a desymmetrization would be meaningless. The desymmetrized quantum states show a simple connection to the guiding motions of the classical dynamics which can be used for a complete assignment of the states even though the system is not integrable in the sense of Liouville and shows chaotic behaviour in large parts of the classical phase space.     

Interrelation of spatial and temporal instabilities in a system of two nonlinear thin films

The spatiotemporal dynamics of a system of two thin films possessing a resonance nonlinearity and irradiated on both sides with spatially uniform monochromatic light with the same intensity is investigated. The conditions under which bistability and symmetry breaking occur in the system are obtained. It is shown that self-pulsations can arise in the system as a result of the retardation of the light between the films, if the aperture of the incident beam is sufficiently small, and the dynamical regimes arising in the process are investigated numerically. As the beam aperture increases, the pulsations break down and a stationary spatially nonuniform field distribution is established. The transverse structures arising in this case are studied, and the relation between the symmetry breaking, bistability, self-pulsations, and spatial structures in the system investigated is established.     

Large Deviations of Lattice Hamiltonian Dynamics Coupled to Stochastic Thermostats

We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics which satisfy natural properties under time reversal. Next, we discuss the characterization of the stationary states as the solution of a variational principle and its relation to the minimum entropy production principle. Finally, we compute the large deviation functional of the current in the case of a harmonic chain thermostated by a Gaussian stochastic coupling.     

The Szilard engine revisited: Entropy,macroscopic randomness,and symmetry breaking phase transitions

The role of symmetry breaking phase transitions in the Szilard engine is analyzed. It is shown that symmetry breaking is the only necessary ingredient for the engine to work. To support this idea, we show that the Ising model behaves exactly as the Szilard engine. We design a purely macroscopic Maxwell demon from an Ising model, demonstrating that a demon can operate with information about the macrostate of the system. We finally discuss some aspects of the definition of entropy and how thermodynamics should be modified to account for the variations of entropy in second-order phase transitions. (c) 2001 American Institute of Physics.     

The “harmonic liquid” away from equilibrium: I. Stationary correlation functions

Some aspects of the linear chain of harmonic oscillators (“harmonic liquid”) are studied. In particular we compute the stationary correlation functions of coordinates and momenta of the oscillators for a particular non-equilibrium steady state. We find that the coordinates and momenta autocorrelation functions are analogous to their equilibrium counterparts whereas the coordinates-momenta correlation functions exhibit long-range behaviour due to time reversal symmetry breaking. The non-equilibrium entropy of the chain is also computed. It contains a non-equilibrium part that depends on the temperature of the external sources and on the stationary temperature. A comparison with a non-equilibrium entropy obtained from information theory is made.     

Current Symmetries for Particle Systems with Several Conservation Laws

We consider stochastic interacting particle systems with more than one conservation law in a regime far from equilibrium. Using time reversal we derive symmetry relations for the stationary currents of the conserved quantities that are reminiscent of Onsager’s reciprocity relations. These relations are valid for a very large class of particles with only some mild assumption on the decay of stationary relations and imply that the coarse-grained macroscopic dynamics is governed by a system of hyperbolic conservation laws. An explicit expression for the conserved Lax entropy is obtained.     

Pair breaking and density of states in disordered superconductors

It is shown that pair breaking occurs in a disordered superconductor due to spatial variations of the order parameter, although the system is time reversal invariant. The pair breaking effect is reflected by the occurence of some interesting fine structure in the one particle density of states. Discrete bound states and split off impurity bands show up in the single impurity case and for very dilute alloys, respectively. For finite alloy concentrations the calculations are done within the CPA. Although principally important, the fine structure is concentrated in an energy range too narrow to be detected experimentally.     

