Boundary conditions for distribution functions at interfaces between crystalline grains

The paper concerns a derivation of boundary conditions at a planar interface between two crystalline grains for distribution functions of quasiparticles of a given kind. The derivation is performed under the assumption that the equi-energy surfaces (in thek-space) which, in general, need not be the same in both the grains, are convex. The boundary conditions take into account a jump of the (electro) chemical potential and temperature induced when a current of the quasiparticles passes through the interface. The Bezák-Krempaský boundary conditions that were originally formulated for longitudinal currents are thus generalized to the case when the currents may have a transversal component.The author thanks Dr. V.Bezák for many helpful comments.     

Velocity fluctuations in a homogeneous 2D granular gas in steady state

We have measured the spectrum of velocity fluctuations in a granular system confined to a vertical plane and driven into a homogeneous, steady state by strong vertical vibration. The distribution of horizontal velocities is not Maxwell-Boltzmann and is given by P(v) = Cexp[-beta(|v|/sigma)(alpha)] where alpha = 1.55+/-0.1 at all frequencies and amplitudes investigated, and also for varying boundary conditions. The deviation from Maxwell-Boltzmann statistics occurs in the absence of spatial clustering and does not result from an inhomogeneous average over regions of varying local density. Surprisingly, P(v) has the same shape over a wide range of densities.     

Indistinguishability or distinguishability of the particles of Maxwell-Boltzmann statistics

Recently the following dichotomy has been established: either the familiar three statistics (Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac) all describe indistinguishable particles or (exclusively) they all describe distinguishable particles. We consider permutation invariance of the state as the ultimate criterium for indistinguishability and give some arguments which elucidate that the particles of Maxwell-Boltzmann statistics are indistinguishable.     

The dissipative dynamics of the He A-B interface in finite geometries

The ³He A-B interface velocity and the stationary field of temperature and counterflow accompanying the phase transition are calculated employing general boundary conditions and superfluid hydrodynamics. All dissipative mechanisms that may occur are considered, especially including the effects of lateral walls. There are three contributions to the total growth resistance: (i) a microscopically abrupt temperature discontinuity at the interface arising from Andreev scattering of quasiparticles, (ii) two hydrodynamically gentle temperature variations (sq- or diffusive modes) on both sides of the interface that come from collisions among quasiparticles, and (iii) the drag exerted directly on the interface by the wall's roughness.     

Fractional exclusion statistics applied to relativistic nuclear matter

The effect of statistics of the quasiparticles in the nuclear matter at extreme conditions of density and temperature is evaluated in the relativistic mean-field model generalized to the framework of the fractional exclusion statistics (FES). In the model, the nucleons are described as quasiparticles obeying FES and the model parameters were chosen to reproduce the ground state properties of the isospin-symmetric nuclear matter. In this case, the statistics of the quasiparticles is related to the strengths of the nucleon-nucleon interaction mediated by the neutral scalar and vector meson fields. The relevant thermodynamic quantities were calculated as functions of the nucleons density, temperature and fractional exclusion statistics parameter α. It has been shown that at high temperatures and densities the thermodynamics of the system has a strong dependence on the statistics of the particles. The scenario in which the nucleon-nucleon interaction strength is independent of the statistics of particles was also calculated, but it leads in general to unstable thermodynamics.     

Fractional statistics in the fractional quantum Hall effect

A microscopic confirmation of the fractional statistics of the quasiparticles in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at nu=1/3 and nu=2/5 by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the statistics. The conditions for the applicability of the fractional statistics concept are discussed.     

From fractional exclusion statistics back to Bose and Fermi distributions

Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this Letter I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.     

