Mass Transfer Mechanism in Real Crystals by Pulsed Laser Irradiation

The dynamic processes in the surface layers of metals subjected activity of a pulsing laser irradiation, which destroyed not the crystalline structure in details surveyed. The procedure of calculation of a dislocation density generated in bulk of metal during the relaxation processes and at repeated pulse laser action is presented. The results of evaluations coincide with high accuracy with transmission electron microscopy dates. The dislocation-interstitial mechanism of laser-stimulated mass-transfer in real crystals is presented on the basis of the ideas of the interaction of structure defects in dynamically deforming medium. The good compliance of theoretical and experimental results approves a defining role of the presented mechanism of mass transfer at pulse laser action on metals. The possible implementation this dislocation-interstitial mechanism of mass transfer in metals to other cases of pulsing influences is justifiedComment: 10 pages, 2 figures, Late

Formation of Quantum Shock Waves by Merging and Splitting Bose-Einstein Condensates

The processes of merging and splitting dilute-gas Bose-Einstein condensates are studied in the nonadiabatic, high-density regime. Rich dynamics are found. Depending on the experimental parameters, uniform soliton trains containing more than ten solitons or the formation of a high-density bulge as well as quantum (or dispersive) shock waves are observed experimentally within merged BECs. Our numerical simulations indicate the formation of many vortex rings. In the case of splitting a BEC, the transition from sound-wave formation to dispersive shock-wave formation is studied by use of increasingly stronger splitting barriers. These experiments realize prototypical dispersive shock situations.Comment: 10 pages, 8 figure

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

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

On the temperature dependence of ballistic Coulomb drag in nanowires

We have investigated within the theory of Fermi liquid dependence of Coulomb drag current in a passive quantum wire on the applied voltage $V$ across an active wire and on the temperature $T$ for any values of $eV/k_BT$. We assume that the bottoms of the 1D minibands in both wires almost coincide with the Fermi level. We come to conclusions that 1) within a certain temperature interval the drag current can be a descending function of the temperature $T$; 2) the experimentally observed temperature dependence $T^{-0.77}$ of the drag current can be interpreted within the framework of Fermi liquid theory; 3) at relatively high applied voltages the drag current as a function of the applied voltage saturates; 4) the screening of the electron potential by metallic gate electrodes can be of importance.Comment: 7 pages, 1 figur

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

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

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