On the Poisson equation and diffusion approximation 3

We study the Poisson equation Lu+f=0 in R^d, where L is the infinitesimal generator of a diffusion process. In this paper, we allow the second-order part of the generator L to be degenerate, provided a local condition of Doeblin type is satisfied, so that, if we also assume a condition on the drift which implies recurrence, the diffusion process is ergodic. The equation is understood in a weak sense. Our results are then applied to diffusion approximation.Comment: Published at http://dx.doi.org/10.1214/009117905000000062 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Sub-exponential mixing rate for a class of Markov chains

We establish sub-exponential bounds for the β-mixing rate and for the rate of convergence to invariant measures for discrete time Markov processes under recurrence type conditions weaker than used for exponential inequalities and stronger than for polynomial ones

On improved convergence conditions and bounds for Markov chains

Improved rates of convergence for ergodic Markov chains and relaxed conditions for them, as well as analogous convergence results for non-homogeneous Markov chains are studied. The setting from the previous works is extended. Examples are provided where the new bounds are better and where they give the same convergence rate as in the classical Markov -- Dobrushin inequality.Comment: 33 pages, 27 reference

The Divine Clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state

We consider the Bohr correspondence limit of the Schrodinger wave function for an atomic elliptic state. We analyse this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Kelperian orbit for eccentricities greater than 1/\sqrt{2} which do not occur classically.Comment: 42 pages, 18 figures, with typos corrected, updated abstract and updated section 6.

Centers of crystallization in antimony thin films studied by transnission electron microscopy

We performed TEM studies of 7 crystallization centers using specially evaporated Sb thin films in finite areas. Strong internal lattice bending is revealed by use of the bend contour method.Partial support of project 3.6121.2017/8.9 (RF Ministry of Education and Science) and agreement № 02.A03.21.0006 (Act 211 Government of the RF) is acknowledged

Transitions between "π\pi" and "0" states in superconductor -- ferromagnet -- superconductor junctions

Experimental and theoretical study of superconductor (S) -- ferromagnet (F) -- superconductor junctions showed that in certain range of parameters (e.g., the length of the ferromagnet $d_F$, the exchange field, $E_{\rm ex}$) the ground state of a SFS junction corresponds to superconducting phase difference $\pi$ or 0. The phase diagram of a SFS junction with the respect to $\pi$ and 0 states is investigated in this letter in $E_{\rm ex}, d_{F}, T$ space. It is shown that the phase diagram is very sensitive to the geometry of the system, in particular, to the amount of disorder.Comment: Minor changes. References adde