“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.     

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.     

Relativistic kinetics of phonon gas in superfluids

The relativistic kinetic theory of the phonon gas in superfluids is developed. The technique of the derivation of macroscopic balance equations from microscopic equations of motion for individual particles is applied to an ensemble of quasi-particles. The necessary expressions are constructed in terms of a Hamilton function of a (quasi-)particle. A phonon contribution into superfluid dynamic parameters is obtained from energy-momentum balance equations for the phonon gas together with the conservation law for superfluids as a whole. Relations between dynamic flows being in agreement with results of relativistic hydrodynamic consideration are found. Based on the kinetic approach a problem of relativistic variation of the speed of sound under phonon influence at low temperature is solved.     

An exact solution of the relativistic equation of motion of acharged particle driven by a circularly polarized electromagnetic waveand a constant magnetic field

An exact solution is found for the relativistic equation of motion of a charged particle driven by a circularly polarized electromagnetic wave and a constant magnetic field. The explicit expressions of particle position and velocity are obtained for certain initial conditions. The results are of interest to the interaction of the high-power laser with the magnetized plasma, electromagnetically pumped free-electron laser with a guide magnetic field, propagation of electromagnetic wave signals through a re-entry plasma sheath in the presence of a strong magnetic field, and magnetic confinement plasmas     

Resonance fluctuation-electromagnetic energy losses during the glancing reflection of a neutral atomic beam from the smooth amorphous surface of a solid

The energy losses of a Cs⁺ion beam are theoretically studied during its glancing reflection from a smooth amorphous surface of a dielectric or a semiconductor and films made of these materials on a metallic substrate. The conditions of resonance fluctuation-electromagnetic interaction between neutralized Cs atoms and surface polaritons are considered for surfaces where the effects of interest seem to be the most significant. Calculations indicate that, at the optimized initial glancing angle and the Cs⁺ ion beam energy (ψ_in = 0.1–1.0 mrad, E ₀ ～ 50–100 keV), the fluctuation-electromagnetic forces substantially contribute to the total energy losses and this contribution has characteristic dependences on the temperature, particle velocity, and material parameters.     

On the theory of the relativistic motion of a charged particle in the field of intense electromagnetic radiation

Averaged relativistic equations of motion of a charged particle in the field of intense electromagnetic radiation have been obtained in the geometrical optics approximation using the Bogoliubov method. Constraints are determined under which these equations are valid. Oscillating additions to the smoothed dynamical variables of the particle have been found; they are reduced to known expressions in the case of the circularly and linearly polarized plane waves. It has been shown that the expressions for the averaged relativistic force in both cases contain new additional small terms weakening its action. The known difference between the expressions for the ponderomotive force in the cases of circularly and linearly polarized waves has been confirmed.     

Constants of Motion for Several One-Dimensional Systems and Problems Associated with Getting Their Hamiltonians

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation; a no-relativistic particle with a time explicitly depending force; a no-relativistic particle with a constant force and time depending mass; and a relativistic particle under a conservative force with position depending mass. The Hamiltonian for these systems, which is determined by getting the velocity as a function of position and generalized linear momentum, can be found explicitly at first approximation for the first system. The Hamiltonians for the other systems are kept implicitly in their expressions for their constants of motion.     

Kinetic theory of the plasma-dynamical modes and the transport coefficients of a relativistic plasma

The kinetic equation of an inhomogeneous relativistic plasma, consisting of an electron gas and a radiation field, is studied with particular regard to its eigenvalues in the hydrodynamical limit. The treatment is classical for the particles and quantum-mechanical for the field oscillators.After a suitable regularization, the eigenvalues are obtained by a perturbation theory through second order in the strength of the gradients. It is shown that these eigenvalues are in exact correspondence with the macroscopic relativistic plasma-dynamical modes. The important role played by the Vlassov operator in building up the peculiar structure of these modes is underlined. From a comparison of the macroscopic and microscopic eigenvalues we obtain general expressions for the thermal conductivity, the shear viscosity and the bulk viscosity of a relativistic plasma. The contribution of the radiation field to these quantities is a noteworthy feature of these expressions.     

