Thermodynamic Limit for Dipolar Media

We prove existence of a shape- and boundary-condition-independent thermodynamic limit for fluids and solids of identical particles with electric or magnetic dipole moments. Our result applies to fluids of hard-core particles, to dipolar soft spheres and Stockmayer fluids, to disordered solid composites, and to regular crystal lattices. In addition to their permanent dipole moments, particles may further polarize each other. Classical and quantum models are treated. Shape independence depends on the reduction in free energy accomplished by domain formation, so our proof applies only in the case of zero applied field. Existence of a thermodynamic limit implies texture formation in spontaneously magnetized liquids and disordered solids analogous to domain formation in crystalline solids.     

Thermodynamic Limit for Polydisperse Fluids

We examine the thermodynamic limit of fluids of hard core particles that are polydisperse in size and shape. In addition, particles may interact magnetically. Free energy of such systems is a random variable because it depends on the choice of particles. We prove that the thermodynamic limit exists with probability 1, and is independent of the choice of particles. Our proof applies to polydisperse hard-sphere fluids, colloids and ferrofluids. The existence of a thermodynamic limit implies system shape and size independence of thermodynamic properties of a system.     

Triviality of a model of particles with point interactions in the thermodynamic limit

We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles effectively decreases the interaction strength. We show that the model becomes trivial in the thermodynamic limit, in the sense that the free energy density at any given particle density and temperature agrees with the corresponding expression for non-interacting particles.     

Canonical versus Grand-Canonical Free Energies and Phase Diagrams of a Bipolaronic Superconductor Model

We continue the discussion of a bipolaronic superconductor (resp. an anisotropic antiferromagnet in quasispin formulation) as formulated in a previous work, based on a quantum-statistical, microscopic mean-field model. The grand-canonical thermodynamic limit is compared with the canonical thermodynamic limit in terms of a net of perturbations, becoming singular in the infinite lattice limit. A generalized thermostatistical framework is elaborated which covers model potentials with infinite parts. The function of the limiting free energy density in selecting the (stable) phases with broken symmetry is graphically illustrated. The phase diagrams for the two types of ensembles are shown to differ in the region where both the gauge symmetry and the invariance under sublattice exchange are broken. In particular, the type of the phase transitions, the order of the critical points, and the shape of some phase boundaries are found to depend on the ensemble, which clarifies certain controversial topics for these models. The uniqueness of the limiting Gibbs states with free boundary conditions in all thermodynamic phase regions is proved, and their decomposition into pure phase states in terms of a symmetric measure is evaluated. The field operators of the condensed particles are determined in the representations over the limiting Gibbs states.     

Effects of a finite number of particles on the thermodynamic properties of a harmonically trapped ideal charged Bose gas in a constant magnetic field

We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic potential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose–Einstein transition temperature, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties,particularly the Bose–Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N →∞.     

Local Thermodynamical Stability of Fermion Lattice Systems

We study the magnetic moment of neutral atoms in large magnetic fields. Asymptotic formulas for the energy exist with high precision in different regions depending on how large the nuclear charge Z is compared to the magnetic field strength B. All these formulas take the splitting of the kinetic energy into Landau levels as the principal feature and then treat the electric potential as a perturbation. We prove that these approximate formulas predict correctly'(to highest order) the total magnetic moment of the atom. The proof of this fact relies on a 'virial theorem' for Coulomb systems in a constant magnetic field.     

Quantum shape effects and novel thermodynamic behaviors at nanoscale

Thermodynamic properties of confined systems depend on sizes of the confinement domain due to quantum nature of particles. Here we show that shape also enters as a control parameter on thermodynamic state functions. By considering specially designed confinement domains, we demonstrate how shape effects alone modify Helmholtz free energy, entropy and internal energy of a confined system. We propose an overlapped quantum boundary layer method to analytically predict quantum shape effects without even solving Schrödinger equation or invoking any other mathematical tools. Thereby we reduce a thermodynamic problem into a simple geometric one and reveal the profound link between geometry and thermodynamics. We report also a torque due to quantum shape effects. Furthermore, we introduce isoformal, shape preserving, process which opens the possibility of a new generation of thermodynamic cycles operating at nanoscale with unique features.     

