130 research outputs found
Random matrix theory for low-frequency sound propagation in the ocean: a spectral statistics test
Problem of long-range sound propagation in the randomly-inhomogeneous deep
ocean is considered. We examine a novel approach for modeling of wave
propagation, developed by K.C.Hegewisch and S.Tomsovic. This approach relies on
construction of a wavefield propagator using the random matrix theory (RMT). We
study the ability of the RMT-based propagator to reproduce properties of the
propagator corresponding to direct numerical solution of the parabolic
equation. It is shown that mode coupling described by the RMT-based propagator
is basically consistent with the direct Monte-Carlo simulation. The agreement
is worsened only for relatively short distances, when long-lasting cross-mode
correlations are significant. It is shown that the RMT-based propagator with
properly chosen range step can reproduce some coherent features in spectral
statistics.Comment: 23 pages, 13 figure
Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation
Motion of randomly-driven quantum nonlinear pendulum is considered. Utilizing
one-step Poincar\'e map, we demonstrate that classical phase space
corresponding to a single realization of the random perturbation involves
domains of finite-time stability. Statistical analysis of the finite-time
evolution operator (FTEO) is carried out in order to study influence of
finite-time stability on quantum dynamics. It is shown that domains of
finite-time stability give rise to ordered patterns in distributions of FTEO
eigenfunctions. Transition to global chaos is accompanied by smearing of these
patterns; however, some of their traces survive on relatively long timescales
Dynamics of BEC mixtures loaded into the optical lattice in the presence of linear inter-component coupling
We consider dynamics of a two-component Bose-Einstein condensate where the
components correspond to different hyperfine states of the same sort of atoms.
External microwave radiation leads to resonant transitions between the states.
The condensate is loaded into the optical lattice. We invoke the tight-binding
approximation and examine the interplay of spatial and internal dynamics of the
mixture. It is shown that internal dynamics qualitatively depends on the
intra-component interaction strength and the phase configuration of the initial
state. We focus attention on two intriguing phenomena occurring for certain
parameter values. The first phenomenon is the spontaneous synchronization of
Rabi oscillations running inside neighbouring lattice sites. Another one is the
demixing of the condensate with formation of immiscible solitons when
nonlinearity becomes sufficiently strong. Demixing is preceded by the transient
regime with highly irregular behavior of the mixture.Comment: Accepted for publication in the Journal of Russian Laser Researc
A numeric-analytical method for solving the Cauchy problem for ordinary differential equations
In the paper we offer a functional-discrete method for solving the Cauchy
problem for the first order ordinary differential equations (ODEs). This method
(FD-method) is in some sense similar to the Adomian Decomposition Method. But
it is shown that for some problems FD-method is convergent whereas ADM is
divergent. The results presented in the paper can be easily generalized on the
case of systems of ODEs
Stability preserving structural transformations of systems of linear second-order ordinary differential equations
In the paper we have developed a theory of stability preserving structural
transformations of systems of second-order ordinary differential equations
(ODEs), i.e., the transformations which preserve the property of Lyapunov
stability. The main Theorem proved in the paper can be viewed as an analogous
of the Erugin's theorem for the systems of second-order ODEs. The Theorem
allowed us to generalize the 3-rd and 4-th Kelvin -- Tait -- Chetayev theorems.
The obtained theoretical results were successfully applied to the stability
investigation of the rotary motion of a rigid body suspended on a string.Comment: 40 page
Quantum transport in a driven disordered potential: onset of directed current and noise-induced current reversal
We study motion of a quantum wavepacket in a one-dimensional potential with
correlated disorder. Presence of long-range potential correlations allows for
existence of both localized and extended states. Weak time-dependent
perturbation in the form of a fluctuating plane wave is superimposed onto the
potential. This model can be realized in experiments with optically trapped
cold atoms. Time-dependent perturbation causes transitions between localized
and extended states. Owing to violation of space-time symmetries, there arises
atomic current which is codirectional with the wave-like perturbation. However,
it is shown that the perturbation can drag atoms only within some limited time
interval, and then the current changes its direction. Increasing of the
perturbation bandwidth and/or amplitude results in decreasing of the time of
current reversal. We argue that onset of the current reversal is associated
with inhomogeneity of diffusion in the momentum space
A Superexponentially Convergent Functional-Discrete Method for Solving the Cauchy Problem for Systems of Ordinary Differential Equations
In the paper a new numerical-analytical method for solving the Cauchy problem
for systems of ordinary differential equations of special form is presented.
The method is based on the idea of the FD-method for solving the operator
equations of general form, which was proposed by V.L. Makarov. The sufficient
conditions for the method converges with a superexponential convergence rate
were obtained. We have generalized the known statement about the local
properties of Adomian polynomials for scalar functions on the operator case.
Using the numerical examples we make the comparison between the proposed method
and the Adomian Decomposition Method.Comment: 33 pages, 6 figure
Exponentially convergent functional-discrete method for eigenvalue transmission problems with discontinuous flux and potential as a function in the space
Based on the functional-discrete technique (FD-method), an algorithm for
eigenvalue transmission problems with discontinuous flux and integrable
potential is developed. The case of the potential as a function belonging to
the functional space is studied for both linear and nonlinear eigenvalue
problems. The sufficient conditions providing superexponential convergence rate
of the method were obtained. Numerical examples are presented to support the
theory. Based on the numerical examples and the convergence results, conclusion
about analytical properties of eigensolutions for nonself-adjoint differential
operators is made.Comment: 27 pages, 11 tables, 9 figure
The FD-method for solving nonlinear Klein-Gordon equation
In the paper we present a functional-discrete method for solving the Goursat
problem for nonlinear Klein-Gordon equation. The sufficient conditions
providing that the proposed method converges superexponentially are obtained.
The results of numerical example presented in the paper are in good agreement
with the theoretical conclusions.Comment: 20 page
Exponentially convergent functional-discrete method for solving Sturm-Liouville problems with potential including Dirac \delta-function
In the paper we present a functional-discrete method for solving
Sturm-Liouville problems with potential including function from L_{1}(0,1) and
\delta-function. For both, linear and nonlinear cases the sufficient conditions
providing superexponential convergence rate of the method are obtained. The
question of possible software implementation of the method is discussed in
detail. The theoretical results are successfully confirmed by the numerical
example included in the paper.Comment: 29 pages, 7 figures, 3 table
- β¦