The relativistic theory of fluctuation electromagnetic interactions of moving neutral particles with a flat surface

The problem concerning the fluctuation electromagnetic interaction of a neutral particle moving parallel to the boundary of a semi-infinite homogeneous isotropic medium characterized by a permittivity and permeability dependent on the frequency is considered in terms of the fluctuation electrodynamic theory within the relativistic formalism. It is assumed that, in the general case, the particle and the medium have different temperatures. Within the proposed approach, general expressions are derived both for conservative (normal to the boundary of the medium) and nonconservative (tangential) forces of the interaction between the particle and the medium and for the thermal heating (cooling) rate of the particle. In the nonrelativistic limit (c → ∞), the derived relationships coincide with nonrelativistic analogs available in the literature. It is demonstrated that the tangential force acting on the particle can be either accelerating or decelerating. There can occur a situation when the hot moving particle will be heated and the cold medium will be cooled. The interaction of the high-conductivity medium with a high-conductivity particle is analyzed numerically. The asymptotics of the radiative contributions to the heat flux and the tangential force is investigated. It is shown that the inclusion of the relativistic effects leads to a substantial increase in the tangential force and the heat flux at distances greater than 1 μm (as compared to the nonrelativistic case); however, the corresponding dependences exhibit a monotonic decreasing behavior over the entire range of studied distances (from zero to several hundreds of microns). __________ Translated from Fizika Tverdogo Tela, Vol. 45, No. 10, 2003, pp. 1729–1741. Original Russian Text Copyright ? 2003 by Dedkov, Kyasov.     

Relativistic Single Particle Kinetic Theory

Single particle kinetic theory is the study of the dynamics of a single particle moving through a medium. The only mechanism for change in this theory is through two-body collisions between the single particle and the particles of the medium given by the collision term of Boltzmann's equation in kinetic theory. This article contains a summery of relativistic dynamics and a method of projecting the relativistic dynamical system into phase space. This enables us to express relativistic kinetic theory in terms of phase space variables and also to apply the techniques of approximation in the non-relativistic theory to the relativistic domain.     

强磁场中超冷费米气体的相对论效应

由单粒子的弱相对论能谱及泊松公式,导出强磁场中费米气体的热力学势函数.在此基础上,运用热力学关系求解低温条件下系统的统计特征量的解析式,分析相对论效应对统计性质的影响机理.研究表明,磁场愈强,相对论效应愈明显.相对论效应引发的单调项与相应的振荡项的振幅相比,对总能,单调项远大于振幅;对化学势及磁矩,单调项与振幅几乎同一量级. 关键词： 强磁场 费米气体 相对论效应     

Estimation of shift parameters of a quantum state

Estimation of shift parameters such as arrival time, phase, angle of rotation, position of a non-relativistic or relativistic particle is considered. An approach from the point of view of quantum estimation theory enables to give a proper definition of the time observable and the position observables of a massless relativistic particle, i.e. observables to which there do not correspond self-adjoint operators. Some new inequalities for estimates of shift parameters are obtained; in particular a rigorous uncertainty relation for coordinates of the photon is established.     

Relativistic breakdown of a non-linear classical field theory

It is shown that the relativistic generalization of a certain classical, non-linear, scalar, field theory displays unphysical behavior not found for the non-relativistic case. An explicit, unphysical solution of the relativistic equation is given. The different properties of relativistic and non-relativistic particle densities affect the behavior of the solutions in the respective cases.     

Kinetic theory of transport coefficients of a relativistic binary mixture

Within the framework of relativistic kinetic theory expressions are derived for the diffusion and thermal diffusion coefficient of a binary mixture.     

Leontovich relations in thermal field theory

The application of generalized Kramers-Kronig relations, the so-called Leontovich relations, to thermal field theory is discussed. Medium effects contained in the full, thermal propagators can easily be taken into account by this method. As examples the collisional energy loss of a charged particle in a relativistic plasma and the radiation of energetic photons from a quark-gluon plasma are considered. Within the leading logarithmic approximation the results based on the hard thermal loop resummation technique are reproduced easily. However, the method presented here is more general and provides exact expressions, which allow in principle non-perturbative calculations. Received: 17 April 2000 / Published online: 6 July 2000     

Relativistic motion of a free particle in a uniform gravitational field

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.     

Heat Flux for a Relativistic Dilute Bidimensional Gas

Relativistic kinetic theory predicts substantial modifications to the dissipation mechanisms of a dilute gas. For the heat flux, these include (in the absence of external forces) a correction to the thermal conductivity and the appearance of a new, purely relativistic, term proportional to the density gradient. In this work we obtain such constitutive equation for the particular case of a bidimensional gas. The calculation is based on the Chapman–Enskog solution to the relativistic Boltzmann equation and yields analytical expressions for the corresponding transport coefficients, which are evaluated for the particular case of hard disks. These results will be useful for numerical simulations and may be applied to bidimensional non-dense materials.     

Phase-space path integration of the relativistic particle equations

Hamilton-Jacobi theory is applied to find appropriate canonical transformations for the calculation of the phase-space path integrals of the relativistic particle equations. Hence, canonical transformations and Hamilton-Jacobi theory are also introduced into relativistic quantum mechanics. Moreover, from the classical physics viewpoint, it is very interesting to find and to solve the Hamilton-Jacobi equations for the relativistic particle equations.