2,895 research outputs found
Whitham systems and deformations
We consider the deformations of Whitham systems including the "dispersion
terms" and having the form of Dubrovin-Zhang deformations of Frobenius
manifolds. The procedure is connected with B.A. Dubrovin problem of
deformations of Frobenius manifolds corresponding to the Whitham systems of
integrable hierarchies. Under some non-degeneracy requirements we suggest a
general scheme of the deformation of the hyperbolic Whitham systems using the
initial non-linear system. The general form of the deformed Whitham system
coincides with the form of the "low-dispersion" asymptotic expansions used by
B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius
manifolds.Comment: 27 pages, Late
Thermal Fluctuations of the Electric Field in the Presence of Carrier Drift
We consider a semiconductor in a non-equilibrium steady state, with a dc
current. On top of the stationary carrier motion there are fluctuations. It is
shown that the stationary motion of the carriers (i.e., their drift) can have a
profound effect on the electromagnetic field fluctuations in the bulk of the
sample as well as outside it, close to the surface (evanescent waves in the
near field). The effect is particularly pronounced near the plasma frequency.
This is because drift leads to a significant modification of the dispersion
relation for the bulk and surface plasmons.Comment: Comments are welcom
Propagation of sound in a Bose Einstein condensate in an optical lattice
We study the propagation of sound waves in a Bose-Einstein condensate trapped
in a one-dimensional optical lattice. We find that the velocity of propagation
of sound wavepackets decreases with increasing optical lattice depth, as
predicted by the Bogoliubov theory. The strong interplay between nonlinearities
and the periodicity of the external potential raise new phenomena which are not
present in the uniform case. Shock waves, for instance, can propagate slower
than sound waves, due to the negative curvature of the dispersion relation.
Moreover, nonlinear corrections to the Bogoliubov theory appear to be important
even with very small density perturbations, inducing a saturation on the
amplitude of the sound signal
Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion
We consider the space-time evolution of initial discontinuities of depth and
flow velocity for an integrable version of the shallow water Boussinesq system
introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq
model" for which a flat water surface is modulationally stable, we speak below
of "positive dispersion" model. This model also appears as an approximation to
the equations governing the dynamics of polarisation waves in two-component
Bose-Einstein condensates. We describe its periodic solutions and the
corresponding Whitham modulation equations. The self-similar, one-phase wave
structures are composed of different building blocks which are studied in
detail. This makes it possible to establish a classification of all the
possible wave configurations evolving from initial discontinuities. The
analytic results are confirmed by numerical simulations
Whitham method for Benjamin-Ono-Burgers equation and dispersive shocks in internal waves in deep fluid
The Whitham modulation equations for the parameters of a periodic solution
are derived using the generalized Lagrangian approach for the case of damped
Benjamin-Ono equation. The structure of the dispersive shock in internal wave
in deep water is considered by this method.Comment: 8 pages, 4 figure
Analytic model for a frictional shallow-water undular bore
We use the integrable Kaup-Boussinesq shallow water system, modified by a
small viscous term, to model the formation of an undular bore with a steady
profile. The description is made in terms of the corresponding integrable
Whitham system, also appropriately modified by friction. This is derived in
Riemann variables using a modified finite-gap integration technique for the
AKNS scheme. The Whitham system is then reduced to a simple first-order
differential equation which is integrated numerically to obtain an asymptotic
profile of the undular bore, with the local oscillatory structure described by
the periodic solution of the unperturbed Kaup-Boussinesq system. This solution
of the Whitham equations is shown to be consistent with certain jump conditions
following directly from conservation laws for the original system. A comparison
is made with the recently studied dissipationless case for the same system,
where the undular bore is unsteady.Comment: 24 page
Flux flow of Abrikosov-Josephson vortices along grain boundaries in high-temperature superconductors
We show that low-angle grain boundaries (GB) in high-temperature
superconductors exhibit intermediate Abrikosov vortices with Josephson cores,
whose length along GB is smaller that the London penetration depth, but
larger than the coherence length. We found an exact solution for a periodic
vortex structure moving along GB in a magnetic field and calculated the
flux flow resistivity , and the nonlinear voltage-current
characteristics. The predicted dependence describes well our
experimental data on unirradiated and irradiated
bicrystals, from which the core size , and the intrinsic depairing
density on nanoscales of few GB dislocations were measured for the
first time. The observed temperature dependence of
indicates a significant order parameter suppression in current channels between
GB dislocation cores.Comment: 5 pages 5 figures. Phys. Rev. Lett. (accepted
Coulomb drag between ballistic one-dimensional electron systems
The presence of pronounced electronic correlations in one-dimensional systems
strongly enhances Coulomb coupling and is expected to result in distinctive
features in the Coulomb drag between them that are absent in the drag between
two-dimensional systems. We review recent Fermi and Luttinger liquid theories
of Coulomb drag between ballistic one-dimensional electron systems, and give a
brief summary of the experimental work reported so far on one-dimensional drag.
Both the Fermi liquid (FL) and the Luttinger liquid (LL) theory predict a
maximum of the drag resistance R_D when the one-dimensional subbands of the two
quantum wires are aligned and the Fermi wave vector k_F is small, and also an
exponential decay of R_D with increasing inter-wire separation, both features
confirmed by experimental observations. A crucial difference between the two
theoretical models emerges in the temperature dependence of the drag effect.
Whereas the FL theory predicts a linear temperature dependence, the LL theory
promises a rich and varied dependence on temperature depending on the relative
magnitudes of the energy and length scales of the systems. At higher
temperatures, the drag should show a power-law dependence on temperature, R_D
\~ T^x, experimentally confirmed in a narrow temperature range, where x is
determined by the Luttinger liquid parameters. The spin degree of freedom plays
an important role in the LL theory in predicting the features of the drag
effect and is crucial for the interpretation of experimental results.Comment: 25 pages, 14 figures, to appear in Semiconductor Science and
Technolog
Delayed feedback control of self-mobile cavity solitons
Control of the motion of cavity solitons is one the central problems in
nonlinear optical pattern formation. We report on the impact of the phase of
the time-delayed optical feedback and carrier lifetime on the self-mobility of
localized structures of light in broad area semiconductor cavities. We show
both analytically and numerically that the feedback phase strongly affects the
drift instability threshold as well as the velocity of cavity soliton motion
above this threshold. In addition we demonstrate that non-instantaneous carrier
response in the semiconductor medium is responsible for the increase in
critical feedback rate corresponding to the drift instability
Sensitivity analysis of fluid substitution in a porous medium with aligned fractures
We study the effect of fluid substitution in a porous fractured medium using explicit expressions developed for aligned fractured medium. We investigate the effect of porosity and water saturation on (1) P-wave moduli, (2) horizontal and vertical velocities, (3) anisotropic parameters, and (4) reflection coefficients. Effects of fracture density on these four parameters are also analyzed. The systematic variations of the moduli and reflection coefficients reported in this paper can thus be used in developing AVO with azimuth in a porous fractured reservoir
- …