73 research outputs found
Two-dimensional periodic waves in supersonic flow of a Bose–Einstein condensate
Stationary periodic solutions of the two-dimensional Gross–Pitaevskii equation are obtained and analysed for different parameter values in the context of the problem of a supersonic flow of a Bose–Einstein condensate past an obstacle. The asymptotic connections with the corresponding periodic solutions of the Korteweg–de Vries and nonlinear Schrödinger equations are studied and typical spatial wave distributions are discussed
The quasi-classical model of the spherical configuration in general relativity
We consider the quasi-classical model of the spin-free configuration on the
basis of the self-gravitating spherical dust shell in General Relativity. For
determination of the energy spectrum of the stationary states on the basis of
quasi-classical quantization rules it is required to carry out some
regularization of the system. It is realized by an embedding of the initial
system in the extended system with rotation. Then, the stationary states of the
spherical shells are S-states of the system with the intrinsic momentum. The
quasi-classical treatment of a stability of the configuration is associated
with the Langer modification of a square of the quantum mechanical intrinsic
momentum. It gives value of critical bare mass of the shell determining
threshold of stability. For the shell with the bare mass smaller or equal to
the Planck's mass, the energy spectra of bound states are found. We obtain the
expression for tunneling probability of the shell and construct the
quasi-classical model of the pair creation and annihilation of the shells.Comment: 22 pages, sprocl.sty, 3 figure
On the variational principle for dust shells in General Relativity
The variational principle for a thin dust shell in General Relativity is
constructed. The principle is compatible with the boundary-value problem of the
corresponding Euler-Lagrange equations, and leads to ``natural boundary
conditions'' on the shell. These conditions and the gravitational field
equations which follow from an initial variational principle, are used for
elimination of the gravitational degrees of freedom. The transformation of the
variational formula for spherically-symmetric systems leads to two natural
variants of the effective action. One of these variants describes the shell
from a stationary interior observer's point of view, another from the exterior
one. The conditions of isometry of the exterior and interior faces of the shell
lead to the momentum and Hamiltonian constraints. The canonical equivalence of
the mentioned systems is shown in the extended phase space. Some particular
cases are considered.Comment: 25 pages, RevTeX, no figures, revised version, typos corrected,
accepted for publication in Journal of Mathematical Physic
Linear "ship waves" generated in stationary flow of a Bose-Einstein condensate past an obstacle
Using stationary solutions of the linearized two-dimensional Gross-Pitaevskii
equation, we describe the ``ship wave'' pattern occurring in the supersonic
flow of a Bose-Einstein condensate past an obstacle. It is shown that these
``ship waves'' are generated outside the Mach cone. The developed analytical
theory is confirmed by numerical simulations of the flow past body problem in
the frame of the full non-stationary Gross-Pitaevskii equation.Comment: 5 pages, 4 figure
The Features of Surface Plasmon-Polariton Pulses Generation Via Cooperative Effects in Waveguide Spaser
The problem of sub-picosecond plasmon-polariton pulse formation in metal/dielectric interface due to collective decay of excited quantum dots, placed in the dielectric layer near the metal surface, is considered. Theoretical approach to selection of semiconductor quantum dots and dielectric host medium to increase the energy transmission of quantum dot collective excitations into surface plasmon-polariton modes of waveguide spaser is developed
Matter sound waves in two-component Bose-Einstein condensates
The creation and propagation of sound waves in two-component Bose-Einstein
condensates (BEC) are investigated and a new method of wave generation in
binary BEC mixtures is proposed. The method is based on a fast change of the
inter-species interaction constant and is illustrated for two experimental
settings: a drop-like condensate immersed into a second large repulsive
condensate, and a binary mixture of two homogeneous repulsive BEC's. A
mathematical model based on the linearized coupled Gross-Pitaevskii equations
is developed and explicit formulae for the space and time dependence of sound
waves are provided. Comparison of the analytical and numerical results shows
excellent agreement, confirming the validity of the proposed approach.Comment: 16 pages, 9 figure
Transcritical flow of a Bose-Einstein condensate through a penetrable barrier
The problem of the transcritical flow of a Bose-Einstein condensate through a
wide repulsive penetrable barrier is studied analytically using the combination
of the localized "hydraulic" solution of the 1D Gross-Pitaevskii equation and
the solutions of the Whitham modulation equations describing the resolution of
the upstream and downstream discontinuities through dispersive shocks. It is
shown that within the physically reasonable range of parameters the downstream
dispersive shock is attached to the barrier and effectively represents the
train of very slow dark solitons, which can be observed in experiments. The
rate of the soliton emission, the amplitudes of the solitons in the train and
the drag force are determined in terms of the BEC oncoming flow velocity and
the strength of the potential barrier. A good agreement with direct numerical
solutions is demonstrated. Connection with recent experiments is discussed.Comment: Revised version. 22 pages, 24 figures. Accepted for publication in
Phys. Rev.
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