80 research outputs found
Random pure states: quantifying bipartite entanglement beyond the linear statistics
We analyze the properties of entangled random pure states of a quantum system
partitioned into two smaller subsystems of dimensions and . Framing the
problem in terms of random matrices with a fixed-trace constraint, we
establish, for arbitrary , a general relation between the -point
densities and the cross-moments of the eigenvalues of the reduced density
matrix, i.e. the so-called Schmidt eigenvalues, and the analogous functionals
of the eigenvalues of the Wishart-Laguerre ensemble of the random matrix
theory. This allows us to derive explicit expressions for two-level densities,
and also an exact expression for the variance of von Neumann entropy at finite
. Then we focus on the moments of the Schmidt number
, the reciprocal of the purity. This is a random variable supported on
, which quantifies the number of degrees of freedom effectively
contributing to the entanglement. We derive a wealth of analytical results for
for and and arbitrary , and also for
square systems by spotting for the latter a connection with the
probability that the smallest eigenvalue
of a matrix belonging to the Gaussian Unitary
Ensemble is larger than . As a byproduct, we present an exact
asymptotic expansion for for finite as
. Our results are corroborated by numerical simulations
whenever possible, with excellent agreement.Comment: 22 pages, 8 figures. Minor changes, typos fixed. Accepted for
publication in PR
Two-temperature Langevin dynamics in a parabolic potential
We study a planar two-temperature diffusion of a Brownian particle in a
parabolic potential. The diffusion process is defined in terms of two Langevin
equations with two different effective temperatures in the X and the Y
directions. In the stationary regime the system is described by a non-trivial
particle position distribution P(x,y), which we determine explicitly. We show
that this distribution corresponds to a non-equilibrium stationary state,
characterised by the presence of space-dependent particle currents which
exhibit a non-zero rotor. Theoretical results are confirmed by the numerical
simulations.Comment: 9 pages, 2 figure
Asymmetry relations and effective temperatures for biased Brownian gyrators
We focus on a paradigmatic two-dimensional model of a nanoscale heat engine,
- the so-called Brownian gyrator - whose stochastic dynamics is described by a
pair of coupled Langevin equations with different temperature noise terms. This
model is known to produce a curl-carrying non-equilibrium steady-state with
persistent angular rotations. We generalize the original model introducing
constant forces doing work on the gyrator, for which we derive exact asymmetry
relations, that are reminiscent of the standard fluctuation relations. Unlike
the latter, our relations concern instantaneous and not time averaged values of
the observables of interest. We investigate the full two-dimensional dynamics
as well as the dynamics projected on the - and -axes, so that information
about the state of the system can be obtained from just a part of its degrees
of freedom. Such a state is characterized by effective "temperatures" that can
be measured in nanoscale devices, but do not have a thermodynamic nature.
Remarkably, the effective temperatures appearing in full dynamics are
distinctly different from the ones emerging in its projections, confirming that
they are not thermodynamic quantities, although they precisely characterize the
state of the system.Comment: 6 pages, 1 figur
Phase behaviour and structure of a superionic liquid in nonpolarized nanoconfinement
The ion-ion interactions become exponentially screened for ions confined in
ultranarrow metallic pores. To study the phase behaviour of an assembly of such
ions, called a superionic liquid, we develop a statistical theory formulated on
bipartite lattices, which allows an analytical solution within the
Bethe-lattice approach. Our solution predicts the existence of ordered and
disordered phases in which ions form a crystal-like structure and a homogeneous
mixture, respectively. The transition between these two phases can potentially
be first or second order, depending on the ion diameter, degree of confinement
and pore ionophobicity. We supplement our analytical results by
three-dimensional off-lattice Monte Carlo simulations of an ionic liquid in
slit nanopores. The simulations predict formation of ionic clusters and ordered
snake-like patterns, leading to characteristic close-standing peaks in the
cation-cation and anion-anion radial distribution functions
Polymer translocation across a corrugated channel: Fick-Jacobs approximation extended beyond the mean first passage time
Polymer translocation across a corrugated channel is a paradigmatic
stochastic process encountered in diverse systems.
The instance of time when a polymer first arrives to some prescribed location
defines an important characteristic time scale for various phenomena, which are
triggered or controlled by such an event.
Here we discuss the translocation dynamics of a Gaussian polymer in a
periodically-corrugated channel using an appropriately generalized Fick-Jacobs
approach.
Our main aim is to probe an effective broadness of the first passage time
distribution (FPTD), by determining the so-called coefficient of variation
of the FPTD, defined as the ratio of the standard deviation versus the
mean first passage time (MFPT).
We present a systematic analysis of as a function of a variety of
system's parameters. We show that never significantly drops below 1
and, in fact, can attain very large values, implying that the MFPT alone cannot
characterize the first-passage statistics of the translocation process
exhaustively well
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