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.     

Thermodynamics of relativistic rotating perfect fluids

A new formulation of thermodynamics for special and general relativistic rotating perfect fluids is developed. Both isolated systems and portions of isolated systems electrically uncharged or charged are treated. Exploiting the symmetry of motion of stationary axisymmetric fluids, the global thermodynamic functions, including total energy and spin, are defined as free scalars, represented by hypersurface integrals of conserved vectors. Local equilibrium parameters such as local temperature and chemical potential are scalar functions. There also exist global equilibrium parameters, global temperature and global chemical potential, which are free scalars. The connection between local and global conditions of thermodynamic equilibrium is made clear and explicit. Thermodynamic potentials are introduced in the context of treating open systems in a relativistically invariant way.     

Magnetism of a relativistic Fermi gas

The parametric dependence of the magnetic susceptibility of an extremely degenerate relativistic gas of charged fermions on the induction of the quantizing magnetic field and particle density is obtained taking into account the anomalous static magnetic moments of the particles. The case of the quantum limit of ultrastrong magnetic fields is examined.A. S. Pushkin Brest State Pedagogical Institute. Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 1, pp. 37–38, January, 1994.     

Boundary crisis and transient in a dissipative relativistic standard map

Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent −1 is observed.     

Distribution of a nonstationary electron beam in a dense gas

The problem of the temporal and spatial dependences of the parameters of the action of a modulated fast-electron beam on a dense gas is posed on the basis of the transport equation. The problem is simplified by making it nondimensional and by transforming to the Fokker-Planck approximation. A Green's function formalism is developed for this problem and is used to express the solution of the general nonstationary problem in the form of a convolution of a nonstationary boundary flow with a stationary Green's function. The use of the derived equation is illustrated using as an example the solution of a problem with the simplest stationary Green's function corresponding to the straight-ahead approximation. This approximation is used to consider a general relativistic case with model scattering cross sections. The methods and results of a numerical computer solution of the nonstationary problem of electron retardation in the upper layer of the atmosphere are surveyed.Translated from Trudy Ordena Lenina Fizicheskogo Instituta im. P. N. Lebedeva AN SSSR, Vol. 145, pp. 172–188, 1984.     

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.     

Dispersion of gravitational waves in a relativistic gas

The propagation of gravitational waves in a relativistic gas which is in a static gravitational field in the unperturbed state is considered. The group velocity of the transverse gravitational waves and the decrements of collisional and collisionless damping are calculated.     

Diffusion coefficients of a relativistic Lorentz gas

With the help of two different methods the diffusion coefficient is calculated for a relativistic Lorentz gas of hard spheres. Numerical results are given for a range of temperatures.     

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.     

Chapman-Enskog method for a relativistic ionized gas

A linearized transport equation is derived for a multicomponent ionized gas. The magnetic field is treated as a zeroth-order, the electric field as a first-order effect.     

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.     

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.     

Diffusion and thermal diffusion coefficients of a relativistic gas mixture

Values up to order c^-2 are given for the diffusion and thermal diffusion coefficients of binary relativistic gas mixtures of hard spheres and Israel particles.     

Thermodynamics of a gas-coal massif and a nonuniform gas distribution in a coal bed

The thermodynamic potential of a coal bed is calculated, and the gas pressure in the crack-pore system of the bed is shown to be nonuniformly distributed. This pressure is high in “weak“ regions in the bed, i.e., at the sites of a high porosity, low elastic moduli, and low solubility, as well as at high bearing pressure sites. All these phenomena are caused by the elastic interaction of a gas with a solid-state coal frame and the possibility of the formation of a solid solution in the coal. The relative increase in the gas pressure at these sites is estimated. The results obtained can be used to predict the localization of explosive and outburst regions in coal beds.     

Self-defocusing/focusing of a relativistic laser pulse in a multiple-ionizing gas

A fast rising flattop high power laser pulse, with Gaussian intensity distribution along its wavefront, causes single and double ionizations of the gas through which it propagates. The foot of the pulse causes single ionization of the gas and creates a sharp radial density profile resulting in strong defocusing of the front part of the pulse. After a little while, single state ionization saturates, creating a flat density profile in the axial region and weakening the divergence of the pulse. As the intensity of the pulse rises further, second state ionization occurs, causing strong defocusing of the beam. Later in time when the second state ionization saturates, the relativistic mass nonlinearity together with the electron cavitation tends to focus the pulse.     

Equilibrium distribution function of a relativistic dilute perfect gas

An alternative to the Jüttner distribution has been recently proposed by several authors. The literature on the topic is reviewed critically. It is found that the Jüttner distribution is correct and that the alternative distribution contradicts quantum field theory, statistical physics and continuum mechanics.     

Magnetism of a relativistic degenerate electron gas in a strong magnetic field

The magnetization and magnetic susceptibility of a degenerate electron gas in a strong magnetic field in which electrons are located on the ground Landau level and the electron gas has the properties of a nonlinear paramagnet have been calculated. The paradoxical properties of the electron gas under these conditions??a decrease in the magnetization with the field and an increase in the magnetization with the temperature??have been revealed. It has been shown that matter under the corresponding conditions of neutron stars is a paramagnet with a magnetic susceptibility of ?? ?? 0.001.