arXiv subjects

P. P. J. M. Schram

Publications and source records attributed to P. P. J. M. Schram.

10 recordsLinked to original sources

arXiv2013

Aharonov--Bohm effect, electrodynamics postulates, and Lorentz condition

The problem of the relation between the Ahronov-Bohm effect and traditional postulates of electrodynamics, which claim that only electric and magnetic fields are observable, is resolved by denial of the statement about validity of the Maxwell equations for microscopic fields. We proceed from the idea that the Maxwell equations, as the generalization of experimental data, are valid only for averaged values. We show that microscopic electrodynamics should be based on postulation of the d'Alembert equations for four-vector of the electromagnetic field potential. The Lorentz condition is valid only for the averages and provides the implementation of the Maxwell equations for averages. This concept eliminates the problem of electromagnetic field quantization and provides the correctness of all known results of quantum electrodynamics. Therefore, the "virtuality" of the longitudinal and scalar photons has a formal mathematical character, conditioned by the Maxwell equations for averaged fields. The longitudinal and scalar photons provide not only the Coulomb interaction of charged particles, but also allow the electrical Aharonov-Bohm effect.

quant-ph↗

arXiv2010

Diffusion in a Time-dependent External Field

The problem of diffusion in a time-dependent (and generally inhomogeneous) external field is considered on the basis of a generalized master equation with two times, introduced in [1,2]. We consider the case of the quasi Fokker-Planck approximation, when the probability transition function for diffusion (PTD-function) does not possess a long tail in coordinate space and can be expanded as a function of instantaneous displacements. The more complicated case of long tails in the PTD will be discussed separately. We also discuss diffusion on the basis of hydrodynamic and kinetic equations and show the validity of the phenomenological approach. A new type of "collision" integral is introduced for the description of diffusion in a system of particles, which can transfer from a moving state to the rest state (with some waiting time distribution). The solution of the appropriate kinetic equation in the external field also confirms the phenomenological approach of the generalized master equation.

cond-mat.stat-mech↗

arXiv2010

Kramers-Kronig Relations For The Dielectric Function And The Static Conductivity Of Coulomb Systems

The mutual influence of singularities of the dielectric permittivity e(q,w) in a Coulomb system in two limiting cases w tends to zero, q tends to zero, and opposite q tends to zero, w tends to zero is established. It is shown that the dielectric permittivity e(q,w) satisfies the Kramers-Kronig relations, which possesses the singularity due to a finite value of the static conductivity. This singularity is associated with the long "tails" of the time correlation functions.

cond-mat.stat-mech↗

arXiv2010

On anomalous diffusion in a plasma in velocity space

The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in momentum space. The generalized Fokker-Planck equation for description of diffusion (in momentum space) of particles (ions, grains etc.) in a stochastic system of light particles (electrons, or electrons and ions, respectively) is applied to the evolution of the momentum particle distribution in a plasma. In a plasma the developed approach is also applicable to the diffusion of particles with an arbitrary mass relation, due to the small characteristic momentum transfer. The cases of an exponentially decreasing in momentum space (including the Boltzmann-like) kernel in the PT-function, as well as the more general kernels, which create the anomalous diffusion in velocity space due to the long tail in the PT-function, are considered. Effective friction and diffusion coefficients for plasma-like systems are found.

cond-mat.stat-mech↗

arXiv2006

Remarks on the Nyquist and Callen-Welton Theorems

The connection of the Callen-Welton and Nyquist fluctuation-dissipation relations is considered for plasma-like classical and quantum systems. The conditions for appearance of the dissipative parameters in the equilibrium current-current correlation function are investigated. The paper presents the arguments for the restrictions of the Nyquist theorem and against violation of the Callen-Welton theorem in the quantum case.

cond-mat.stat-mech↗

arXiv2004

Retarded Many-Sphere Hydrodynamic Interactions in a Viscous Fluid

An alternative method is suggested for the description of the velocity and pressure fields in an unbounded incompressible viscous fluid induced by an arbitrary number of spheres moving and rotating in it. Within the framework of this approach, we obtain the general relations for forces and torques exerted by the fluid on the spheres. The behavior of the translational, rotational, and coupled friction and mobility tensors in various frequency domains are analyzed up to the terms of the third order in the dimensionless parameter equal to the ratio of a typical radius of a sphere to the penetration depth of transverse waves and a certain power of the dimensionless parameter equal to the ratio of a typical radius of a sphere to the distance between the centers of two spheres. We establish that the retardation effects can essentially affect the character of the hydrodynamic interactions between the spheres.

physics.flu-dyn↗

arXiv2004

Velocity-Dependent Friction and Diffusion for Grains in Neutral Gases, Dusty Plasmas and Active Systems

A self-consistent and universal description of friction and diffusion for Brownian particles (grains) in different systems, as a gas with Boltzmann collisions, dusty plasma with ion absorption by grains, and for active particles (e.g., cells in biological systems) is suggested on the basis of the appropriate Fokker-Planck equation. Restrictions for application of the Fokker-Planck equation to the problem of velocity-dependent friction and diffusion coefficients are found. General description for this coefficient is formulated on the basis of master equation. Relation of the diffusion coefficient in the coordinate and velocity spaces is found for active (capable to transfer momentum to the ambient media) and passive particles in the framework of the Fokker-Planck equation. The problem of anomalous space diffusion is formulated on the basis of the appropriate probability transition (PT) function. The method of partial differentiation is avoided to construct the correct probability distributions for arbitrary distances, what is important for applications to different stochastic problems. Generale equation for time-dependent PT function is formulated and discussed. Generalized friction in the velocity space is determined and applied to describe the friction force itself as well as the drag force in the case of a non-zero driven ion velocity in plasmas. The negative friction due to ion scattering on grains exists and can be realized for the appropriate experimental conditions.

cond-mat.stat-mech↗

arXiv2003

Surface-active dust in a plasma sheath

The inhomogeneity of the plasma pressure near a conducting electrode is a cause for introducing the surface tension associated with the plasma-electrode interface. We evaluate the dependence of the surface tension on the density of the charged dust immersed in the plasma sheath. In a wide range of parameters, the surface tension turns out to be an increasing function of the dust density.

physics.plasm-ph↗

arXiv1999

Stationary Velocity and Charge Distributions of Grains in Dusty Plasmas

Within the kinetic approach velocity and charge distributions of grains in stationary dusty plasmas are calculated and the relations between the effective temperatures of such distributions and plasma parameters are established. It is found that the effective temperature which determines the velocity grain distribution could be anomalously large due to the action of accelerating ionic bombarding force. The possibility to apply the results obtained to the explanation of the increasing grain temperature in the course of the Coulomb-crystal melting by reduction of the gas pressure is discussed. This paper was received by Phys.Rev.Lett. on 11 August 1999. As potential referees the authors offered to Editor the following persons: V.N.Tsytovich, Russia; R.Bingham, UK; D.Resendes, Portugal; G.Morfill, P.Shukla, Y.M.Yu., Germany.

physics.plasm-ph↗

arXiv1999

Inhomogeneity of dusty crystals and plasma diagnostics

Real dusty crystals are inhomogeneous due to the presence of external forces. We suggest approximations for calculations of different types of inhomogeneous DC (chain and DC with a few slabs) in the equilibrium state. The results are in a good agreement with experimental results and can be used as an effective diagnostic method for many dusty systems.

physics.plasm-ph↗