Trace formula for an ensemble of bumpy billiards.

We study the semiclassical quantization of an ensemble of billiards with a small random shape deformation. We derive a trace formula averaged over shape disorder. The results are illustrated by the study of supershells in rough metal clusters.Comment: 12 pages, latex, 3 figures available by fax upon request

Hawking radiation in a two-component Bose-Einstein condensate

We consider a simple realization of an event horizon in the flow of a one-dimensional two-component Bose-Einstein condensate. Such a condensate has two types of quasiparticles; In the system we study, one corresponds to density fluctuations and the other to polarization fluctuations. We treat the case where a horizon occurs only for one type of quasiparticles (the polarization ones). We study the one- and two-body signal associated to the analog of spontaneous Hawking radiation and demonstrate by explicit computation that it consists only in the emission of polarization waves. We discuss the experimental consequences of the present results in the domain of atomic Bose-Einstein condensates and also for the physics of exciton-polaritons in semiconductor microcavities

Interference effects in the two-dimensional scattering of microcavity polaritons by an obstacle: phase dislocations and resonances

We consider interference effects within the linear description of the scattering of two-dimensional microcavity polaritons by an obstacle. The polariton wave may exhibit phase dislocations created by the interference of the incident and the scattered fields. We describe these structures within the general framework of singular optics. We also discuss another type of interference effects appearing due to the formation of (quasi)resonances in the potential of a repulsive obstacle with sharp boundaries. We discuss the relevance of our approach for the description of recent experimental results and propose a criterion for evaluating the importance of nonlinear effects.Comment: 11 pages, 9 figure

Dispersive hydrodynamics of nonlinear polarization waves in two-component Bose-Einstein condensates

We study one dimensional mixtures of two-component Bose-Einstein condensates in the limit where the intra-species and inter-species interaction constants are very close. Near the mixing-demixing transition the polarization and the density dynamics decouple. We study the nonlinear polarization waves, show that they obey a universal (i.e., parameter free) dynamical description, identify a new type of algebraic soliton, explicitly write simple wave solutions, and study the Gurevich-Pitaevskii problem in this context

Nonlinear waves in coherently coupled Bose-Einstein condensates

We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the elementary excitations. The spectrum has two branches which are affected in different ways. The upper branch experiences a modulational instability which is stabilized by a long wave-short wave resonance with the lower branch. The lower branch is stable. In the limit of weak nonlinearity and small dispersion it is described by a Korteweg-de Vries equation or by the Gardner equation, depending on the value of the parameters of the system

Bogoliubov Theory of acoustic Hawking radiation in Bose-Einstein Condensates

We apply the microscopic Bogoliubov theory of dilute Bose-Einstein condensates to analyze quantum and thermal fluctuations in a flowing atomic condensate in the presence of a sonic horizon. For the simplest case of a step-like horizon, closed-form analytical expressions are found for the spectral distribution of the analog Hawking radiation and for the density correlation function. The peculiar long-distance density correlations that appear as a consequence of the Hawking emission features turns out to be reinforced by a finite initial temperature of the condensate. The analytical results are in good quantitative agreement with first principle numerical calculations.Comment: 11 pages, 7 figure

Propagation of a Dark Soliton in a Disordered Bose-Einstein Condensate

We consider the propagation of a dark soliton in a quasi 1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary transmission coefficients through a nonlinear disordered slab, it is a well defined problem. It is found that a dark soliton decays algebraically, over a characteristic length which is independent of its initial velocity, and much larger than both the healing length and the 1D scattering length of the system. We also determine the characteristic decay time.Comment: 4 pages, 2 figure

Polarization hydrodynamics in a one-dimensional polariton condensate

We study the hydrodynamics of a nonresonantly-pumped polariton condensate in a quasi-one-dimensional quantum wire taking into account the spin degree of freedom. We clarify the relevance of the Landau criterion for superfluidity in this dissipative two-component system. Two Cherenkov-like critical velocities are identified corresponding to the opening of different channels of radiation: one of (damped) density fluctuations and another of (weakly damped) polarization fluctuations. We determine the drag force exerted onto an external obstacle and propose experimentally measurable consequences of the specific features of the fluctuations of polarization