Arbitrary External Field Research Articles

Meissner response of anisotropic superconductors

The response field of a half-space anisotropic superconductor is evaluated for an arbitrary weak external field source. Example sources of a point magnetic moment and a circular current are considered in detail. For the penetration depth $\lambda \ll L$ with $L$ being any other relevant distance (the source size, or the distance between the source and the superconductor), the major contribution to the response is the $\lambda$ independent field of the source image. It is shown that the absolute value of $\lambda$ cannot be extracted from the response field with a better accuracy than that for the source position. Similar problems are considered for thin films.

Gauge-invariant relativistic Wigner functions

On the basis of the Hamiltonian form of the Klein–Gordon equation for a charged scalar particle field introduced by Feshbach and Villars, the gauge-invariant 2 × 2W igner matrix has been constructed whose diagonal elements describe positive and negative charge densities and whose off-diagonal elements correspond to cross-densities in phase space. The system of coupled transport equations has been derived in the case of interaction with an arbitrary external electromagnetic field. A gauge-independent generalization of the free particle representation due to Feshbach and Villars is given, and on the basis of it both the nonrelativistic an dt he classical limits of the relativistic quantum Boltzmann–Vlasov equation are discussed. In the nonrelativistic limit (p/mc → 0) the set of equations of motion decouple to two independent quantum transport equations describing the dynamics of oppositely charged positon and negaton densities. In the classical limit (¯ → 0) two relativistic Boltzmann–Vlasov equations result for the diagonal positon and negaton

Gauge‐independent quantum dynamics on phase‐space of charged scalar particles

AbstractOn the basis of the Hamiltonian form of the Klein‐Gordon equation of a charged scalar particle field introduced by Feshbach and Villars, the gauge‐invariant 2×2 Wigner matrix has been constructed whose diagonal elements describe positive and negative charge densities and the off‐diagonal elements correspond to cross‐densities in phase‐space. The system of coupled transport equations has been derived in case of interaction with an arbitrary external electromagnetic field. A gauge‐independent generalization of the free particle representation due to Feshbach and Villars is given, and on the basis of it both the nonrelativistic and the classical limits of the general relativistic quantum Boltzmann‐Vlasov equation(RQBVE) is discussed. In the non‐relativistic limit (p/mc→0) the set of equations of motion decouple to two independent quantum transport equations describing the dynamics of oppositely charged positon and negaton densities separately. In the classical limit(ℏ→0) two relativistic Boltzmann‐Vlasov equations result for the diagonal positon and negaton densities. It is obtained that, though in the latter equations the Planck constant ℏ is absent, the real part of the cross‐density does not vanish.

Nonrelativistic Quantum Mechanics with Spin in the Framework of a Classical Subquantum Kinetics

Recently it has been shown that the spinless one-particle quantum mechanics can be obtained in the framework of entirely classical subquantum kinetics. In the present paper we argue that, within the same scheme and without any extra assumption, it is possible to obtain both the nonrelativistic quantum mechanics with spin, in the presence of an arbitrary external electromagnetic field, as well as the nonlinear quantum mechanics.

Boundary conditions for the electromagnetic field in a waveguide with a thin-walled annular plasma in the context of application to plasma microwave electronics

Effective boundary conditions for the electromagnetic field of the slow surface waves of a thinwalled annular plasma in a metal waveguide are derived and justified. With the boundary conditions obtained, there is no need to solve field equations in the plasma region of the waveguide, so that the dispersion properties of plasma waveguides can be investigated analytically for an arbitrary strength of the external magnetic field. Examples are given that show how to use the effective boundary conditions in order to describe surface waves with a normal and an anomalous dispersion. The boundary conditions are then employed to construct a theory of the radiative Cherenkov instabilities of a thin-walled annular electron beam in a waveguide with a thinwalled annular plasma. The single-particle and collective Cherenkov effects associated with low-and high-frequency surface waves in an arbitrary external magnetic field are studied analytically. The method of the effective boundary conditions is justified in the context of application to the problems of plasma relativistic microwave electronics.

Nonlinear nonviscous hydrodynamical models for charge transport in the framework of extended thermodynamic methods

This paper develops a procedure, based on methods of extended thermodynamics, to design nonlinear hydrodynamical models for charge transport in metals or in semiconductors, neglecting viscous phenomena. Models obtained in this way allow the study of the motion of electric charges in the presence of arbitrary external electric fields and may be useful when one wishes to study phenomena in a neighborhood of a stationary nonequilibrium process: indeed, the drift velocity of the charge gas with respect to the crystal lattice is not regarded as a small parameter.