Growth and Nonlinear Saturation of Fluctuations in a Nonlinear Oscillator at the Threshold of a Bifurcation of Spontaneous Symmetry Breaking

We consider the phenomenon of prebifurcation noise amplification in a nonlinear oscillator at the threshold of a bifurcation of spontaneous symmetry breaking. The studies are based on the model of a nonlinear oscillator in which the potential relief transforms from monostable to symmetric bistable and the noise acting on the system is assumed Gaussian and short-correlated. The fluctuation variance as a function of the regime of the system and the rate at which the bifurcation threshold is reached are examined. Our analytical estimates are in good agreement with the results of numerical simulation for both the linear growth and the nonlinear saturation of fluctuations. It is noted that in the case of fast bifurcation transitions, a loop of noise-dependent hysteresis and breaking of probability symmetry of stable final states are observed in the nonlinear oscillator. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 425–435, May 2005.     

Induced Chern-Simons term of a paired electron state in the quantum Hall system

The induced Chern-Simons term for a paired electron state is calculated in the quantum Hall system by using a field theory on the von Neumann lattice. The coefficient of the Chern-Simons term, which is the Hall conductance, has not only the usual term proportional to a filling factor due to P (parity) & T (time reversal) symmetry breaking but also correction terms due to P & T & U(1) symmetry breaking. The correction term essentially comes from the Nambu-Goldstone mode and depends on an infrared limit. It is shown that the correction term is related to a topological number of a gap function in the momentum space.     

Stability of symmetry breaking states in finite-size Dicke model with photon leakage

We investigate the finite-size Dicke model with photon leakage. It is shown that the symmetry breaking states, which are characterized by non-vanishing $〈\stackrel{?}{a}〉\ne 0$ and correspond to the ground states in the superradiant phase in the thermodynamic limit, are stable, while the eigenstates of the isolated finite-size Dicke Hamiltonian conserve parity symmetry. We introduce and analyze an effective master equation that describes the dynamics of a pair of the symmetry breaking states that are the degenerate lowest energy eigenstates in the superradiant region with photon leakage. It becomes clear that photon leakage is essential to stabilize the symmetry breaking states and to realize the superradiant phase without the thermodynamic limit. Our theoretical analysis provides an alternative interpretation using the finite-size model to explain results from cold atomic experiments showing superradiance with the symmetry breaking in an optical cavity.     

Reversible maps in two-degrees of freedom Hamiltonian systems

It has been shown that a sub-class of two-degrees of freedom Hamiltonian systems possesses a reversing symmetry discovered by Birkhoff in the restricted problem of three bodies. This mixed space-time reversing symmetry, which is different from the classical time reversal symmetry, can be shared by time-reversible as well as time-irreversible systems. Examples of time-irreversible systems which possess this reversing symmetry are the restricted problem of three bodies as shown by Birkhoff in 1915, and a special case of the motion of a rigid body with a fixed point discussed in this paper. If a Hamiltonian system possesses this Birkhoff reversing symmetry, then there exists a surface of section for which the corresponding Poincare map is Birkhoff-reversible. The Birkhoff-reversibility of this map may be used to study its global dynamics such as the locations and the distribution of the stable and unstable periodic points, the distribution of stable and chaotic regions, and the identification of the scattering regions. (c) 2002 American Institute of Physics.     

Masses of the 70(-) baryons in large N(c) QCD

The masses of the negative parity 70-plet baryons are analyzed in large N(c) QCD to order 1/N(c) and to first order in SU(3) symmetry breaking. The existing experimental data are well reproduced and 20 new observables are predicted. The leading order SU(6) spin-flavor symmetry breaking is small and, as it occurs in the quark model, the subleading in 1/N(c) hyperfine interaction is the dominant source of the breaking. It is found that the Lambda(1405) and Lambda(1520) are well described as three-quark states and spin-orbit partners. New relations between splittings in different SU(3) multiplets are found.     

The explicit symmetry breaking solutions of the Kadomtsev-Petviashvili equation

To describe two correlated events, the Alice–Bob (AB) systems were constructed by Lou through the symmetry of the shifted parity, time reversal and charge conjugation. In this paper, the coupled AB system of the Kadomtsev–Petviashvili equation, which is a useful model in natural science, is established. By introducing an extended Bäcklund transformation and its bilinear formation, the symmetry breaking soliton, lump and breather solutions of this system are derived with the aid of some ansatze functions. Figures show these fascinating symmetry breaking structures of the explicit solutions.