Domain statistics in a finite Ising chain

We present a comprehensive study for the statistical properties of random variables that describe the domain structure of a finite Ising chain with nearest-neighbor exchange interactions and free boundary conditions. By use of extensive combinatorics we succeed in obtaining the one-variable probability functions for (i) the number of domain walls, (ii) the number of up domains, and (iii) the number of spins in an up domain. The corresponding averages and variances of these probability distributions are calculated and the limiting case of an infinite chain is considered. Analyzing the averages and the transition time between differing chain states at low temperatures, we also introduce a criterion of the ferromagnetic-like behavior of a finite Ising chain. The results can be used to characterize magnetism in monatomic metal wires and atomic-scale memory devices.Comment: 19 page

Space-time velocity correlation function for random walks

Space-time correlation functions constitute a useful instrument from the research toolkit of continuous-media and many-body physics. We adopt here this concept for single-particle random walks and demonstrate that the corresponding space-time velocity auto-correlation functions reveal correlations which extend in time much longer than estimated with the commonly employed temporal correlation functions. A generic feature of considered random-walk processes is an effect of velocity echo identified by the existence of time-dependent regions where most of the walkers are moving in the direction opposite to their initial motion. We discuss the relevance of the space-time velocity correlation functions for the experimental studies of cold atom dynamics in an optical potential and charge transport on micro- and nano-scales.Comment: Phys. Rev. Lett., in pres

From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems

The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy walk description, which was so far invoked to explain anomalous heat conductivity in the context of non-interacting particles is here shown to extend to the general case of truly many-body systems. Our approach does not only provide a firm evidence that energy diffusion is anomalous in the HPG, but proves definitely superior to direct methods for estimating the divergence rate of heat conductivity which turns out to be $0.333\pm 0.004$, in perfect agreement with the dynamical renormalization--group prediction (1/3).Comment: 4 pages, 3 figure

Levy walks with velocity fluctuations

The standard Levy walk is performed by a particle that moves ballistically between randomly occurring collisions, when the intercollision time is a random variable governed by a power-law distribution. During instantaneous collision events the particle randomly changes the direction of motion but maintains the same constant speed. We generalize the standard model to incorporate velocity fluctuations into the process. Two types of models are considered, namely, (i) with a walker changing the direction and absolute value of its velocity during collisions only, and (ii) with a walker whose velocity continuously fluctuates. We present full analytic evaluation of both models and emphasize the importance of initial conditions. We show that the type of the underlying Levy walk process can be identified by looking at the ballistic regions of the diffusion profiles. Our analytical results are corroborated by numerical simulations

ac-driven atomic quantum motor

We invent an ac-driven quantum motor consisting of two different, interacting ultracold atoms placed into a ring-shaped optical lattice and submerged in a pulsating magnetic field. While the first atom carries a current, the second one serves as a quantum starter. For fixed zero-momentum initial conditions the asymptotic carrier velocity converges to a unique non-zero value. We also demonstrate that this quantum motor performs work against a constant load.Comment: 4 pages, 4 figure

ac-driven Brownian motors: a Fokker-Planck treatment

We consider a primary model of ac-driven Brownian motors, i.e., a classical particle placed in a spatial-time periodic potential and coupled to a heat bath. The effects of fluctuations and dissipations are studied by a time-dependent Fokker-Planck equation. The approach allows us to map the original stochastic problem onto a system of ordinary linear algebraic equations. The solution of the system provides complete information about ratchet transport, avoiding such disadvantages of direct stochastic calculations as long transients and large statistical fluctuations. The Fokker-Planck approach to dynamical ratchets is instructive and opens the space for further generalizations