Fluctuation-electromagnetic interaction of a moving neutral particle with a condensed-medium surface: relativistic approach

A relativistic theory of the fluctuation-electromagnetic interaction of a moving small particle with a flat boundary of a homogeneous isotropic polarizable medium is presented for the first time with a maximum degree of completeness. The theory is based on the dipole approximation of fluctuation-electromagnetic theory. Fundamental relativistic expressions are derived for conservative and dissipative forces and heating power of a particle. These expressions reduce to earlier nonrelativistic results in particular cases. The results obtained in other approaches and experimental studies of fluctuation-electromagnetic interactions are critically analyzed.     

Dynamic fluctuation electromagnetic interaction of a nonrelativistic quadrupole particle with a flat surface

Within the framework of the nonrelativistic fluctuation electromagnetic theory, relationships for the quadrupole-quadrupole contribution to the tangential and normal components of the force acting on a particle moving parallel to the polarizing surface are derived for the first time. Consideration is given to the cases when the particle possesses a permanent quadrupole moment or a fluctuation quadrupole moment and the surface is characterized by a local dielectric function.     

“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.     

Conservative–dissipative forces and heating mediated by fluctuation electromagnetic field: Two plates in relative nonrelativistic motion

We calculate heating rate, attractive conservative and tangential dissipative fluctuation electromagnetic forces felt by a thick plate moving with nonrelativistic velocity parallel to a closely spaced another plate in rest using relativistic fluctuation electrodynamics. We argue that recently developed relativistic out of equilibrium theory of fluctuation electromagnetic interactions [A.I. Volokitin, B.N.J. Persson, Phys. Rev. B78 (2008) 155437; arXiv:/cond-mat.other/0807.1004v1, 2008] has serious drawbacks.     

Conservative—dissipative interaction forces and heating caused by a fluctuation electromagnetic field: Two plates in a nonrelativistic relative motion

The heating rate and conservative—dissipative forces in a system of two parallel plates moving at a nonrelativistic velocity with respect to each other have been calculated in terms of the fluctuation electromagnetic electrodynamics for the first time. It has been demonstrated that the recently proposed relativistic theory of fluctuation electromagnetic interactions in the configuration under consideration offers fundamental disadvantages.     

Nonrelativistic mean-field description of the deformation of Λ hypernuclei

The deformations of light Λ hypernuclei are studied in an extended nonrelativistic deformed Skyrme-Hartree-Fock approach with realistic modern nucleonic Skyrme forces,pairing correlations,and a microscopical lambda-nucleon interaction derived from Brueckner-Hartree-Fock calculations.Compared to the large effect of an additional Λ particle on nuclear deformation in the light soft nuclei within relativistic mean field method,this effect is much smaller in the nonrelativistic mean-field approximation.     

Fluctuation-induced electromagnetic interaction of a moving particle with a plane surface

The most general (nonrelativistic) formulas for the force of attraction to the surface and for the drag of a nonrelativistic atom moving parallel to it, as well as for the lateral and normal forces acting on a moving dipole molecule and on a charged particle (in the case of parallel and perpendicular motion), are derived for the first time in the framework of the fluctuational electromagnetic theory. The dependences of these forces on the velocity, temperature, separation, and dielectric properties of the atom and the surface are derived. The effect of the nondissipative resonance interaction between a moving neutral atom and the field of surface plasmons, as well as the possible emergence of a positive (accelerating) force acting on the atom (nanoprobe), is substantiated theoretically. The role of dynamic fluctuational forces and their possible experimental measurement when using the quartz microbalance technique and an atomic-force microscope (in the dynamic mode), as well as during deceleration of atomic beams in open nanotubes, are considered. The correctness of the obtained results is confirmed by their agreement with most of the available theoretical relations derived by other authors.     

Inertial mass and the quantum vacuum fields

Even when the Higgs particle is finally detected, it will continue to be a legitimate question to ask whether the inertia of matter as a reaction force opposing acceleration is an intrinsic or extrinsic property of matter. General relativity specifies which geodesic path a free particle will follow, but geometrodynamics has no mechanism for generating a reaction force for deviation from geodesic motion. We discuss a different approach involving the electromagnetic zero‐point field (ZPF) of the quantum vacuum. It has been found that certain asymmetries arise in the ZPF as perceived from an accelerating reference frame. In such a frame the Poynting vector and momentum flux of the ZPF become non‐zero. Scattering of this quantum radiation by the quarks and electrons in matter can result in an acceleration‐dependent reaction force. Both the ordinary and the relativistic forms of Newton's second law, the equation of motion, can be derived from the electrodynamics of such ZPF‐particle interactions. Conjectural arguments are given why this interaction should take place in a resonance at the Compton frequency, and how this could simultaneously provide a physical basis for the de Broglie wavelength of a moving particle. This affords a suggestive perspective on a deep connection between electrodynamics, the origin of inertia and the quantum wave nature of matter.     

Calculation of the volume polarization field of a relativistic particle

The polarization fields of a relativistic particle moving in a homogeneous medium are calculated. The results are illustrated by graphs that show the behavior of the electric and magnetic fields in the reference frame comoving with the particle. The behavior of the fields at large distances from the particle is analyzed.     

