7,174 research outputs found
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 , 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
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