250 research outputs found
Nearest-neighbor distribution for singular billiards
The exact computation of the nearest-neighbor spacing distribution P(s) is
performed for a rectangular billiard with point-like scatterer inside for
periodic and Dirichlet boundary conditions and it is demonstrated that for
large s this function decreases exponentially. Together with the results of
[Bogomolny et al., Phys. Rev. E 63, 036206 (2001)] it proves that spectral
statistics of such systems is of intermediate type characterized by level
repulsion at small distances and exponential fall-off of the nearest-neighbor
distribution at large distances. The calculation of the n-th nearest-neighbor
spacing distribution and its asymptotics is performed as well for any boundary
conditions.Comment: 38 pages, 10 figure
Effect of Preparation Conditions in the Pressure Range of Atmospheric Nitrogen (2 ... 50) 10-4 Torr on the Structural and Phase State of the Vacuum-Arc Coatings of Mo-N
Nanocrystalline vacuum-arc nitride coatings
possess the totality of unique structural states and
properties (high hardness, wear resistance, oxidation
stability, etc.). The coatings of the Mo-N system
show a high hardness and low solubility of
nonferromagnetic materials, thereby attracting great
interest in their industrial use. Unfortunately, at
present there is an apparent lack of information on the
regularities of phase-structural state formation in the
Mo-N system.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3535
Spectral Statistics: From Disordered to Chaotic Systems
The relation between disordered and chaotic systems is investigated. It is
obtained by identifying the diffusion operator of the disordered systems with
the Perron-Frobenius operator in the general case. This association enables us
to extend results obtained in the diffusive regime to general chaotic systems.
In particular, the two--point level density correlator and the structure factor
for general chaotic systems are calculated and characterized. The behavior of
the structure factor around the Heisenberg time is quantitatively described in
terms of short periodic orbits.Comment: uuencoded file with 1 eps figure, 4 page
Accelerated Algorithm of Least-Sguares Approximation of Signals by Exponentials for Wideband Frequency-Domain Reflectometry
In the paper the possibility of acceleration of procedure of best least-squares approximation of signals by exponentials was considered. For this purpose the analytical expressions for components of gradient vector and Hessian matrix of the objective function were obtained. The algorithms of quasisolution searching were constructed. Method of conjugate gradient and modified Newton method were used. The obtained algorithms were compared with modification of Nelder-Mead method which used information about only values of objective function. The comparison of the novel method and Prony’s method and matrix pencil method was held.В статье рассмотрена возможность ускорения аппроксимации сигналов экспонентами методом наименьших квадратов. Для этого были получены аналитические выражения для компонент вектора градиента и матрицы Гессе оптимизируемой функции. Был сконструирован алгоритм поиска квазирешения. Использовались метод сопряженных градиентов и модифицированный метод Ньютона. Полученные алгоритмы были сравнены с модификацией метода Нелдера-Мида, который использует информацию только о значениях оптимизируемой функции. Было проведено сравнение нового метода с методом Прони и методом пучка матриц.У статті розглянуто можливість прискорення апроксимації сигналів експонентами методом найменших квадратів. Для цього було отримано аналітичні вирази для компонент вектора градієнта та матриці Гессе функції, що оптимізується. Було сконструйовано алгоритм пошуку квазірозв’язку. Використано метод спряжених градієнтів та модифікований метод Ньютона. Отримані алгоритми були порівняні з модифікацією методу Нелдера-Міда, який використовує інформацію тільки про значення функції, що оптимізується. Було проведене порівняння нового методу з методом Проні та методом пучка матриць
Wigner--Dyson statistics for a class of integrable models
We construct an ensemble of second--quantized Hamiltonians with two bosonic
degrees of freedom, whose members display with probability one GOE or GUE
statistics. Nevertheless, these Hamiltonians have a second integral of motion,
namely the boson number, and thus are integrable. To construct this ensemble we
use some ``reverse engineering'' starting from the fact that --bosons in a
two--level system with random interactions have an integrable classical limit
