Classical Coulomb systems: Screening and correlations revisited

From the laws of macroscopic electrostatics of conductors (in particular, the existence of screening), taken as given, one can deduce universal properties for the thermal fluctuations in a classical Coulomb system at equilibrium. The universality is especially apparent in the long-range correlations of the electrical potentials and fields. The charge fluctuations are derived from the field fluctuations. This is a convenient way to study the surface charge fluctuations on a conductor with boundaries. Explicit results are given for simple geometries. The potentials and the fields have Gaussian fluctuations, except for a short-distance cutoff.laboratory associated with the Centre National de la Recherche Scientifique.     

Anomalous magnetic moment of high energy electrons and positrons moving in a crystal and in an amorphous medium

The coherent and incoherent contributions to the anomalous magnetic moment of electrons and positrons of high energies, incident at small angles with a crystallographic plane, have been found. It is shown that in the limit of a weak crystal field averaged along the planes, the obtained formulas describe the anomalous magnetic moment of electrons moving in an amorphous medium.     

Equilibrium configurations and transitions between them in annular magnetic nanodipole systems

The equilibrium states of annular systems of magnetic dipoles have been studied by computer simulation. The bistability conditions under which the total magnetic moment of one of equilibrium configurations is zero, while the magnetic moment of another equilibrium configuration lies in the ring plane and is close to the sum of the magnetic moments of dipoles in the system, have been determined. The realization of other equilibrium configurations has also been demonstrated. We analyze transitions between equilibrium configurations by acting on the system by longitudinal and circular static fields, as well as transitions from the configuration with the maximal magnetic moment of the system to the configuration with zero total magnetic moment after the relaxation of oscillatory regimes excited by a varying field.     

Random Motion of a Charged Test Particle with a Constant Classical Velocity in a Spacetime with a Plane Boundary

We study the random motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary with a nonzero classical constant velocity in a direction parallel to the plane. We calculate the mean squared fluctuations in the velocity and position of the test particle taking into account both fluctuating electric and magnetic forces. Our results show that the influence of fluctuating magnetic fields is, in general, of the higher order than that caused by fluctuating electric fields and is thus negligible.     

Phonon or electron friction of a quantum heavy particle

Summary In this paper we analyse, with the path integral method, the diffusion of a quantum heavy particle moving in a strongly corrugated periodic potential both in the case when the particle is interacting with a thermal bath of phonons or of electrons. In the first case, the integration over the phonon degrees of freedom is performed exactly and in the large mass limit of the heavy particle it gives rise to an ohmic effective action which includes a nonlocal self-interacting term whose strength is the classical friction coefficient. In the second case, the integration over the electronic degrees of freedom is more difficult; we are able to derive an approximate effective action for the heavy particle in two different limiting cases: i) arbitrary large coupling between heavy particle and electrons and linear dissipation; ii) weak coupling and nonlinear dissipation. In i) we obtain an effective action for the particle equal to that found for the phonons but with a friction coefficient given by that of a classical heavy particle in a fermionic bath. In ii) we obtain a nonlinear, but still ohmic, dissipative term. Using an instanton approach we evaluate the mobility (and the diffusion coefficient) of the particle, whose temperature dependence shows a crossover from diffusive to localized behaviour at a critical value of the friction. Finally we discuss whether the electronic and phononic frictions can reach such a critical value. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

Equilibrium state of charged particles in a wave propagating along the magnetic field

This investigation examines the adiabatic motion of a charged particle near the equilibrium state in a field of a plane, circularly polarized, electromagnetic wave which is propagating with a changing velocity phase along the magnetic field. Approximate equations are found which describe the behavior of the equilibrium state parameters when the wave leaves the medium and enters a vacuum. It is shown that compared to the equilibrium value in this situation under the adiabatic approximation there is a decrease in amplitude of the particle energy fluctuation; this establishes the possibility of a prolonged acceleration of the particle to high energies. It is further demonstrated that a particle moving close to equilibrium state can appear to be in the autoresonance regime when the wave enters vacuum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 117–122, October, 1976.     