Thermodynamics of the anisotropic two-channel Kondo problem

We construct and solve numerically the thermodynamic Bethe Ansatz equations for the spin-anisotropic two-channel Kondo model in arbitrary external field $h$. At high temperatures the specific heat and the susceptibility show power law dependence. For $h \to 0$ and at temperatures below the Kondo temperature $T_K$ a two-channel Kondo effect develops characterized by a Wilson ratio 8/3, and a logarithmic divergence of the susceptibility and the linear specific heat coefficient. Finite magnetic field, $h>0$ drives the system to a Fermi liquid fixed point with an unusual Wilson ratio which depends sensitively on $h$.

Lorentz force-induced stresses in long current-carrying conductors

Technique for calculation of Lorentz force-induced stresses in long straight conductors with the uniform current density in the presence of an external magnetic field is proposed. Reduction of the plane elastic problem for the conductor of a narrow rectangular cross section embedded in an arbitrary external field to the known homogeneous problems is considered. As an example stress analysis of an elliptical conductor with the stress-free lateral surface under the interaction of the current with its self field is performed and particular solutions of the problem of the interaction with the external field produced by the current flowing in an analogous conductor are given.

A New Pseudospectral Method for Calculations of Hydrogen Atom in Arbitrary External Fields

A new pseudospectral method was introduced to calculate wavefunctions and energy levels of hydrogen atom in arbitrary potential. Some results of hydrogen atom in uniform magnetic fields were presented, high accuracy of results was obtained with simple calculations, and our calculations show very fast convergence. It suggests a new method for calculations of hydrogen atom in external fields.

Homopolymers with Intrachain Interactions

The system under consideration is a classical homopolymeric chain under an arbitrary external field, and in the grand canonical ensemble of its monomeric units. The ideal case of only symmetric next neighbor interactions is first analyzed in the relative density format. Arbitrary monomer-monomer interactions are introduced in a graphical perturbation series, and the leading order is expressed as a relative density functional with the aid of a sequence of redundant fields under whose variation the thermodynamic potential—here the excess grand potential—is stationary. Various reduction methods are suggested to compress the set of redundant fields of this overcomplete description.

Levitation force between a superconductor and a permanent magnet with cylindrical symmetry

In order to understand the levitation phenomena of superconductors (SCs), experiments are often realized by studying the levitation force between a cylindrical SC and a coaxial permanent magnet. In this work, we study these experiments by theoretical models we have derived in two stages. In the first stage, we assume both that the SC has no demagnetizing effects and that the applied field is vertical in the SC volume. Within these approximations, we derive simple analytical models that can explain the main features of levitation. In a second step, we present a numerical model which simulates the general case, including the effect of demagnetizing fields in the SC and the application of an arbitrary external field that keeps the cylindrical symmetry. The conditions for using either the simplified analytical models or the complete numerical one are discussed.

Integral equations for molecular fluids based on the interaction site model: Density-functional formulation

An integral equation for rigid-body molecules with respect to site-density distribution function under arbitrary external fields is derived by the density-functional theory. Using a grand canonical partition function of molecular systems, we extend original Percus’ idea to molecular fluids. The extended Percus’ idea provides a relation between the site–site pair distribution function and site–density distribution function under an external field composed of the site–site interaction potentials of a molecule fixed at the origin. The site–density integral equation combined with the extended Percus’ relation to molecular fluids gives a closure relation of reference interaction site model equation. The site–site pair distribution functions of homonuclear diatomic Lennard-Jones fluids obtained by the integral equation agree well with those of Monte Carlo simulation.

From gauge transformations to topology computation in quantum lattice gas automata

The evolution of a quantum lattice gas automaton (LGA) for a single charged particle is invariant under multiplication of the wave function by a global phase. Requiring invariance under the corresponding local gauge transformations determines the rule for minimal coupling to an arbitrary external electromagnetic field. We develop the Aharonov-Bohm effect in the resulting model into a constant time algorithm to distinguish a one dimensional periodic lattice from one with boundaries; any classical deterministic LGA algorithm distinguishing these two spatial topologies would have expected running time on the order of the cardinality of the lattice.

Single homopolymers in the relative density representation.