Radiative damping of a relativistic electron in classical electrodynamics

An exact solution of the problem of the reaction of the field generated by a relativistic classical electron is derived. It is found that the solution differs dramatically from the known formulas by the presence of a component that is even under time reversal. It is also shown that the component of the generalized radiative damping force that is odd under time reversal coincides with the well-known relativistic damping force obtained from the approximate nonrelativistic formula via a Lorentz transformation. Zh. éksp. Teor. Fiz. 114, 1661–1671 (November 1998)     

A charged particle in a homogeneous magnetic field accelerated by a time-periodic Aharonov–Bohm flux

We consider a nonrelativistic quantum charged particle moving on a plane under the influence of a uniform magnetic field and driven by a periodically time-dependent Aharonov–Bohm flux. We observe an acceleration effect in the case when the Aharonov–Bohm flux depends on time as a sinusoidal function whose frequency is in resonance with the cyclotron frequency. In particular, the energy of the particle increases linearly for large times. An explicit formula for the acceleration rate is derived with the aid of the quantum averaging method, and then it is checked against a numerical solution and a very good agreement is found.     

Transition radiation measurements at distances from the transition point comparable to the formation length

The spatial distribution of the electromagnetic field excited by a relativistic particle crossing the surface of a metal is studied. It is shown that the field of the uniformly moving charge must also be taken into account during measurements at distances comparable to the path length for formation of the radiation. Expressions describing the effect of the self-field of the charge on the transition radiation field are derived. Zh. Tekh. Fiz. 67, 89–93 (September 1997)     

Relativistic generalization and extension to the non-Abelian gauge theory of Feynman's proof of the Maxwell equations

R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which the obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. We formulate both a special relativistic and a general relativistic versions of Feynman's derivation. Especially in the general relativistic version we prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. We also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context.     

Relativistic ponderomotive forces

The interaction of a relativistic classical electron with an inhomogeneous electromagnetic field is investigated. In second-order perturbation theory the motion is separated into fast and slow motions, and the relativistic Newtonian equation is averaged over the fast oscillations. The rate of change obtained for the slow component of the electron momentum is interpreted as a relativistic ponderomotive force. The result is generalized to the relativistic case of the wellknown expression for the Gaponov-Miller force acting on an electron at rest. The expressions obtained for the relativistic ponderomotive forces are very complicated in the general case. They simplify in the limit of a stationary field (pulses of long duration) and a small gradient. The most typical and simplest special case of an inhomogeneous field—a stationary plane-focused beam—is investigated. The main difference between relativistic ponderomotive forces and their nonrelativistic limit is they have multiple components. In addition to the usual force directed along the gradient of the field, the relativistic case is also characterized by force components that do not have the form of the gradient of a potential and are parallel to the wave vector and the direction of the field polarization. It is shown that when a relativistic electron travels in a direction close to the direction of the wave vector of a focused laser beam, these components can greatly exceed the gradient force. A force directed along the field polarization vector arises even when the gradient of the field in this direction is zero. Zh. éksp. Teor. Fiz. 116, 1198–1209 (October 1999)     

Fluctuation electromagnetic interaction of moving particles with a cylindrical surface and a channel

The most general (nonrelativistic) analytical formulas are deduced in the framework of the fluctuation electromagnetic theory for the dynamic conservative and dissipative forces experienced by a neutral atom moving parallel to the generatrix of a cylindrical surface. As in the case of a flat surface, a finite friction force proportional to the velocity exists at T=0.     

General Requirements for a Relativistic Quantum Theory

The equations of a relativistic quantum theory for two or more particles should satisfy at least the following criteria. (1) They should be Poincaré invariant. (2) The cluster property should hold. (3) Causality should not be violated over distances much larger than the Compton wavelengths of the particles involved. (4) The electromagnetic interaction between charged particles should be formulated in a gauge-invariant way. (5) If, for a two-particle system, one of the masses becomes infinitely large, the equations should reduce to the relevant relativistic equation for the other particle. (6) In the nonrelativistic limit the equation should reduce to the Schr?dinger equation. In this paper it will be shown how a quasi-potential theory, which was introduced many years ago [1] and which was applied to a number of systems [2–12], meets all these requirements. Received March 25, 1997; revised July 15, 1997; accepted for publication March 18, 1998     

Motion of a charged particle in the field of a grounded conductive sphere

Motion of a charged particle in the field of a grounded conductive sphere is investigated. It is assumed that the field created by the sphere is quasi-static that implies limitation on particle velocities by nonrelativistic values and the possibility of neglecting magnetic interaction and heat losses. A classification is provided and possible particle trajectories are constructed in the examined case.     

On the acoustic approximation of thermomechanical description of a liquid crystal

Based on dynamic equations of a heterogeneous elastic medium which take into account rotational degrees of freedom of microstructure particles, a simplified mathematical model was constructed to describe the wave motions of a nematic liquid crystal under weak mechanical and temperature perturbations. It is shown that in the medium under plane deformation, the tangential stress obeys the Klein-Gordon equation of oscillatory particle rotation. Consideration is given to the possibility of initiating rotational waves in a nematic liquid crystal, which change its optical properties, due to heat sources acting at its boundary.     

从陈子定理看相对论力学

通过巧妙地让陈子定理包含光速，可以得到粒子运动的相对论速度基本关系．根据这个相对论速度基本关系，可以推导出相对论质点动力学方程，能量质量关系，动量能量关系，洛伦兹变换等结果．