531 research outputs found
Coulomb blockade and transport in a chain of one-dimensional quantum dots
A long one-dimensional wire with a finite density of strong random impurities
is modelled as a chain of weakly coupled quantum dots. At low temperature T and
applied voltage V its resistance is limited by "breaks": randomly occuring
clusters of quantum dots with a special length distribution pattern that
inhibits the transport. Due to the interplay of interaction and disorder
effects the resistance can exhibit T and V dependences that can be approximated
by power laws. The corresponding two exponents differ greatly from each other
and depend not only on the intrinsic electronic parameters but also on the
impurity distribution statistics.Comment: 4 pages, 1 figure. Changes from v2: Dropped discussion of the
high-field regime. Added discussion of mesoscopic fluctuations and multiple
channels in the quasi-1D case. Improved presentation styl
Theory of Systematic Computational Error in Free Energy Differences
Systematic inaccuracy is inherent in any computational estimate of a
non-linear average, due to the availability of only a finite number of data
values, N. Free energy differences (DF) between two states or systems are
critically important examples of such averages in physical, chemical and
biological settings. Previous work has demonstrated, empirically, that the
``finite-sampling error'' can be very large -- many times kT -- in DF estimates
for simple molecular systems. Here, we present a theoretical description of the
inaccuracy, including the exact solution of a sample problem, the precise
asymptotic behavior in terms of 1/N for large N, the identification of
universal law, and numerical illustrations. The theory relies on corrections to
the central and other limit theorems, and thus a role is played by stable
(Levy) probability distributions.Comment: 5 pages, 4 figure
Correction to the Casimir force due to the anomalous skin effect
The surface impedance approach is discussed in connection with the precise
calculation of the Casimir force between metallic plates. It allows to take
into account the nonlocal connection between the current density and electric
field inside of metals. In general, a material has to be described by two
impedances and corresponding to two
different polarization states. In contrast with the approximate Leontovich
impedance they depend not only on frequency but also on the wave
vector along the plate . In this paper only the nonlocal effects happening
at frequencies (plasma frequency) are analyzed. We refer to
all of them as the anomalous skin effect. The impedances are calculated for the
propagating and evanescent fields in the Boltzmann approximation. It is found
that significantly deviates from the local impedance as a result of the
Thomas-Fermi screening. The nonlocal correction to the Casimir force is
calculated at zero temperature. This correction is small but observable at
small separations between bodies. The same theory can be used to find more
significant nonlocal contribution at due to the plasmon
excitation.Comment: 29 pages. To appear in Phys. Rev.
Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field
We propose fractional Fokker-Planck equation for the kinetic description of
relaxation and superdiffusion processes in constant magnetic and random
electric fields. We assume that the random electric field acting on a test
charged particle is isotropic and possesses non-Gaussian Levy stable
statistics. These assumptions provide us with a straightforward possibility to
consider formation of anomalous stationary states and superdiffusion processes,
both properties are inherent to strongly non-equilibrium plasmas of solar
systems and thermonuclear devices. We solve fractional kinetic equations, study
the properties of the solution, and compare analytical results with those of
numerical simulation based on the solution of the Langevin equations with the
noise source having Levy stable probability density. We found, in particular,
that the stationary states are essentially non-Maxwellian ones and, at the
diffusion stage of relaxation, the characteristic displacement of a particle
grows superdiffusively with time and is inversely proportional to the magnetic
field.Comment: 15 pages, LaTeX, 5 figures PostScrip
An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums
By a modification of the method that was applied in (Korolev and Shevtsova,
2009), here the inequalities
and
are proved for the
uniform distance between the standard normal distribution
function and the distribution function of the normalized sum of an
arbitrary number of independent identically distributed random
variables with zero mean, unit variance and finite third absolute moment
. The first of these inequalities sharpens the best known version of
the classical Berry--Esseen inequality since
by virtue of
the condition , and 0.4785 is the best known upper estimate of the
absolute constant in the classical Berry--Esseen inequality. The second
inequality is applied to lowering the upper estimate of the absolute constant
in the analog of the Berry--Esseen inequality for Poisson random sums to 0.3051
which is strictly less than the least possible value of the absolute constant
in the classical Berry--Esseen inequality. As a corollary, the estimates of the
rate of convergence in limit theorems for compound mixed Poisson distributions
