Integrable turbulence generated from modulational instability of cnoidal waves

We study numerically the nonlinear stage of modulational instability (MI) of cnoidal waves, in the framework of the focusing one-dimensional Nonlinear Schrodinger (NLS) equation. Cnoidal waves are the exact periodic solutions of the NLS equation and can be represented as a lattice of overlapping solitons. MI of these lattices lead to development of "integrable turbulence" [Zakharov V.E., Stud. Appl. Math. 122, 219-234 (2009)]. We study the major characteristics of the turbulence for dn-branch of cnoidal waves and demonstrate how these characteristics depend on the degree of "overlapping" between the solitons within the cnoidal wave. Integrable turbulence, that develops from MI of dn-branch of cnoidal waves, asymptotically approaches to it's stationary state in oscillatory way. During this process kinetic and potential energies oscillate around their asymptotic values. The amplitudes of these oscillations decay with time as t^{-a}, 1<a<1.5, the phases contain nonlinear phase shift decaying as t^{-1/2}, and the frequency of the oscillations is equal to the double maximal growth rate of the MI, s=2g_{max}. In the asymptotic stationary state the ratio of potential to kinetic energy is equal to -2. The asymptotic PDF of wave amplitudes is close to Rayleigh distribution for cnoidal waves with strong overlapping, and is significantly non-Rayleigh one for cnoidal waves with weak overlapping of solitons. In the latter case the dynamics of the system reduces to two-soliton collisions, which occur with exponentially small rate and provide up to two-fold increase in amplitude compared with the original cnoidal wave.Comment: 36 pages, 25 figure

Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation

By performing two parallel numerical experiments -- solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation -- we examined the applicability of the theory of weak turbulence to the description of the time evolution of an ensemble of free surface waves (a swell) on deep water. We observed qualitative coincidence of the results. To achieve quantitative coincidence, we augmented the kinetic equation by an empirical dissipation term modelling the strongly nonlinear process of white-capping. Fitting the two experiments, we determined the dissipation function due to wave breaking and found that it depends very sharply on the parameter of nonlinearity (the surface steepness). The onset of white-capping can be compared to a second-order phase transition. This result corroborates with experimental observations by Banner, Babanin, Young.Comment: 5 pages, 5 figures, Submitted in Phys. Rev. Letter

Anomalous mass dependence of radiative quark energy loss in a finite-size quark-gluon plasma

We demonstrate that for a finite-size quark-gluon plasma the induced gluon radiation from heavy quarks is stronger than that for light quarks when the gluon formation length becomes comparable with (or exceeds) the size of the plasma. The effect is due to oscillations of the light-cone wave function for the in-medium $q\to gq$ transition. The dead cone model by Dokshitzer and Kharzeev neglecting quantum finite-size effects is not valid in this regime. The finite-size effects also enhance the photon emission from heavy quarks.Comment: 8 pages, 3 figure

An all-optical event horizon in an optical analogue of a Laval nozzle

Exploiting the fact that light propagation in defocusing nonlinear media can mimic the transonic flow of an equivalent fluid, we demonstrate experimentally the formation of an all-optical event horizon in a waveguide structure akin to a hydrodynamic Laval nozzle. The analogue event horizon, which forms at the nozzle throat is suggested as a novel platform for analogous gravity experiments

Weak Wave Turbulence Scaling Theory for Diffusion and Relative Diffusion in Turbulent Surface Waves

We examine the applicability of the weak wave turbulence theory in explaining experimental scaling results obtained for the diffusion and relative diffusion of particles moving on turbulent surface waves. For capillary waves our theoretical results are shown to be in good agreement with experimental results, where a distinct crossover in diffusive behavior is observed at the driving frequency. For gravity waves our results are discussed in the light of ocean wave studies.Comment: 5 pages; for related work visit http://www.imedea.uib.es/~victo

Solitary waves in mixtures of Bose gases confined in annular traps

A two-component Bose-Einstein condensate that is confined in a one-dimensional ring potential supports solitary-wave solutions, which we evaluate analytically. The derived solutions are shown to be unique. The corresponding dispersion relation that generalizes the case of a single-component system shows interesting features.Comment: 4 pages, 1 figur

Solitary-wave solutions in binary mixtures of Bose-Einstein condensates under periodic boundary conditions

We derive solitary-wave solutions within the mean-field approximation in quasi-one-dimensional binary mixtures of Bose-Einstein condensates under periodic boundary conditions, for the case of an effective repulsive interatomic interaction. The particular gray-bright solutions that give the global energy minima are determined. Their characteristics and the associated dispersion relation are derived. In the case of weak coupling, we diagonalize the Hamiltonian analytically to obtain the full excitation spectrum of "quantum" solitary-wave solutions.Comment: 11 pages, 2 figure

Massive Cosmologies

We explore the cosmological solutions of a recently proposed extension of General Relativity with a Lorentz-invariant mass term. We show that the same constraint that removes the Boulware-Deser ghost in this theory also prohibits the existence of homogeneous and isotropic cosmological solutions. Nevertheless, within domains of the size of inverse graviton mass we find approximately homogeneous and isotropic solutions that can well describe the past and present of the Universe. At energy densities above a certain crossover value, these solutions approximate the standard FRW evolution with great accuracy. As the Universe evolves and density drops below the crossover value the inhomogeneities become more and more pronounced. In the low density regime each domain of the size of the inverse graviton mass has essentially non-FRW cosmology. This scenario imposes an upper bound on the graviton mass, which we roughly estimate to be an order of magnitude below the present-day value of the Hubble parameter. The bound becomes especially restrictive if one utilizes an exact self-accelerated solution that this theory offers. Although the above are robust predictions of massive gravity with an explicit mass term, we point out that if the mass parameter emerges from some additional scalar field condensation, the constraint no longer forbids the homogeneous and isotropic cosmologies. In the latter case, there will exist an extra light scalar field at cosmological scales, which is screened by the Vainshtein mechanism at shorter distances.Comment: 21 page