Stochastically perturbed flows: Delayed and interrupted evolution

We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed evolution, in which the flow alternates with a quiescent state in which the variate remains frozen at its current value for random intervals of time; and interrupted evolution, in which the variate is also re-set in the quiescent state to a random value drawn from a fixed distribution. In the former case, the effect of the delay upon the first passage time statistics is analyzed. In the latter case, the conditions under which an extended stationary distribution can exist as a consequence of the competition between an attractor in the flow and the random re-setting are examined. We elucidate the role of the normalization condition in eliminating the singularities arising from the unstable critical points of the flow, and present a number of representative examples. A simple formula is obtained for the stationary distribution and interpreted physically. A similar interpretation is also given for the known formula for the stationary distribution in a full-fledged dichotomous flow.Comment: 27 pages; no figures. Submitted to Stochastics and Dynamic

Analytic calculation of energy transfer and heat flux in a one-dimensional system

In the context of the problem of heat conduction in one-dimensional systems, we present an analytical calculation of the instantaneous energy transfer across a tagged particle in a one-dimensional gas of equal-mass, hard-point particles. From this, we obtain a formula for the steady-state energy flux, and identify and separate the mechanical work and heat conduction contributions to it. The nature of the Fourier law for the model, and the nonlinear dependence of the rate of mechanical work on the stationary drift velocity of the tagged particle, are analyzed and elucidated.Comment: 17 pages including title pag

Wave packet dynamics of the matter wave field of a Bose-Einstein condensate

We show in the framework of a tractable model that revivals and fractional revivals of wave packets afford clear signatures of the extent of departure from coherence and from Poisson statistics of the matter wave field in a Bose-Einstein condensate, or of a suitably chosen initial state of the radiation field propagating in a Kerr-like medium.Comment: 10 pages, 4 figures, RevTeX

Rate coefficients for rovibrational transitions in H_2 due to collisions with He

We present quantum mechanical and quasiclassical trajectory calculations of cross sections for rovibrational transitions in ortho- and para-H_2 induced by collisions with He atoms. Cross sections were obtained for kinetic energies between 10^-4 and 3 eV, and the corresponding rate coefficients were calculated for the temperature range 100<T<4000 K. Comparisons are made with previous calculations.Comment: 21 pages, 2 figures, AAS, eps