A single symmetric homopolymer is studied in the grand ensemble of its monomeric units. For an arbitrary external field but next neighbor interactions alone, such a system is represented as a functional of the local density to local fugacity ratio, conjugate to the fugacity, with the excess grand potential as thermodynamic generating function. A sample case in a spherical enclosure is solved, where a complementary exclusion from a spherical volume requires an extension to a grand ensemble of polymers. A preliminary extension is also made in mean field form to non-neighbor interactions, as well as to nonsymmetric interactions.

Operator representation of the wave function for a charged particle in an external field and its applications

A consistent derivation of the operator form for the solution of the wave equation for a charged particle in an arbitrary external electromagnetic field is presented. The expressions obtained can be used for solving any problems in quantum electrodynamics in external fields in the framework of the semiclassical operator method. The peculiarities of the application of this method are demonstrated for the small-angle elastic scattering of a high-energy photon in an arbitrary localized electric field. The problem is solved for the first time without presuming the central symmetry of the external field potential.

Non-homogeneous random walks, generalised master equations, fractional Fokker-Planck equations, and the generalised Kramers-Moyal expansion

A generalised random walk scheme for random walks in an arbitrary external potential field is investigated. From this concept which accounts for the symmetry breaking of homogeneity through the external field, a generalised master equation is constructed. For long-tailed transfer distance or waiting time distributions we show that this generalised master equation is the genesis of apparently different fractional Fokker-Planck equations discussed in literature. On this basis, we introduce a generalisation of the Kramers-Moyal expansion for broad jump length distributions that combines multiples of both ordinary and fractional spatial derivatives. However, it is shown that the nature of the drift term is not changed through the existence of anomalous transport statistics, and thus to first order, an external potential Φ(x) feeds back on the probability density function W through the classical term ∝∞ ∂/∂ xФ´(x)W(x, t), i.e., even for Levy flights, there exists a linear infinitesimal generator that accounts for the response to an external field.

Algorithm for obtaining the gradient expansion of the local density of states and the free energy of a superconductor

We present an efficient algorithm for obtaining the gauge-invariant gradient expansion of the local density of states and the free energy of a clean superconductor. Our method is based on a new mapping of the semiclassical linearized Gorkov equations onto a pseudo-Schr\"odinger equation for a three-component wave function $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\psi}}(x),$ where one component is directly related to the local density of states. Because $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\psi}}(x)$ satisfies a linear equation of motion, successive terms in the gradient expansion can be obtained by simple linear iteration. Our method works equally well for real and complex order parameter, and in the presence of arbitrary external fields. We confirm a recent calculation of the fourth order correction to the free energy by Kosztin, Kos, Stone, and Leggett [Phys. Rev. B 58, 9365 (1998)], who obtained a discrepancy with an earlier result by Tewordt [Z. Phys. 180, 385 (1964)]. We also give the fourth order correction to the local density of states, which has not been published before.

Gibbs states of graphical representations of the Potts model with external fields

We consider the ferromagnetic q-state Potts model, with each of the q spin values coupled to an external field. We also introduce a generalized random cluster model, which includes both the Potts model in arbitrary homogeneous external fields and the noninteger q random cluster model as special cases. We establish the FKG property, the finite energy condition, uniqueness of the infinite cluster, and Gibbsianness of limit states for this generalized model. Furthermore, we develop the theory of Gibbs states for the Edwards–Sokal representation of the Potts model in a field, and relate the phase structure in this representation to those in the spin and random cluster representations. Finally, we characterize the possible color(s) of the infinite cluster(s) and show that the correspondence between Edwards–Sokal Gibbs states and their random cluster marginals is bijective, once the color of the infinite cluster is fixed.

Quantitative vector magnetometry using generalized magneto-optical ellipsometry

We recently developed the method of generalized magneto-optical ellipsometry (GME), which enabled us to achieve a complete magneto-optical characterization of a magnetic material, including the magnetization orientation. For the present study, we have modified our original setup to allow for measurements at arbitrary external fields including entire field scans. Consequently, GME can be used as a tool to perform vector magnetometry measurements. In this article, we present our first experimental results on polycrystalline Co films which demonstrate the feasibility of GME as a magneto-optical vector magnetometer.

General solution of the WZNW system and 2D induced gravity in curved space-time

We find the general solution of the equations of motion for the Wess-Zumino-Novikov-Witten (WZNW) system in curved space-time for arbitrary external gauge fields. Using the connection between the WZNW system for the $\mathrm{SL}(2,R)$ group and two-dimensional (2D) induced gravity we obtain the general solution of the equations of motion for 2D induced gravity in curved space-time from that of the WZNW system. We independently present the direct solution of 2D induced gravity equations of motion and obtain the same result.