Scattering forces and electromagnetic momentum density in crossed circularly polarized standing waves

We analyze the forces on a small dipolar particle and the electromagnetic momentum density in a configuration consisting in two perpendicular circularly polarized stationary waves. The field distribution shows regions in which the electric and magnetic fields are parallel corresponding to a null Poynting vector. Although the average value of the momentum density, proportional to the Poynting vector, is zero in these regions, there are scattering forces acting on small particles due to light's spin force. The total scattering force suggests a new definition of the average value of the momentum density for free propagating electromagnetic fields.     

Scattering forces and electromagnetic momentum density in crossed circularly polarized standing waves

We analyze the forces on a small dipolar particle and the electromagnetic momentum density in a configuration consisting in two perpendicular circularly polarized stationary waves. The field distribution shows regions in which the electric and magnetic fields are parallel corresponding to a null Poynting vector. Although the average value of the momentum density, proportional to the Poynting vector, is zero in these regions, there are scattering forces acting on small particles due to light's spin force. The total scattering force suggests a new definition of the average value of the momentum density for free propagating electromagnetic fields.     

Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties

We consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate (the tube axis). Inside the random tube, which is stationary and ergodic, non-interacting particles move straight with constant speed. Upon hitting the tube walls, they are reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the cosine of the angle between this direction and the normal vector. Steady state transport is studied by introducing an open tube segment as follows: We cut out a large finite segment of the tube with segment boundaries perpendicular to the tube axis. Particles which leave this piece through the segment boundaries disappear from the system. Through stationary injection of particles at one boundary of the segment a steady state with non-vanishing stationary particle current is maintained. We prove (i) that in the thermodynamic limit of an infinite open piece the coarse-grained density profile inside the segment is linear, and (ii) that the transport diffusion coefficient obtained from the ratio of stationary current and effective boundary density gradient equals the diffusion coefficient of a tagged particle in an infinite tube. Thus we prove Fick’s law and equality of transport diffusion and self-diffusion coefficients for quite generic rough (random) tubes. We also study some properties of the crossing time and compute the Milne extrapolation length in dependence on the shape of the random tube.     

Optical absorption by small metallic particles

We study theoretically the dependence of absorption by small metallic particles on particle shape and wave polarization in the IR frequency range. We examine the electric and magnetic absorption by small particles. The particles may be either larger or smaller than the electron mean free path. We show that for asymmetric particles smaller than the mean free path the light-induced conductivity is a tensor. We also show that the total absorption and the electric-to-magnetic absorption ratio are strongly dependent on particle shape and wave polarization. Finally, we construct curves representing the dependence of the ratio of the electric and magnetic contributions to absorption on the degree of particle asymmetry for different wave polarizations. Similar curves are constructed for the ratio of the components of the light-induced conductivity tensor. Zh. éksp. Teor. Fiz. 112, 661–678 (August 1997)     

Investigation of magnetic field effect on surface and finite-site free energy in one-dimensional Ising model of nanosystems

We investigate a one-dimensional (1-D) Ising model for finite-site systems. The finite-site free energy and the surface free energy are calculated via the transfer matrix method. We show that, at high magnetic fields, the surface free energy has an asymptotic limit. The absolute surface energy increases when the value of f (the ratio of magnetic field to nearest-neighbor interactions) increases, and for f?≥?10 approaches a constant value. For the values of f?≥?0.2, the finite-site free energy also increases, but slowly. The thermodynamic limit in which physical properties approach the bulk value is also explored.     

