21 research outputs found
Approach to a stationary state in an external field
International audienceWe study relaxation towards a stationary out of equilibrium state by analizing a one-dimensional stochastic process followed by a particle accelerated by an external field and propagating through a thermal bath. The effect of collisions is described within Botlzmann's kinetic theory. We present analytical solutions for the Maxwell gas and for the very hard particle model. The exponentially fast relaxation of the velocity distribution toward the stationary form is demonstrated. In the reference frame moving with constant drift velocity the hydrodynamic diffusive mode is shown to govern the distribution in the position space. We show that the exact value of the diffusion coefficient for any value of the field is correctly predicted by Green-Kubo autocorrelation formula generalized to the stationary state
Front localization in a ballistic annihilation model
We study the possibility of localization of the front present in a
one-dimensional ballistically-controlled annihilation model in which the two
annihilating species are initially spatially separated. We construct two
different classes of initial conditions, for which the front remains localized.Comment: Using elsart (Elsevier Latex macro) and epsf. 12 Pages, 2 epsf
figures. Submitted to Physica
Kinetic models of ion transport through a nanopore
Kinetic equations for the stationary state distribution function of ions
moving through narrow pores are solved for a number of one-dimensional models
of single ion transport. Ions move through pores of length , under the
action of a constant external field and of a concentration gradient. The
interaction of single ions with the confining pore surface and with water
molecules inside the pore are modelled by a Fokker-Planck term in the kinetic
equation, or by uncorrelated collisions with thermalizing centres distributed
along the pore. The temporary binding of ions to polar residues lining the pore
is modelled by stopping traps or energy barriers. Analytic expressions for the
stationary ion current through the pore are derived for several versions of the
model, as functions of key physical parameters. In all cases, saturation of the
current at high fields is predicted. Such simple models, for which results are
analytic, may prove useful in the study of the current/voltage relations of ion
channels through membranes
Self-consistent equation for an interacting Bose gas
We consider interacting Bose gas in thermal equilibrium assuming a positive
and bounded pair potential such that 0<\int d\br V(r) = a<\infty.
Expressing the partition function by the Feynman-Kac functional integral yields
a classical-like polymer representation of the quantum gas. With Mayer graph
summation techniques, we demonstrate the existence of a self-consistent
relation between the density and the
chemical potential , valid in the range of convergence of Mayer series.
The function is equal to the sum of all rooted multiply connected graphs.
Using Kac's scaling V_{\gamma}(\br)=\gamma^{3}V(\gamma r) we prove that in
the mean-field limit only tree diagrams contribute and function
reduces to the free gas density.
We also investigate how to extend the validity of the self-consistent
relation beyond the convergence radius of Mayer series (vicinity of
Bose-Einstein condensation) and study dominant corrections to mean field. At
lowest order, the form of function is shown to depend on single polymer
partition function for which we derive lower and upper bounds and on the
resummation of ring diagrams which can be analytically performed.Comment: 33 pages, 6 figures, submitted to Phys.Rev.
The linearized kinetic equation for a classical gas
The linearized kinetic equation satisfied by the one-particle velocity distribution function of a classical gas is derived. The explicit dependence of the corresponding generalized Boltzmann operator on the equilibrium correlations is displayed. © 1972.SCOPUS: ar.jinfo:eu-repo/semantics/publishe