Search

In this paper we consider a chemical process, for which the reagent of interest decays shortly after it is created. For such a system the standard theory of nonequilibrium spatial correlations in the density fluctuations, which leads to Ornstein–Zernike type of expression, does not work. We compare results of molecular simulations with another theoretical description based on the assumption that the lifetime of the reagent is short enough to treat its motion as a ballistic rather than diffusive one.

Thermal conduction in a chain of colliding harmonic oscillators, sometimes called the ding-dong model, is investigated. We first argue that this system is equivalent to the Dawson plasma sheet model. Next we show the Lyapunov analysis for this system to characterize its dynamical property. Finally, we reconsider the numerical study of thermal conduction for this system using the Green-Kubo relation and the direct simulation of Fourier law. Both show that thermal conduction is normal in that kappa(N,T) approximately equals N(0), at least, at low temperature in a large system.

We derive the path integral representation of the conditional probability for a Markovian process starting from the master equation. Existing derivations require both the variable and the transition probability to be extensive. We show that this requirement may be relaxed if Langer's formula for the transition probability is used. We prove that different path integral representations appearing in the literature are in fact equivalent and correspond to various choices of an arbitrary parameter.

We present a model hamiltonian for quantum light-particle diffusion in a lattice which differs from that of previous investigations by the addition of a phonon coupling to the hopping term. In one dimension we derive a set of master equations which is valid in the high-temperature regime and calculate the diffusion coefficient.

A general method to calculate explicitly the stationary probability of nonlinear systems subjected to a special case of coloured noise is presented. For a simple model system the “phase diagram” for the various noise-induced transitions is determined.

The spin depolarization of a spin-carrying particle which can tunnel between two sites is investigated. The sites have different Zeeman energies and dynamical fluctuations are included in the frame of the Haken-Strobl model. Different behavior of the polarization decay is found depending on the strength of the site-diagonal and offdiagonal fluctuations. Also the ensemble average over distributions of the Zeeman energies is studied.

We present a stochastic theory of the kinetics of phase transitions in univariant, nonuniform systems. We assume a master equation and a relation of the transition probability to the free energy [J. S. Langer, Ann. Phys. (N.Y) 65, 53 (1971)]. The free energy is taken to be of the Cahn–Hilliard form. By means of path integral methods we obtain a formal solution from which we derive a deterministic differential equation for the most probable variation of the density distribution in time. This equation is of the Landau–Ginzburg type. We show the existence of a Liapunoff function for this kinetic equation, which is then used to derive simply the classical result of nucleation theory for the critical radius of a droplet. Next we show from the kinetic equation that if the structure of the free energy is such that a phase transition occurs and metastable states are possible, then the kinetics of the decay to the stable and metastable states is nonlinear, of the cubic type. Finally we derive from the kinetic equa...

The formulation of nonequilibrium thermodynamics with convective flow under the influence of external potential field is made from the two view points of Lagrangian and Eulerian. Specifying two meanings of the local equilibrium assumption, we define two sets of the thermodynamic forces and fluxes, and derive two evolulion criteria in each picture.

A dynamical theory of an adsorbed atom on solid surfaces is developed starting from a Hamiltonian which includes: (1) motion of the adsorbed atom parallel to the surface; (2) the vibration of the adsorbed atom perpendicular to the surface; (3) the lattice vibrations (phonons) of the solid; (4) the coupling between the vibration of the adsorbed atom and its parallel motion; (5) the coupling between the lattice vibrations and the parallel motion of the adsorbed atom; (6) the concerted interaction among the phonons, the vibration, and the parallel motion. Using a canonical transformation, we describe the motion of the adsorbed atom as one of a pseudomolecule formed from the adsorbed atom and the distorted lattice. An equation for the probability of finding the adsorbed atom at a lattice site is derived and the mean square displacement of the motion of the adsorbed atom is calculated. At low temperature, the migration of the adsorbed atom is coherent and the mean square displacement is proportional to the squ...

Assuming that a macrovariable follows a Markovian process, the extensive property of its probability distribution is proved to propagate. This is a generalization of the Gaussian properties of the equilibrium distribution to nonequilibrium nonstationary processes. It is basically a WKB-like asymptotic evaluation in the inverse of the size of the macrosystem. Evolution of the variable along the most probable path and fluctuation properties around the path are considered from a general point of view with an emphasis on the relation of nonlinearity of evolution and the associated fluctuation. Anomalous behavior of the fluctuation is discussed in connection with unstable, critical, or marginal states. A general treatment is given for the asymptotic properties of relaxation eigenmodes.

By using the formula for the steady state probability distribution of fluctuations in a non-linear system under the influence of two-level Markovian noise, the existence of phase transitions of such a system with the variation of intensity and correlation time of the noise is shown. Explicit results for the Verhulst model and a model for population genetics are given and compared with the previous results for the white noise case., info:eu-repo/semantics/published