by the old Heisenberg association of boson operators to actions and angles. By
choosing an --body random interaction and degenerate levels we end up with
GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.Comment: 3 pages, 1 figur
A pseudointegrable Andreev billiard
A circular Andreev billiard in a uniform magnetic field is studied. It is
demonstrated that the classical dynamics is pseudointegrable in the same sense
as for rational polygonal billiards. The relation to a specific polygon, the
asymmetric barrier billiard, is discussed. Numerical evidence is presented
indicating that the Poincare map is typically weak mixing on the invariant
sets. This link between these different classes of dynamical systems throws
some light on the proximity effect in chaotic Andreev billiards.Comment: 5 pages, 5 figures, to appear in PR
Modification of the Gelfand-Levitan Method for 1-D Multylaered Structure Inverse Problem
For dielectric slab with step profile of dielectric constant the Gelfand-Levitan method is correct if peaks of time-domain reflected signal are close to δ-pulses. Combination of parametric spectral methods for obtaining time-domain signal from frequency domain data and Gelfand-Levitan method for time-domain signal processing can help to improve the solution of the problem. Results of numerical simulation are presented.Для диэлектрической плиты со ступенчатым профилем диэлектрической постоянной применим метод Гельфанда-Левитана, если пики отраженного сигнала близки к δ -импульсам. Комбинация параметрических спектральных методов для получения сигнала во временной области по данным из частотной области и метод Гельфанда-Левитана для обработки сигнала во временной области позволяют получить усовершенствованный алгоритм решения задачи. Приведены результаты численного моделирования.Для діелектричної плити зі східчастим профілем діелектричної сталої метод Гельфанда-Левітана застосовний, якщо піки відбитого сигналу близькі до δ - імпульсів. Комбінація параметричних спектральних методів для отримання сигналу в часовій області та метод Гельфанда-Левітана для обробки сигналу в часовій області дозволяють отримати удосконалений алгоритм розв’язання задачі. Наведено результати чисельного моделювання
Phase coherence phenomena in superconducting films
Superconducting films subject to an in-plane magnetic field exhibit a gapless
superconducting phase. We explore the quasi-particle spectral properties of the
gapless phase and comment on the transport properties. Of particular interest
is the sensitivity of the quantum interference phenomena in this phase to the
nature of the impurity scattering. We find that films subject to columnar
defects exhibit a `Berry-Robnik' symmetry which changes the fundamental
properties of the system. Furthermore, we explore the integrity of the gapped
phase. As in the magnetic impurity system, we show that optimal fluctuations of
the random impurity potential conspire with the in-plane magnetic field to
induce a band of localized sub-gap states. Finally, we investigate the
interplay of the proximity effect and gapless superconductivity in thin normal
metal-superconductor bi-layers.Comment: 13 pages, 8 figures include
Current correlations and quantum localization in 2D disordered systems with broken time-reversal invariance
We study long-range correlations of equilibrium current densities in a
two-dimensional mesoscopic system with the time reversal invariance broken by a
random or homogeneous magnetic field. Our result is universal, i.e. it does not
depend on the type (random potential or random magnetic field) or correlation
length of disorder. This contradicts recent sigma-model calculations of
Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well
as for the renormalization of the conductivity. We show explicitly that the new
term in the sigma-model derived by TS&E and claimed to lead to delocalization
does not exist. The error in the derivation of TS&E is traced to an incorrect
ultraviolet regularization procedure violating current conservation and gauge
invariance.Comment: 8 pages, 3 figure
Spectral correlations : understanding oscillatory contributions
We give a different derivation of a relation obtained using a supersymmetric nonlinear sigma model by Andreev and Altshuler [Phys. Rev. Lett. 72, 902 (1995)], which connects smooth and oscillatory components of spectral correlation functions. We show that their result is not specific to the random matrix theory. Also, we show that despite an apparent contradiction, the results obtained using their formula are consistent with earlier perspectives on random matrix models
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