Example of shock wave in unstaible medium: The focusing nonlinear Schrodinger equation

Dissipationless shock waves in modulational unstable one-dimensional medium are investigated on the simplest example of integrable focusing nonlinear Schr\''odinger (NS) equation. Our approach is based on the construction of special exact solution of the Whitham-NS system, which ''partially saturates'' the modulational instability.Comment: 4 pages, LaTEX, version 2.09, submitted to Phys. Lett.

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

Detection of Quantum Noise from an Electrically-Driven Two-Level System

Quantum mechanics can strongly influence the noise properties of mesoscopic devices. To probe this effect we have measured the current fluctuations at high-frequency (5-90 GHz) using a superconductor-insulator-superconductor tunnel junction as an on-chip spectrum analyser. By coupling this frequency-resolved noise detector to a quantum device we can measure the high-frequency, non-symmetrized noise as demonstrated for a Josephson junction. The same scheme is used to detect the current fluctuations arising from coherent charge oscillations in a two-level system, a superconducting charge qubit. A narrow band peak is observed in the spectral noise density at the frequency of the coherent charge oscillations.Comment: 16 pages, 4 figure

Phonon drag in ballistic quantum wires

The acoustic phonon-mediated drag-contribution to the drag current created in the ballistic transport regime in a one-dimensional nanowire by phonons generated by a current-carrying ballistic channel in a nearby nanowire is calculated. The threshold of the phonon-mediated drag current with respect to bias or gate voltage is predicted.Comment: 5 pages, 2 figure

Radiation Front Sweeping the Ambient Medium of Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are emitted by relativistic ejecta from powerful cosmic explosions. Their light curves suggest that the gamma-ray emission occurs at early stages of the ejecta expansion, well before it decelerates in the ambient medium. If so, the launched gamma-ray front must overtake the ejecta and sweep the ambient medium outward. As a result a gap is opened between the ejecta and the medium that surfs the radiation front ahead. Effectively, the ejecta moves in a cavity until it reaches a radius R_{gap}=10^{16}E_{54}^{1/2} cm where E is the isotropic energy of the GRB. At R=R_{gap} the gap is closed, a blast wave forms and collects the medium swept by radiation. Further development of the blast wave is strongly affected by the leading radiation front: the front plays the role of a precursor where the medium is loaded with e+- pairs and preaccelerated just ahead of the blast. It impacts the emission from the blast at R < R_{load}=5R_{gap} (the early afterglow). A spectacular observational effect results: GRB afterglows should start in optical/UV and evolve fast (< min) to a normal X-ray afterglow. The early optical emission observed in GRB 990123 may be explained in this way. The impact of the front is especially strong if the ambient medium is a wind from a massive progenitor of the GRB. In this case three phenomena are predicted: (1) The ejecta decelerates at R<R_{load} producing a lot of soft radiation. (2) The light curve of soft emission peaks at t_{peak}=40(1+z)E_{54}^{1/2}(Gamma_{ej}/100)^{-2} s where Gamma_{ej} is the Lorentz factor of the ejecta. Given measured redshift z and t_{peak}, one finds Gamma_{ej}. (3) The GRB acquires a spectral break at 5 - 50 MeV because harder photons are absorbed by radiation scattered in the wind.Comment: 20 pages, accepted to Ap