are refined.Comment: 33 page
Steady-State L\'evy Flights in a Confined Domain
We derive the generalized Fokker-Planck equation associated with a Langevin
equation driven by arbitrary additive white noise. We apply our result to study
the distribution of symmetric and asymmetric L\'{e}vy flights in an infinitely
deep potential well. The fractional Fokker-Planck equation for L\'{e}vy flights
is derived and solved analytically in the steady state. It is shown that
L\'{e}vy flights are distributed according to the beta distribution, whose
probability density becomes singular at the boundaries of the well. The origin
of the preferred concentration of flying objects near the boundaries in
nonequilibrium systems is clarified.Comment: 10 pages, 1 figur
Dependence on Orbital Parameters for NEA Depletion Rate
В работе проводится численное моделирование динамической эволюции населения АСЗ на время 20 млн лет. В результате получено характерное время убыли населения АСЗ для различных областей пространства орбит, а также рассмотрены различные каналы убыли АСЗ.A numerical simulation of the dynamical evolution of the NEA population is made. Dependence of NEA depletion rate on orbit parameters is obtained. Different channels of the NEA depletion are considered.Работа выполнена при поддержке гранта РНФ № 22-12-00115
Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
We report the results of certain integrations of quantum-theoretic interest,
relying, in this regard, upon recently developed parameterizations of Boya et
al of the n x n density matrices, in terms of squared components of the unit
(n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized
volume elements of the Bures (minimal monotone) metric for n = 2 and 3,
obtaining thereby "Bures prior probability distributions" over the two- and
three-state systems. Then, as an essential first step in extending these
results to n > 3, we determine that the "Hall normalization constant" (C_{n})
for the marginal Bures prior probability distribution over the
(n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices
is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it
follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known
to equal 2/pi.) The constant C_{5} is also found. It too is associated with a
remarkably simple decompositon, involving the product of the eight consecutive
prime numbers from 2 to 23.
We also preliminarily investigate several cases, n > 5, with the use of
quasi-Monte Carlo integration. We hope that the various analyses reported will
prove useful in deriving a general formula (which evidence suggests will
involve the Bernoulli numbers) for the Hall normalization constant for
arbitrary n. This would have diverse applications, including quantum inference
and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in
J. Phys. A. We make a few slight changes from the previous version, but also
add a subsection (III G) in which several variations of the basic problem are
newly studied. Rather strong evidence is adduced that the Hall constants are
related to partial sums of denominators of the even-indexed Bernoulli
numbers, although a general formula is still lackin
Escape driven by -stable white noises
We explore the archetype problem of an escape dynamics occurring in a
symmetric double well potential when the Brownian particle is driven by {\it
white L\'evy noise} in a dynamical regime where inertial effects can safely be
neglected. The behavior of escaping trajectories from one well to another is
investigated by pointing to the special character that underpins the
noise-induced discontinuity which is caused by the generalized Brownian paths
that jump beyond the barrier location without actually hitting it. This fact
implies that the boundary conditions for the mean first passage time (MFPT) are
no longer determined by the well-known local boundary conditions that
characterize the case with normal diffusion. By numerically implementing
properly the set up boundary conditions, we investigate the survival
probability and the average escape time as a function of the corresponding
L\'evy white noise parameters. Depending on the value of the skewness
of the L\'evy noise, the escape can either become enhanced or suppressed: a
negative asymmetry causes typically a decrease for the escape rate
while the rate itself depicts a non-monotonic behavior as a function of the
stability index which characterizes the jump length distribution of
L\'evy noise, with a marked discontinuity occurring at . We find that
the typical factor of ``two'' that characterizes for normal diffusion the ratio
between the MFPT for well-bottom-to-well-bottom and well-bottom-to-barrier-top
no longer holds true. For sufficiently high barriers the survival probabilities
assume an exponential behavior. Distinct non-exponential deviations occur,
however, for low barrier heights.Comment: 8 pages, 8 figure
Parameters of the fractional Fokker-Planck equation
We study the connection between the parameters of the fractional
Fokker-Planck equation, which is associated with the overdamped Langevin
equation driven by noise with heavy-tailed increments, and the transition
probability density of the noise generating process. Explicit expressions for
these parameters are derived both for finite and infinite variance of the
rescaled transition probability density.Comment: 5 page
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