Brownian diffusion in a nonuniform gas

An analysis is made of the effects on the diffusion of Brownian particles whose Knudsen number is large compared to unity, of nonuniformities in the host gas. As examples, in one type of nonuniformity of the host gas, the Chapman-Enskog velocity distribution function for the gas molecules is used; in the other, the host gas is a free-molecule Couette flow. In both cases, a new force on the Brownian particles appears. Two techniques are used (extending Kramers' method and utilizing the Chapman-Enskog method) to transform the new Fokker-Planck equation into generalized Smoluchowski and convective diffusion equations. In these equations, the diffusion coefficient appears as a second-order tensor. Thus, it is demonstrated that Brownian diffusion in a nonuniform gas is anisotropic.The work of Slinn was financially supported in part by Battelle Memorial Institute and in part by U.S. Atomic Energy Commission Contract AT(45-1)-1830. The work of Shen was supported in part by U.S. Air Force Office of Scientific Research Contract 49(638)-1346.     

Thermodynamics of a pion gas

The thermodynamics is presented for a gas of uncharged pions coupled to a static nucleon background through a classical Yukawa interaction. By using invariant phase space in the grand canonical ensemble it is possible to write a general analytical form for the thermodynamical functions.     

The energy distribution of an ion in a radiofrequency trap interacting with a nonuniform neutral buffer gas

An ion in a radiofrequency (rf) trap sympathetically cooled by a simultaneously trapped neutral buffer gas exhibits deviations from thermal statistics caused by collision-induced coupling of the rf field to the ion motion. For a uniform density distribution of the buffer gas, the energy distribution of the ion can be described by Tsallis statistics. Moreover, runaway heating of the ion occurs if the buffer gas particles are sufficiently heavy relative to the ion. In typical experiments, however, ultracold buffer gases are confined in traps resulting in localised, non-uniform density distributions. Using a superstatistical approach, we develop an analytical model for an ion interacting with a localised buffer gas. We demonstrate theoretically that limiting collisions to the centre of the ion trap enables cooling at far greater mass ratios than achievable using a uniform buffer gas, but that an upper limit to the usable mass ratio exists even in this case. Furthermore, we analytically derive the functional form of the energy distribution for an ion interacting with a buffer gas held in a harmonic potential. The analytical distribution obtained is found to be in excellent agreement with the results of numerical simulations.     

Thermodynamics of a Sine-Gordon breather gas

A consistent, divergence-free approach to classical soliton-gas phenomenology of integrable nonlinear systems is presented. Difficulties with current approaches are assessed and a method to achieve consistent phase-space sharing between linear and nonlinear excitations is presented. Results for the free energy of the Sine-Gordon chain exhibit only slight discrepancies when compared to exact (transfer integral) calculations. An interesting cutoff structure is revealed, with the exclusion of breathers with energies less than 2k _B T.     

The relativistic fermi gas in a nonuniform velocity field

We review the relativistic Fermi gas in an inhomogeneous velocity field and calculate components of the current vector and the energy-momentum tensor in a comoving frame. We derive quantum corrections to the classical distribution function in the framework of the grand canonical ensemble.     

Thermodynamics of nonstationary and transient effects in a relativistic gas

We show how a system of generalized Fourier and Navier-Stokes equations, containing relaxation terms and couplings between heat flow and viscosity, can be consistently derived from phenomenological thermodynamics and from kinetic theory. The coefficients are given explicitly for a relativistic Boltzmann gas.     

Thermodynamics of a trapped unitary Fermi gas

We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value T(c) = 0.23(2)epsilon(F) in the bulk, as predicted by the present authors in their Monte Carlo calculations.     

Thermodynamics of a photon gas and deformed dispersion relations

We resort to the methods of statistical mechanics in order to determine the effects that a deformed dispersion relation has upon the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function, pressure, internal energy, entropy, and specific heat are calculated. It will be shown that the breakdown of Lorentz invariance can be interpreted as a repulsive interaction, among the photons. Additionally, it will be proved that the presence of a deformed dispersion relation entails an increase in the entropy of the system. In other words, as a consequence of the loss of the aforementioned symmetry the number of microstates available to the corresponding equilibrium state grows.     