Bremsstrahlung of a neutral fermi particle in the field of a plane electromagnetic wave

The bremsstrahlung is considered from a neutral Fermi particle with anomalous magnetic and electric moments in the field of a screened Coulomb center and in the presence of a plane electromagnetic wave. The effect of the wave polarization on the scattering cross section and the behavior of the particle spin during the scattering process are considered. Cross sections are given for scattering of a particle at a Coulomb center in the presence of constant, crossed electric and magnetic fields which are equal in magnitude and also for a free particle. It is shown that the effect of the anomalous electric moment is often decisive.     

Spin-polarized ground state for interacting electrons in two dimensions

We study numerically the ground state magnetization for clusters of interacting electrons in two dimensions in the regime where the single particle wave functions are localized by disorder. It is found that the Coulomb interaction leads to a spontaneous ground state magnetization. For a constant electronic density, the total spin increases linearly with the number of particles, suggesting a ferromagnetic ground state in the thermodynamic limit. The magnetization is suppressed when the single particle states become delocalized.     

Field-driven dynamical demixing of binary mixtures

ABSTRACT

We consider mixtures of two species of spherical colloidal particles that differ in their Stokes coefficients, but are otherwise identical, in the presence of an external field. Since the particle–particle and particle–field interactions are the same for both species, they are completely mixed in the thermodynamic limit in the presence of any static field. Here, we combine Brownian dynamics and dynamic density functional theory of fluids to show that for sufficiently large differences in the Stokes coefficients of the particles (and corresponding differences in their mobilities) dynamical demixing is observed. These demixed states are transient but, under certain conditions, packing effects compromise the relaxation towards the thermodynamic states and the lifetime of the demixed phases increases significantly.     

Asymptotic stability of stationary states in the wave equation coupled to a nonrelativistic particle

We consider the Hamiltonian system consisting of a scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subjected to an external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. It is assumed that the charge density satisfies the Wiener condition, which is a version of the “Fermi Golden Rule.” We prove that in the large time approximation, any finite energy solution, with the initial state close to the some stable stationary solution, is a sum of this stationary solution and a dispersive wave which is a solution of the free wave equation.     

Two-Dimensional Coulomb Systems on a Surface of Constant Negative Curvature

We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to zero at infinity. The pressure can be expanded as a series in integer powers of the density (the virial expansion). The correlation functions have a thermodynamic limit, and remarkably that limit is the same one for the Coulomb interaction and some other interaction law. However, special care is needed for defining a thermodynamic limit of the free energy density. There are sum rules expressing the property of perfect screening. These generic properties can be checked on the Debye–Hückel approximation, and on two exactly solvable models, the one-component plasma and the two-component plasma, at some special temperature.     

Quasi-2D Monte Carlo simulations of a colloidal dispersion composed of magnetic plate-like particles with magnetic moment normal to the particle axis

We have investigated aggregation phenomena of a colloidal dispersion composed of magnetic plate-like particles by means of Monte Carlo simulations. Such plate-like particles have been modelled as disk-like particles with magnetic moment normal to the particle axis at the particle centre, with the section shape of a spherocylinder. The main objective of the present study is to clarify the influences of the magnetic field strength and magnetic interactions between particles on particle aggregation phenomena. We have concentrated our attention on a quasi-2D system from an application point of view such as the development of surface quality changing technology using such magnetic plate-like particles. A magnetic field is applied along the direction perpendicular to the plane of the monolayer. Internal structures of particle aggregates are discussed quantitatively in terms of radial distribution and orientational pair correlation functions. For the case of strong magnetic interactions between particles, particles form long column-like clusters with their magnetic moments alternating in direction between the neighbouring particles. These tendencies appear under circumstances of a weak applied magnetic field. However, as the magnetic field strength increases, particles incline towards the magnetic field direction, so that particles do not form such clusters.     

On the ν-dimensional one-component classical plasma: The thermodynamic limit problem revisited

We prove theH-stability property and the existence of the thermodynamic limit of the free energy density of the two-dimensional, one-component classical plasma. We give lower and upper bounds on the free energy density in any dimensionv and draw some consequences.