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

Weak compressible magnetohydrodynamic turbulence in the solar corona

This Letter presents a calculation of the power spectra of weakly turbulent Alfven waves and fast magnetosonic waves ("fast waves") in low-beta plasmas. It is shown that three-wave interactions transfer energy to high-frequency fast waves and, to a lesser extent, high-frequency Alfven waves. MHD turbulence is thus a promising mechanism for producing the high-frequency waves needed to explain the anisotropic heating of minor ions in the solar corona.Comment: 4 pages, 3 figures, accepted, Phys. Rev. Let

Quantum Many-Body Dynamics of Dark Solitons in Optical Lattices

We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider the quantum dynamics of density and phase engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. The former approach directly models how one may create quantum entangled dark solitons in experiment. While we have already presented results regarding the latter approach elsewhere [Phys. Rev. Lett. {\bf 103}, 140403 (2009)], we expand upon those results in this work. In both cases, quantum fluctuations cause the dark soliton to fill in and may induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system's natural orbitals.Comment: 14 pages, 11 figures -- v3 has only minor changes from v2 -- this is the print versio

Collapse and stable self-trapping for Bose-Einstein condensates with 1/r^b type attractive interatomic interaction potential

We consider dynamics of Bose-Einstein condensates with long-range attractive interaction proportional to $1/r^b$ and arbitrary angular dependence. It is shown exactly that collapse of Bose-Einstein condensate without contact interactions is possible only for $b\ge 2$. Case $b=2$ is critical and requires number of particles to exceed critical value to allow collapse. Critical collapse in that case is strong one trapping into collapsing region a finite number of particles. Case $b>2$ is supercritical with expected weak collapse which traps rapidly decreasing number of particles during approach to collapse. For $b<2$ singularity at $r=0$ is not strong enough to allow collapse but attractive $1/r^b$ interaction admits stable self-trapping even in absence of external trapping potential

Photon emission from bare quark stars

We investigate the photon emission from the electrosphere of a quark star. It is shown that at temperatures T\sim 0.1-1 MeV the dominating mechanism is the bremsstrahlung due to bending of electron trajectories in the mean Coulomb field of the electrosphere. The radiated energy for this mechanism is much larger than that for the Bethe-Heitler bremsstrahlung. The energy flux from the mean field bremsstrahlung exceeds the one from the tunnel e^{+}e^{-} pair creation as well. We demonstrate that the LPM suppression of the photon emission is negligible.Comment: 35 pages, 5 figure

Variational approach for the quantum Zakharov system

The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled, nonlinear system of ordinary differential equations. In the semiclassic case, linear stability analysis of this dynamical system shows a destabilizing r\^ole played by quantum effects. Arbitrary value of the quantum effects are also considered, yielding the ultimate destruction of the localized, Gaussian trial solution. Numerical simulations are shown both for the semiclassic and the full quantum cases.Comment: 6 figure

Critical density of a soliton gas

We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schr\"odinger operator associated with the KdV soliton gas dynamics. As a by-product of our derivation we find the speed of sound in the soliton gas with Gaussian spectral distribution function.Comment: 7 page

Partially integrable systems in multidimensions by a variant of the dressing method. 1

In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially integrable''. Such a construction is achieved using a suitable modification of the classical dressing scheme, consisting in assuming that the kernel of the basic integral operator of the dressing formalism be nontrivial. This new hypothesis leads to the construction of: 1) a linear system of compatible spectral problems for the solution $U(\lambda;x)$ of the integral equation in 3 independent variables each (while the usual dressing method generates spectral problems in 1 or 2 dimensions); 2) a system of nonlinear partial differential equations in $n$ dimensions ($n>3$), possessing a manifold of analytic solutions of dimension ($n-2$), which includes one largely arbitrary relation among the fields. These nonlinear equations can also contain an arbitrary forcing.Comment: 21 page

Solitary waves of Bose-Einstein condensed atoms confined in finite rings

Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schr\"odinger equation subject to periodic boundary conditions. When the circumference of the ring is much larger than the size of the wave, the density profile is well approximated by that of an infinite ring, however the density and the velocity of propagation cannot vanish simultaneously. When the size of the ring becomes comparable to the size of the wave, the density variation becomes sinusoidal and the velocity of propagation saturates to a constant value.Comment: 6 pages, 2 figure

Long-distance radiative corrections to the di-pion tau lepton decay

We evaluate the model-dependent piece of O(alpha) long-distance radiative corrections to tau^- \to \pi^- \pi^0\nu_{\tau} decays by using a meson dominance model. We find that these corrections to the di-pion invariant mass spectrum are smaller than in previous calculations based on chiral perturbation theory. The corresponding correction to the photon inclusive rate is tiny (-0.15%) but it can be of relevance when new measurements reach better precision.Comment: 4 pages, 2 figures. An estimate of the shift produced in the evaluation of the h.v.p. contribution to the muon anomalous magnetic moment is added. Version to appear in Phys. Rev.