33,032 research outputs found
Corrections to the Law of Mass Action and Properties of the Asymptotic State for Reversible Diffusion-Limited Reactions
On example of diffusion-limited reversible
reactions we re-examine two fundamental concepts of classical chemical kinetics
- the notion of "Chemical Equilibrium" and the "Law of Mass Action". We
consider a general model with distance-dependent reaction rates, such that any
pair of particles, performing standard random walks on sites of a
-dimensional lattice and being at a distance apart of each other at
time moment , may associate forming a particle at the rate .
In turn, any randomly moving particle may spontaneously dissociate at the
rate into a geminate pair of s "born" at a distance
apart of each other. Within a formally exact approach based on Gardiner's
Poisson representation method we show that the asymptotic state
attained by such diffusion-limited reactions is generally \textit{not a true
thermodynamic equilibrium}, but rather a non-equilibrium steady-state, and that
the Law of Mass Action is invalid. The classical concepts hold \text{only} in
case when the ratio does not depend on for any .Comment: 30 pages, 2 figure
About Fokker-Planck equation with measurable coefficients and applications to the fast diffusion equation
The object of this paper is the uniqueness for a -dimensional
Fokker-Planck type equation with non-homogeneous (possibly degenerated)
measurable not necessarily bounded coefficients. We provide an application to
the probabilistic representation of the so called Barenblatt solution of the
fast diffusion equation which is the partial differential equation with . Together with the mentioned
Fokker-Planck equation, we make use of small time density estimates uniformly
with respect to the initial conditio
Gap Fluctuations in Inhomogeneous Superconductors
Spatial fluctuations of the effective pairing interaction between electrons
in a superconductor induce variations of the order parameter which in turn lead
to significant changes in the density of states. In addition to an overall
reduction of the quasi-particle energy gap, theory suggests that mesoscopic
fluctuations of the impurity potential induce localised tail states below the
mean-field gap edge. Using a field theoretic approach, we elucidate the nature
of the states in the `sub-gap' region. Specifically, we show that these states
are associated with replica symmetry broken instanton solutions of the
mean-field equations.Comment: 11 pages, 3 figures included. To be published in PRB (Sept. 2001
Stability of the Travelling Front of a Decaying Brane
The dynamics (in light-cone time) of the tachyon on an unstable brane in the
background of a dilaton linear along a null coordinate is a non-local
reaction-diffusion type equation, which admits a travelling front solution. We
analyze the (in-)stability of this solution using linearized perturbation
theory. We find that the front solution obtained in singular perturbation
method is stable. However, these inhomogenous solutions (unlike the homogenous
solution) also have Lyapunov exponents corresponding to unstable modes around
the (meta-)stable vacuum.Comment: 1+15 pages, 4 figure
Quantum state-dependent diffusion and multiplicative noise: a microscopic approach
The state-dependent diffusion, which concerns the Brownian motion of a
particle in inhomogeneous media has been described phenomenologically in a
number of ways. Based on a system-reservoir nonlinear coupling model we present
a microscopic approach to quantum state-dependent diffusion and multiplicative
noise in terms of a quantum Markovian Langevin description and an associated
Fokker-Planck equation in position space in the overdamped limit. We examine
the thermodynamic consistency and explore the possibility of observing a
quantum current, a generic quantum effect, as a consequence of this
state-dependent diffusion similar to one proposed by B\"{u}ttiker [Z. Phys. B
{\bf 68}, 161 (1987)] in a classical context several years ago.Comment: To be published in Journal of Statistical Physics 28 pages, 3 figure
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