On relativistic thermodynamics

The thermodynamics of moving bodies is developed from first principles. To do this, it is necessary to augment the laws of thermodynamics with a new principle, which asserts the impossibility of thermal equilibrium between bodies in relative motion. Clausius' theorem is generalized to heat flow between moving systems, and leads naturally to the identification of heat and temperature as Lorentz scalars. The formulation of relativistic statistical mechanics is carried out and the correspondence with classical quantities is made. The quantum distribution laws are generalized to the relativistic case, and are found to differ from their accepted relativistic form.     

Extension of the fluctuation theorem

Heat fluctuations are studied in a dissipative system with both deterministic and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extension of the stationary state fluctuation theorem is derived. For infinite time, this reduces to the conventional fluctuation theorem only for small fluctuations; for large fluctuations, it gives a much larger ratio of the probabilities of the particle to absorb rather than supply heat. This persists for finite times and should be observable in experiments similar to a recent one carried out by Wang et al.     

Lienard-Wiechert potentials and synchrotron radiation from a relativistic spinning particle in pseudoclassical theory

For a relativistic spinning particle with an anomalous magnetic moment, Lienard-Wiechert potentials are constructed within the pseudoclassical approach. Some specific cases of the motion of a spinning particle are considered on the basis of general expressions obtained in this study for the Lienard-Wiechert potentials. In particular, the intensity of the synchrotron radiation from a transversely polarized particle moving along a circle at a constant speed is investigated as a function of the particle spin. In the specific case of particles having no anomalous magnetic moment and moving in an external uniform magnetic field, the resulting expressions coincide with familiar formulas from the quantum theory of radiation. The spin dependence of the polarization of synchrotron radiation is investigated.     

Nanoscale friction: kinetic friction of magnetic flux quanta and charge density waves

In analogy with the standard macroscopic friction, here we present a comparative study of the friction force felt by moving vortices in superconductors and charge density waves. Using experiments and a model for this data, our observations (1) provide a link between friction at the micro- and macroscopic scales, (2) explain the roundness of the static-kinetic friction transition in terms of thermal fluctuations, particle interactions, and system size (critical-phenomena view), and (3) explain the crossing of the kinetic friction F(k) versus velocity V for our pristine (high density of very weak defects) and our irradiated samples (with lower density of deeper pinning defects).     

Linear Optic Response of a Noncollinear Magnetic System: Hydrodynamic Theory

A hydrodynamic theory of the linear response of a noncollinearly magnetized medium interacting with electromagnetic radiation has been developed. Linear and quadratic magnetization effects caused by the spatial inhomogeneity of the magnetic moment have been analyzed. Linear magnetization effects include an effect similar to nonreciprocal birefringence, as well as reciprocal and nonreciprocal rotation of the plane of polarization, caused by the inhomogeneity of the magnetic moment. It has been shown that an effect caused by the equilibrium spin current can appear in the considered medium. This effect is determined either by the inhomogeneity of the spin current or by the spatial dispersion of a wave. The effect associated with the spatial dispersion of the wave is linear in its wave vector and is similar to nonreciprocal birefringence. The effect associated with the inhomogeneity of the spin current describes the rotation of the plane of polarization, which, however, can occur in the system with zero average magnetization.     

Homogenization of Ornstein-Uhlenbeck Process in Random Environment

We consider a tracer particle moving in a random environment. The velocity of the tracer is modelled by an Ornstein-Uhlenbeck process which takes into account inertia and friction. The medium results in a possibly unbounded random potential. We prove an invariance principle for this kind of motion. The method used is generalized in order to obtain a central limit theorem for a large class of process, the most interesting application being a tagged particle in a medium of infinitely many Ornstein-Uhlenbeck particles.     

