Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach

A method for the study of steady-state nonlinear modes for Gross-Pitaevskii equation (GPE) is described. It is based on exact statement about coding of the steady-state solutions of GPE which vanish as $x\to+\infty$ by reals. This allows to fulfill {\it demonstrative computation} of nonlinear modes of GPE i.e. the computation which allows to guarantee that {\it all} nonlinear modes within a given range of parameters have been found. The method has been applied to GPE with quadratic and double-well potential, for both, repulsive and attractive nonlinearities. The bifurcation diagrams of nonlinear modes in these cases are represented. The stability of these modes has been discussed.Comment: 21 pages, 6 figure

Nonequilibrium Bose systems and nonground-state Bose-Einstein condensates

The theory of resonant generation of nonground-state Bose-Einstein condensates is extended to Bose-condensed systems at finite temperature. The generalization is based on the notion of representative statistical ensembles for Bose systems with broken global gauge symmetry. Self-consistent equations are derived describing an arbitrary nonequilibrium nonuniform Bose system. The notion of finite-temperature topological coherent modes, coexisting with a cloud of noncondensed atoms, is introduced. It is shown that resonant generation of these modes is feasible for a gas of trapped Bose atoms at finite temperature.Comment: Latex file, 16 pages, no figure

The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions

The nonlinear Schroedinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schroedinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary states of periodic potentials. Phenomena well-known from classical chaos are found, such as a bifurcation of periodic stationary states and a transition to spatial chaos. The relation of new features of nonlinear Bloch bands, such as looped and period doubled bands, are analyzed in detail. An analytic expression for the critical nonlinearity for the emergence of looped bands is derived. The results for the delta-comb are generalized to a more realistic potential consisting of a periodic sequence of narrow Gaussian peaks and the dynamical stability of periodic solutions in a Gaussian comb is discussed.Comment: Enhanced and revised version, to appear in J. Nonlin. Math. Phy

Vibrational and electronic heating in nanoscale junctions

Understanding and controlling the flow of heat is a major challenge in nanoelectronics. When a junction is driven out of equilibrium by light or the flow of electric charge, the vibrational and electronic degrees of freedom are, in general, no longer described by a single temperature[1-6]. Moreover, characterizing the steady-state vibrational and electronic distributions {\it in situ} is extremely challenging. Here we show that surface-enhanced Raman emission may be used to determine the effective temperatures for both the vibrational modes and the flowing electrons in a biased metallic nanoscale junction decorated with molecules[7]. Molecular vibrations show mode-specific pumping by both optical excitation[8] and dc current[9], with effective temperatures exceeding several hundred Kelvin. AntiStokes electronic Raman emission\cite[10,11] indicates electronic effective temperature also increases to as much as three times its no-current values at bias voltages of a few hundred mV. While the precise effective temperatures are model-dependent, the trends as a function of bias conditions are robust, and allow direct comparisons with theories of nanoscale heating.Comment: 28 pages, including 4 main figures and 10 supplemental figure

Use of sign language in paediatric cochlear implant users: whys and wherefores.

[No abstract available

Quasi-particle tunneling between fractional quantum Hall edges

Inter-edge tunneling in the fractional quantum Hall regime at temperatures down to is investigated by using split-gate constrictions to induce a controllable scattering between the edges. Both weak- and strong-backscattering regimes are explored. Tunneling characteristics as a function of split-gate bias as well as temperature are measured and compared with available theories