Related papers: Diffusion in disordered systems under iterative me…
The quantum-Zeno and anti-Zeno effects (QZE/AZE) are known for a long time, in a quantum system with coupled levels, the measurement of a particular level population can lead to either acceleration (i.e. AZE) or retardation (i.e. QZE) of…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
For a one dimensional diffusion process $X=\{X(t) ; 0\leq t \leq T \}$, we suppose that $X(t)$ is hidden if it is below some fixed and known threshold $\tau$, but otherwise it is visible. This means a partially hidden diffusion process. The…
We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from…
A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only…
We report the results of calculation of diffusion coefficients for Lennard-Jones liquids, based on the idea of time-scale invariance of relaxation processes in liquids. The results were compared with the molecular dynamics data for…
We develop a new unified theoretical approach enabling us to non-perturbatively study the effect of electron-electron interactions on weak localization in arbitrary arrays of quantum dots. Our model embraces (i) weakly disordered conductors…
This work focuses on stability of regime-switching diffusions consisting of continuous and discrete components, in which the discrete component switches in a countably infinite set and its switching rates at current time depend on the…
Electron transport through disordered quasi one-dimensional quantum systems is studied. Decoherence is taken into account by a spatial distribution of virtual reservoirs, which represent local interactions of the conduction electrons with…
We combine the collisional picture for open system dynamics and the control of the rate of decoherence provided by the quantum (anti-)Zeno effect to illustrate the temporal unfolding of the redundant encoding of information into a…
Local diffusion coefficients in disordered materials such as living cells are highly heterogeneous. Quenched disorder is utilized substantially to study such complex systems, whereas its analytical treatment is difficult to handle. We…
Density dependent families of Markov chains, such as the stochastic models of mass-action chemical kinetics, converge for large values of the indexing parameter $N$ to deterministic systems of differential equations (Kurtz, 1970). Moreover…
We consider the effects of decoherence on Landau-Zener crossings encountered in a large-scale adiabatic-quantum-computing setup. We analyze the dependence of the success probability, i.e. the probability for the system to end up in its new…
We study the effect of quenched disorder on nonequilibrium systems of interacting particles, specifically, driven diffusive lattice gases with spatially disordered jump rates. The exact steady-state measure is found for a class of models…
Shr\"odinger equation for two-step spontaneous cascade transition in a three-level quantum system is solved by means of Markovian approximation for non-Markovian integro-differential evolution equations for amplitudes of states. It is shown…
We analyze a simple and feasible practical scheme displaying Zeno, anti-Zeno, and inverse-Zeno effects in the observation of wave-packet spreading caused by free evolution. The scheme is valid both in spatial diffraction of classical…
As a realization of the quantum Zeno effect, we consider electron tunneling between two quantum dots with one of the dots coupled to a quantum point contact detector. The coupling leads to decoherence and to the suppression of tunneling.…
We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifically, we look at limit cycles of stochastic differential equations (SDE) with Markovian switching, in which the process switches at random…