Loschmidt echo for a chaotic oscillator

Chaotic dynamics of a nonlinear oscillator is considered in the semiclassical approximation. The Loschmidt echo is calculated for a time scale which is of the power law in semiclassical parameter. It is shown that an exponential decay of the Loschmidt echo is due to a Lyapunov exponent and it has a pure classical nature.Comment: Submit to PR

Langevin dynamics with a tilted periodic potential

We study a Langevin equation for a particle moving in a periodic potential in the presence of viscosity $\gamma$ and subject to a further external field $\alpha$. For a suitable choice of the parameters $\alpha$ and $\gamma$ the related deterministic dynamics yields heteroclinic orbits. In such a regime, in absence of stochastic noise both confined and unbounded orbits coexist. We prove that, with the inclusion of an arbitrarly small noise only the confined orbits survive in a sub-exponential time scale.Comment: 38 pages, 6 figure

Contracting the Wigner kernel of a spin to the Wigner kernel of a particle

A general relation between the Moyal formalisms for a spin and a particle is established. Once the formalism has been set up for a spin, the phase-space description of a particle is obtained from contracting the group of rotations to the oscillator group. In this process, turn into a spin Wigner kernel turns into the Wigner kernel of a particle. In fact, only one out of 22s different possible kernels for a spin shows this behavior

Corrections to Einstein's relation for Brownian motion in a tilted periodic potential

In this paper we revisit the problem of Brownian motion in a tilted periodic potential. We use homogenization theory to derive general formulas for the effective velocity and the effective diffusion tensor that are valid for arbitrary tilts. Furthermore, we obtain power series expansions for the velocity and the diffusion coefficient as functions of the external forcing. Thus, we provide systematic corrections to Einstein's formula and to linear response theory. Our theoretical results are supported by extensive numerical simulations. For our numerical experiments we use a novel spectral numerical method that leads to a very efficient and accurate calculation of the effective velocity and the effective diffusion tensor.Comment: 29 pages, 7 figures, submitted to the Journal of Statistical Physic

Discrete Moyal-type representations for a spin

In Moyal’s formulation of quantum mechanics, a quantum spin s is described in terms of continuous symbols, i.e., by smooth functions on a two-dimensional sphere. Such prescriptions to associate operators with Wigner functions, P or Q symbols, are conveniently expressed in terms of operator kernels satisfying the Stratonovich-Weyl postulates. In analogy to this approach, a discrete Moyal formalism is defined on the basis of a modified set of postulates. It is shown that appropriately modified postulates single out a well-defined set of kernels that give rise to discrete symbols. Now operators are represented by functions taking values on (2s+1)2 points of the sphere. The discrete symbols contain no redundant information, contrary to the continuous ones. The properties of the resulting discrete Moyal formalism for a quantum spin are worked out in detail and compared to the continuous formalism

Fokker-Planck Equation for Boltzmann-type and Active Particles: transfer probability approach

Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction and diffusion for Brownian particles. Renormalization of the friction coefficient is shown to occur for two dimensional (2-D) and three dimensional (3-D) cases, due to the tensorial character of diffusion. The specific forms of PT are calculated for the Boltzmann-type of collisions and for the absorption-type of collisions (the later are typical for dusty plasmas and some other systems). Validity of the Einstein's relation for the Boltzmann-type collisions is analyzed for the velocity-dependent friction and diffusion coefficients. For the Boltzmann-type collisions in the region of very high grain velocity as well as it is always for non-Boltzmann collisions, such as, e.g., absorption collisions, the Einstein relation is violated, although some other relations (determined by the structure of PT) can exist. The generalized friction force is investigated in dusty plasma in the framework of the PT approach. The relation between this force, negative collecting friction force and scattering and collecting drag forces is established.+AFwAXA- The concept of probability transition is used to describe motion of active particles in an ambient medium. On basis of the physical arguments the PT for a simple model of the active particle is constructed and the coefficients of the relevant Fokker-Planck equation are found. The stationary solution of this equation is typical for the simplest self-organized molecular machines.+AFwAXA- PACS number(s): 52.27.Lw, 52.20.Hv, 52.25.Fi, 82.70.-yComment: 18 page

Diffusion and Current of Brownian Particles in Tilted Piecewise Linear Potentials: Amplification and Coherence

Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their dependencies on temperature, tilting force, and the shape of the potential are analyzed. The necessary and sufficient conditions for the non-monotonic behavior of the diffusion coefficient as a function of temperature are determined. The diffusion coefficient and coherence level are found to be extremely sensitive to the asymmetry of the potential. It is established that at the values of the external force, for which the enhancement of diffusion is most rapid, the level of coherence has a wide plateau at low temperatures with the value of the Peclet factor 2. An interpretation of the amplification of diffusion in comparison with free thermal diffusion in terms of probability distribution is proposed.Comment: To appear in PR

Effects of Boson Dispersion in Fermion-Boson Coupled Systems

We study the nonlinear feedback in a fermion-boson system using an extension of dynamical mean-field theory and the quantum Monte Carlo method. In the perturbative regimes (weak-coupling and atomic limits) the effective interaction among fermions increases as the width of the boson dispersion increases. In the strong coupling regime away from the anti-adiabatic limit, the effective interaction decreases as we increase the width of the boson dispersion. This behavior is closely related with complete softening of the boson field. We elucidate the parameters that control this nonperturbative region where fluctuations of the dispersive bosons enhance the delocalization of fermions.Comment: 14 pages RevTeX including 12 PS figure

Bosonization in Particle Physics

Path integral techniques in collective fields are shown to be a useful analytical tool to reformulate a field theory defined in terms of microscopic quark (gluon) degrees of freedom as an effective theory of collective boson (meson) fields. For illustrations, the path integral bosonization approach is applied to derive a (non)linear sigma model from a Nambu-Jona-Lasinio (NJL) quark model. The method can be extended to include higher order derivative terms in meson fields or heavy-quark symmetries. It is also approximately applicable to QCD.Comment: 12 pages, LaTeX, uses lamuphys.sty, 5 LaTeX figures, talk given at the Workshop "Field Theoretical Tools in Polymer and Particle Physics", University Wuppertal, June 17-19, 199

Neel Order and Electron Spectral Functions in the Two-Dimensional Hubbard Model: a Spin-Charge Rotating Frame Approach

Using recently developed quantum SU(2)xU(1) rotor approach, that provides a self-consistent treatment of the antiferromagnetic state we have performed electronic spectral function calculations for the Hubbard model on the square lattice. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green's function in the space-time domain as the product CP^1 propagator resulting from the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. As a result the problem of calculating the spectral line shapes now becomes one of performing the convolution of spin, charge and pseudo-fermion Green's functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.Comment: 16 pages, 5 figures, submitted to Phys. Rev.