Kinetic equation for liquids with a multistep potential of interaction. H-theorem

1996 ◽  
Vol 234 (1-2) ◽  
pp. 89-107 ◽  
Author(s):  
I.P. Omelyan ◽  
M.V. Tokarchuk
Keyword(s):  
Kinetic Equation ◽  
H Theorem

KINETIC EQUATION FOR A HOMOGENEOUS PLASMA IN A UNIFORM MAGNETIC FIELD

1964 ◽  
Vol 42 (10) ◽  
pp. 1969-2021 ◽  
Author(s):  
M. J. Haggerty ◽  
L. G. De Sobrino
Keyword(s):  
Magnetic Field ◽  
Kinetic Equation ◽  
Uniform Magnetic Field ◽  
Single Species ◽  
Field Approximation ◽  
Stationary Solutions ◽  
Equilibrium Distributions ◽  
H Theorem ◽  
The One ◽  
Static Uniform Magnetic Field

The theory of Prigogine and Balescu has been applied to a homogeneous single-species plasma in a static uniform magnetic field. A kinetic equation has been obtained for the one-particle velocity distribution, which is assumed initially isotropic in directions perpendicular to the field. The only stationary solutions of the kinetic equation are the Maxwellian equilibrium distributions, and an H theorem has been established. The neglect of "collisions" of the order of duration of one cyclotron period or less (a strong magnetic-field approximation) modifies the kinetic equation so that it no longer predicts any relaxation of the velocity components parallel to the magnetic field. The assumptions and approximations of the theory are stated, and are discussed in some detail.

MODEL KINETIC EQUATION FOR THE DISTRIBUTION OF DISCRETIZED INTERNAL ENERGY

1994 ◽  
Vol 04 (05) ◽  
pp. 669-675 ◽  
Author(s):  
K. NANBU
Keyword(s):  
Kinetic Equation ◽  
Kinetic Theory ◽  
Internal Energy ◽  
Boltzmann Distribution ◽  
Model Kinetic Equation ◽  
Discrete Velocity ◽  
Second Moment ◽  
Exponential Relaxation ◽  
H Theorem

Kinetic equation for discretized internal energy is obtained by using the idea underlying the discrete-velocity kinetic theory. The equation satisfies the Boltzmann H-theorem. The solution of this equation in equilibrium is the Boltzmann distribution. The second moment of distribution shows an exponential relaxation.

Nonequilibrium Quantum Hydrodynamics

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Density Matrix ◽  
Landau Theory ◽  
Reduced Density Matrix ◽  
Quantum Hydrodynamics ◽  
Balance Equations ◽  
Consistent Theory ◽  
H Theorem ◽  
Quasiparticle Energy ◽  
Reduced Density

The balance equations resulting from the nonlocal kinetic equation are derived. They show besides the Landau-like quasiparticle contributions explicit two-particle correlated parts which can be interpreted as molecular contributions. It looks like as if two particles form a short-living molecule. All observables like density, momentum and energy are found as a conserving system of balance equations where the correlated parts are in agreement with the forms obtained when calculating the reduced density matrix with the extended quasiparticle functional. Therefore the nonlocal kinetic equation for the quasiparticle distribution forms a consistent theory. The entropy is shown to consist also of a quasiparticle part and a correlated part. The explicit entropy gain is proved to complete the H-theorem even for nonlocal collision events. The limit of Landau theory is explored when neglecting the delay time. The rearrangement energy is found to mediate between the spectral quasiparticle energy and the Landau variational quasiparticle energy.

ON THE KINETIC THEORY OF A VAN DER WAALS GAS

1967 ◽  
Vol 45 (2) ◽  
pp. 363-385 ◽  
Author(s):  
Luis de Sobrino
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Van Der Waals ◽  
Equilibrium Solutions ◽  
Van Der Waals Gas ◽  
Stable States ◽  
Van Der Waals Equation ◽  
H Theorem ◽  
Two Phases ◽  
Velocity Moments

A kinetic equation is proposed that leads, in equilibrium, to the Van der Waals equation of state. It is shown that this kinetic equation obeys an H theorem, and that its equilibrium solutions are, in the condensation region, of two types, (i) inhomogeneous equilibrium solutions which are absolutely stable and correspond to the two phases in equilibrium, (ii) homogeneous equilibrium solutions which are not absolutely stable but are, if the compressibility is positive, stable against small dynamical (i.e. nonquasi-static) perturbations, and correspond to the metastable states of the system. As a result, it is seen that a linear theory cannot explain the transition from the metastable to the stable states. A system of simplified nonlinear equations for the first three velocity moments of the distribution function is obtained in the hope that its study will contribute to the understanding of the mentioned transition.

BOLTZMANN-LIKE MODELLING OF A SUSPENSION

2002 ◽  
Vol 12 (07) ◽  
pp. 943-964 ◽  
Author(s):  
C. CROIZET ◽  
R. GATIGNOL
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Equation ◽  
Kinetic Model ◽  
Boundary Conditions ◽  
Hard Spheres ◽  
Inelastic Collisions ◽  
Dispersed Phase ◽  
Conservation Of Mass ◽  
The Boltzmann Equation ◽  
H Theorem

This paper deals with the presentation of a kinetic model for a suspension of identical hard spheres. Considering that the collisions between particles are instantaneous, binary, inelastic and taking the diameter of the spheres into account, a Boltzmann equation for the dispersed phase is proposed. It allows one to obtain the conservation of mass and momentum as well as, for slightly inelastic collisions, an H-theorem which conveys the irreversibility of the evolution. The problem of the boundary conditions for the Boltzmann equation is then introduced. From an anisotropic law of rebound characterizing the inelastic and non-punctual impact of a particle to the wall, a parietal behavior for the first moments of the kinetic equation is deduced.

Deep Impurities with Collision Delay

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Wave Function ◽  
Kinetic Equation ◽  
Elastic Scattering ◽  
Response Function ◽  
Plasma Oscillation ◽  
Impurity Scattering ◽  
Fermi Momentum ◽  
Screening Length ◽  
Plasma Mode ◽  
Dissipative Mechanism

The linearised nonlocal kinetic equation is solved analytically for impurity scattering. The resulting response function provides the conductivity, plasma oscillation and Fermi momentum. It is found that virial corrections nearly compensate the wave-function renormalizations rendering the conductivity and plasma mode unchanged. Due to the appearance of the correlated density, the Luttinger theorem does not hold and the screening length is influenced. Explicit results are given for a typical semiconductor. Elastic scattering of electrons by impurities is the simplest but still very interesting dissipative mechanism in semiconductors. Its simplicity follows from the absence of the impurity dynamics, so that individual collisions are described by the motion of an electron in a fixed potential.

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