Heat and mass transfer in a gas in a capillary induced by light with nonuniform intensity distribution over the beam cross section

An analysis is presented of the heat and drift fluxes induced by velocity-selective light absorption in a single-component gas in a capillary tube. The light intensity distribution across the beam is assumed to have a Gaussian profile. Kinetic equations are solved numerically to calculate flux profiles and kinetic coefficients quantifying the contributions of surface and collisional mechanisms to light-induced transfer as functions of the Knudsen number, the ratio of the rate of radiative decay of the exited level and intermolecular collision frequency, accommodation coefficient, and the ratio of the tube radius to the light beam radius.     

Thermodynamics of a general ideal gas under shear

The integrated form of the Gibbs-Duhem relation is obtained for a general ideal gas subjected to a shear flow.     

Instabilities in a liquid-fluidized bed of gas bubbles

Gas bubbles in an aqueous foam can be unjammed, or fluidized, by introducing a forced flow of the continuous liquid phase at a sufficiently high rate. We observe that the resulting bubble dynamics are spatially inhomogeneous, exhibiting a sequence of instabilities vs increasing flow rate. First irregular swirls appear, then a single convective roll, and finally a series of stratified convection rolls each with a different average bubble size.     

On the nonuniform electron-density distribution in a layer adsorbed on a metal

The probability of a transition from a uniform charge distribution (UCD) in the adsorbed layer to a nonuniform one (NCD) caused by the dipole-dipole adatom repulsion is analyzed within the Anderson-Newns Hamiltonian and a simple density-of-states model for the substrate. Two limiting cases are considered, namely, an infinitely wide and a narrow band of allowed substrate states. Criteria for the UCD→NCD transition are obtained. Experimental data on reconstruction of clean metal faces are analyzed. Fiz. Tverd. Tela (St. Petersburg) 41, 1543–1547 (September 1999)     

Kinetics of charged particles in a high-voltage gas discharge in a nonuniform electrostatic field

A high-voltage gas discharge is of interest as a possible means of generating directed flows of low-temperature plasma in the off-electrode space distinguished by its original features [1–4]. We propose a model for calculating the trajectories of charges particles in a high-voltage gas discharge in nitrogen at a pressure of 0.15 Torr existing in a nonuniform electrostatic field and the strength of this field. Based on the results of our calculations, we supplement and refine the extensive experimental data concerning the investigation of such a discharge published in [1, 2, 5–8]; good agreement between the theory and experiment has been achieved. The discharge burning is initiated and maintained through bulk electron-impact ionization and ion–electron emission. We have determined the sizes of the cathode surface regions responsible for these processes, including the sizes of the axial zone involved in the discharge generation. The main effect determining the kinetics of charged particles consists in a sharp decrease in the strength of the field under consideration outside the interelectrode space, which allows a free motion of charges with specific energies and trajectories to be generated in it. The simulation results confirm that complex electrode systems that allow directed plasma flows to be generated at a discharge current of hundreds or thousands of milliamperes and a voltage on the electrodes of 0.3–1 kV can be implemented in practice [3, 9, 10].     

Thermodynamics of a two-dimensional interacting Bose gas trapped in a quartic potential

We have studied the Bose-Einstein condensation (BEC) of an interacting Bose gas confined in a two-dimensional (2D) quartic potential by using a mean-field, semiclassical two-fluid model. A thermodynamic analysis including the chemical potential, condensate fraction, total energy, and specific heat has been carried out by considering different values of the interaction strength. Finally, we have found that the behaviour of the condensate fraction and specific heat of quartically trapped bosons differs from those of bosons trapped in a harmonic potential.     

Thermodynamics of a gas of deconfined bosonic spinons in two dimensions

We consider the quantum phase transition between a Néel antiferromagnet and a valence-bond solid (VBS) in a two-dimensional system of S = 1/2 spins. Assuming that the excitations of the critical ground state are linearly dispersing deconfined spinons obeying Bose statistics, we derive expressions for the specific heat C and the magnetic susceptibility χ at low temperature T in terms of a correlation length ξ(T). Comparing with quantum Monte Carlo results for the J-Q model, which is a candidate for a deconfined Néel-VBS transition, we obtain an almost perfect consistency between C, χ, and ξ. The corresponding expressions for magnon (triplet) excitations are not internally consistent, however, lending strong support for spinon excitations in the J-Q model.     

Energy loss of charged particles in nonuniform electron gas

On the basis of the quantum dielectric formalism energy loss formulas for fast charged particles in a nonuniform electron gas have been obtained. The theory shows that the effect of channeling on the energy loss of charged particles remains in force at relativistic velocities too.