6,620 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
Continuous-time random walk theory of superslow diffusion
Superslow diffusion, i.e., the long-time diffusion of particles whose
mean-square displacement (variance) grows slower than any power of time, is
studied in the framework of the decoupled continuous-time random walk model. We
show that this behavior of the variance occurs when the complementary
cumulative distribution function of waiting times is asymptotically described
by a slowly varying function. In this case, we derive a general representation
of the laws of superslow diffusion for both biased and unbiased versions of the
model and, to illustrate the obtained results, consider two particular classes
of waiting-time distributions.Comment: 4 page
Signatures of many-body localization in steady states of open quantum systems
Many-body localization (MBL) is a result of the balance between
interference-based Anderson localization and many-body interactions in an
ultra-high dimensional Fock space. It is usually expected that dissipation is
blurring interference and destroying that balance so that the asymptotic state
of a system with an MBL Hamiltonian does not bear localization signatures. We
demonstrate, within the framework of the Lindblad formalism, that the system
can be brought into a steady state with non-vanishing MBL signatures. We use a
set of dissipative operators acting on pairs of connected sites (or spins), and
show that the difference between ergodic and MBL Hamiltonians is encoded in the
imbalance, entanglement entropy, and level spacing characteristics of the
density operator. An MBL system which is exposed to the combined impact of
local dephasing and pairwise dissipation evinces localization signatures
hitherto absent in the dephasing-outshaped steady state.Comment: 6 pages, 3 figure
Limiting distributions of continuous-time random walks with superheavy-tailed waiting times
We study the long-time behavior of the scaled walker (particle) position
associated with decoupled continuous-time random walk which is characterized by
superheavy-tailed distribution of waiting times and asymmetric heavy-tailed
distribution of jump lengths. Both the scaling function and the corresponding
limiting probability density are determined for all admissible values of tail
indexes describing the jump distribution. To analytically investigate the
limiting density function, we derive a number of different representations of
this function and, by this way, establish its main properties. We also develop
an efficient numerical method for computing the limiting probability density
and compare our analytical and numerical results.Comment: 35 pages, 4 figure
Photon waiting time distributions: a keyhole into dissipative quantum chaos
Open quantum systems can exhibit complex states, which classification and
quantification is still not well resolved. The Kerr-nonlinear cavity,
periodically modulated in time by coherent pumping of the intra-cavity photonic
mode, is one of the examples. Unraveling the corresponding Markovian master
equation into an ensemble of quantum trajectories and employing the recently
proposed calculation of quantum Lyapunov exponents [I.I. Yusipov {\it et al.},
Chaos {\bf 29}, 063130 (2019)], we identify `chaotic' and `regular' regimes
there. In particular, we show that chaotic regimes manifest an intermediate
power-law asymptotics in the distribution of photon waiting times. This
distribution can be retrieved by monitoring photon emission with a
single-photon detector, so that chaotic and regular states can be discriminated
without disturbing the intra-cavity dynamics.Comment: 7 pages, 5 figure
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