Polar nano-rods under shear: From equilibrium to chaos

The orientational dynamics of rod-like particles with permanent (electric or magnetic) dipole moments in a plane Couette shear flow is investigated using mesoscopic relaxation equations combined with a generalized Landau free energy. The free energy contribution due to the coupling between average alignment and dipole orientation is derived on a microscopic basis. Numerical results of the resulting eight-dimensional dynamical system are presented for the case of longitudinal dipoles and thermodynamic conditions where the equilibrium state is a (polar or non-polar) nematic. Solution diagrams reveal presence of a large variety of periodic, transient chaotic, and chaotic dynamic states of the average alignment and dipole moment, respectively, appearing as a function of Deborah number and tumbling parameter. Compared to rods without dipoles we observe a significant preference of out-of-plane kayaking-tumbling states and, generally, a higher sensitivity to the initial conditions including bistability. We also demonstrate that the average (electric) dipole moment characterizing most of the observed states yields electrodynamic (magnetic) fields of measurable strength.     

“Vacuum” friction and heat exchange of a nano- and a microparticle with a solid surface

The most general relativistic formulas for the tangential force of the fluctuation-electromagnetic interaction and the rate of thermal heating of a spherical neutral particle moving in vacuum near the surface of a condensed medium are obtained for the first time in dipole approximation. It is shown that the existence of a fluctuation-induced magnetic moment for a conducting particle is responsible for a considerable increase in the vacuum heat-exchange rate as compared to contact and radiative heat transfer (in accordance with the Stefan law). It is noted that the coincidence of the absorption peaks for the particle and the surface in the microwave range can explain the damping forces observed for nanoprobes in the dynamic mode of the atomic force microscope.     

Transport and Diffusion in a Random Medium

We consider particle transport in a spatially random medium, the transport governed by the traditional, linear, time- and space-dependent transport equation for “host and guest.” The scattering is elastic and isotropic; there is no absorption. If the host medium has uniform density we know that an initial burst will, in time, approach the solution to the time-dependent diffusion equation. In the case of random medium we find that for a large class of such media the asymptotic behavior is unchanged by the stochasticity; there is neither renormalization of the equation nor the diffusion co-efficient.The nature of the correlation between fluctuations of density at large separation plays an important role in the analysis.     

Fluctuation theorems in inhomogeneous media under coarse graining

We compare the fluctuation relations for work and entropy in underdamped and overdamped systems, when the friction coefficient of the medium is space-dependent. We find that these relations remain unaffected in both cases. We have restricted ourselves to Stratonovich discretization scheme for the overdamped case.     

On the appearance of caustics for plane sound-wave propagation in moving random media

In this paper we derive expressions for the probability densities of the appearance of the first caustic for a plane sound wave propagating in moving random media. Our approach generalizes the previous work by White et al. and Klyatskin in the case of motionless media. It allows us to calculate analytically the probability density functions for two- and three-dimensional media and to express these functions in terms of the diffusion coefficient. Explicit equations are given for Gaussian and von Karman spectra of velocity fluctuations. If the random scalar or vectorial fluctuations of the medium have the same contribution to the refractive-index fluctuations, we demonstrate that in a moving medium caustics appear at shorter distances than in a non-moving one. The two-dimensional version of the theory is tested by numerical simulations in the case of velocity fluctuations with Gaussian spectra. Numerical results are in very good agreement with the theoretical predictions.     

Extension of the fluctuation-dissipation theorem to non-equilibrium systems

The fluctuation-dissipation theorem is generalized to the case of nonequilibrium (albeit in a stable steady state) systems. The relationship between the correlation function of the current fluctuations and the average energy absorbed by the system as a consequence of dissipation is used. For a nonequilibrium classical system, the responce function is connected with the correlation function in which the averaging is over the derivative of the energy distribution function. Using the spectrum of the electromagnetic fluctuations, inverting the fluctuation-dissipation relation one can find the permittivity of the medium.     

Effect of an intermediate layer with space-dependent permittivity on the ground state energy of an electron in a spherical complex nanoheterosystem

The effect of the interfaces of a multilayer spherical microcrystal on a charged particle is investigated. The case is considered where an intermediate layer with space-dependent permittivity exists near the interfaces. The dependence of the potential energy of the charged particle on distance is established by the method of the classical Green’s functions. For the example of an HgS/CdS spherical structure, the energy of the ground and excited states of an electron is calculated both in the presence of an intermediate layer with space-dependent permittivity and in its absence.