Statistical interpretation of the kinetic equation in the adsorption problem

A statistical interpretation for the adsorption phenomenon is presented in the framework of the Maxwell-Boltzmann statistics. A model for an adsorbing surface is proposed and the connection between the phenomenological parameters, entering in the kinetic equation at the boundary surfaces, with the microscopic model is derived.Received: 14 June 2004, Published online: 14 September 2004PACS: 66.10.-x Diffusion and ionic conduction in liquids - 68.43.-h Chemisorption/physisorption: adsorbates on surfaces - 68.43.Mn Adsorption/desorption kinetics     

On a quantum statistics of quasiparticles

An example of quasiparticles whose statistics is neither Bose nor Fermi is presented. Experiments which permit the determination of the statistics are proposed. The collision integral for quasiparticles of arbitrary statistics is presented.     

Entropic derivation of the spectral Eddington factors

In general, the closure of the finite system of moment equations by the corresponding maximum entropy distribution function results in the symmetric conservative system of first-order partial differential equations for the Lagrange multipliers of the constrained Boltzmann entropy maximization problem. Then the transformation of dependent variables yields the system of conservation equations for the moments which is consistent with the additional conservation equation identified with the balance of entropy. The objective of this paper is to employ these facts for the analysis of the spectral Eddington factors obtained from the maximum entropy distribution functions. The supposition that the spectral Eddington factors should depend on the energy density and the heat flux only through the single variable representing the heat flux normalized in some way by the energy density predominates in the literature on the subject. Here, it is demonstrated that this is true only for classical Maxwell-Boltzmann radiation and, in this case, the well-known results of Minerbo are recovered. A similar single-variable dependence postulated by Cernohorsky and Bludman for fermionic radiation cannot be justified since it leads to the contradiction with the consistency conditions between the moment evolution equations and the entropy balance. For Bose-Einstein radiation, we rederive and analyze the results given in the literature for low-energy and high-energy limits. We also show that, except for those limiting cases, the Eddington factor for bosonic radiation cannot be represented as a function of a single normalized variable. In the present approach, the entropy function plays a crucial role in determining the system of evolution equations for the energy density and the heat flux. In this system, the flux of the heat flux, and hence the Eddington factor, is determined by the additional scalar potential uniquely related to the entropy function for each type of statistics. Since the Eddington factor cannot be expressed in terms of elementary functions, we propose to use the polynomial approximation. Namely, for Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics, we expand the entropy function in powers of the square of the heat flux and also calculate the corresponding power series expansion of the additional potential. By truncating the latter, we obtain the Eddington factor represented as the eighth-order polynomial in the heat flux with coefficients being the elementary functions of the energy density and the parameter which determines statistics. Finally, we analyze the behavior of the scalar Eddington factors in the limiting case when the normalized heat flux tends to one.     

Simulation of Shock Wave Diffraction over 90° Sharp Corner in Gases of Arbitrary Statistics

The unsteady shock wave diffraction over a 90° sharp corner in gases of arbitrary particle statistics is simulated using an accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space. The numerical method is based on the usage of discrete ordinate method for discretizing the velocity space of the distribution function; whereas a second order accurate TVD scheme (Harten in J. Comput. Phys. 49(3):357–393, 1983) with Van Leer’s limiter (J. Comput. Phys. 32(1):101–136, 1979) is used for evolving the solution in physical space and time. The specular reflection surface boundary condition is assumed. The complete diffraction patterns are recorded using various flow property contours. Different range of relaxation times approximately corresponding to continuum, slip and transitional regimes are considered and the equilibrium Euler limit solution is also computed for comparison. The effects of gas particles that obey the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics are examined and depicted.     

Switching noise as a probe of statistics in the fractional quantum Hall effect

We propose an experiment to probe the unconventional quantum statistics of quasiparticles in fractional quantum Hall states by measurement of current noise. The geometry we consider is that of a Hall bar where two quantum point contacts introduce two interfering amplitudes for backscattering. Thermal fluctuations of the number of quasiparticles enclosed between the two point contacts introduce current noise, which reflects the statistics of the quasiparticles. We analyze Abelian nu=1/q states and the non-Abelian nu=5/2 state.     

Non-equilibrium thermodynamics of interfacial systems: II. Boundary conditions for fluids with spin

The theory of non-equilibrium thermodynamics is applied to a system of two immiscible fluids whose molecules possess internal angular momentum (spin) which are separated by an interface. The conservation laws and the Gibbs relation are used to derive the entropy production at the interface. The resulting linear laws relating the fluxes and forces represent boundary conditions on the hydrodynamic equations for the bulk phases. A limiting case is considered and boundary conditions derived by previous authors are obtained.     

Exact maximal height distribution of fluctuating interfaces

We present an exact solution for the distribution P(h(m),L) of the maximal height h(m) (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h(m),L)=L(-1/2)f(h(m)L(-1/2)) for all L>0, where the function f(x) is the Airy distribution function that describes the probability density of the area under a Brownian excursion over a unit interval. For the free boundary case, the same scaling holds, but the scaling function is different from that of the periodic case. Numerical simulations are in excellent agreement with our analytical results. Our results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables.     

Effect of Landau level mixing on braiding statistics

We examine the effect of Landau level mixing on the braiding statistics of quasiparticles of Abelian and non-Abelian quantum Hall states. While path dependent geometric phases can perturb the Abelian part of the statistics, we find that the non-Abelian properties remain unchanged to an accuracy that is exponentially small in the distance between quasiparticles.     

Signatures of non-Abelian statistics in nonlinear Coulomb blockade transport

Signatures of the non-Abelian statistics of quasiparticles in the ν=5/2 quantum Hall state are predicted to be present in the current-voltage characteristics of tunneling through one or two quantum Hall puddles of Landau filling ν(a) embedded in a bulk of filling ν(b) with (ν(a),ν(b))=(2,5/2) and (ν(a),ν(b))=(5/2,2).     

The concept of indistinguishable particles in classical and quantum physics

The consequences of the following definition of indistinguishability are analyzed. Indistinguishable classical or quantum particles are identical classical or quantum particles in a state characterized by a probability measure, a statistical operator respectively, which is invariant under any permutation of the particles. According to this definition the particles of classical Maxwell-Boltzmann statistics are indistinguishable.     

The effect of velocity-dependent boundary conditions on pattern formation

We discuss the role played by velocity-dependent boundary conditions in several problems of non-local interface dynamics. Qualitative and quantitative effects are demonstrated through three examples which are: (i) quantitative verification of the scenario of ‘microscopic solvability’ in pattern selection for the case of viscous fingering in a rectangular Hele-Shaw cell, (ii) detection of the presence of this type of boundary condition through an analysis of the statistical properties of the interface for radial Hele-Shaw flow and, (iii) generation of qualitatively different interface morphologies by tuning the magnitude of this effect in the case of radial Hele-Shaw flow. We also point out the possible implications of this last example for the observation of similar morphologies in some problems of solidification.     

Primary information sensors for AFM based on quasiparticle flows

A new class of experimental techniques is presented which allows the behavior of elementary collective excitations (quasiparticles) in solids to be studied at the mesoscopic scale. New experimental equipment is being constructed in the classical scheme of an atomic force microscope in which the sensor of primary information is a cantilever. The defining feature of the proposed sensor based on a cantilever is the addition of a generator and detector of quasiparticles to its design. The generator is located either on the tip of the cantilever or in close proximity to the needle on the cantilever, so that the flow of quasiparticles emitted by the generator propagates along the needle of the cantilever to the point where the needle tip touches the surface. The detector is located in a similar way. The measured quantity is the reflection coefficient of the flux of quasiparticles from the interface between the cantilever needle tip and the surface being scanned.     

Normalization of interface optical phonon modes in cylindrical quantum wires with semiconductor-semiconductor and metal-semiconductor boundary conditions

In this work, analytical solutions for the interface longitudinal optical (LO) phonons in cylindrical polar-semiconductor quantum wires are normalized by the standard quantization condition. Two cases are considered: polar-semiconductor quantum wires encapsulated in another polar-semiconductor and polar-semiconductor quantum wires encapsulated in metal. For the case of metal encapsulation it is demonstrated that unwanted inelastic interface LO phonon scattering is eliminated since the interface modes do not satisfy the appropriate boundary conditions.