Bright solitons in Bose-Fermi mixtures

We consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases confined in a three-dimensional elongated harmonic trap. The Bose and Fermi atoms are assumed to effectively attract each other whereas bosonic atoms repel each other. Strong enough attraction between bosonic and fermionic components can change the character of the interaction within the bosonic cloud from repulsive to attractive making thus possible the generation of bright solitons in the mixture. On the other hand, such structures might be in danger due to the collapse phenomenon existing in attractive gases. We show, however, that under some conditions (defined by the strength of the Bose-Fermi components attraction) the structures which neither spread nor collapse can be generated. For elongated enough traps the formation of solitons is possible even at the ``natural'' value of the mutual Bose-Fermi ($^{87}$Rb -$^{40}$K in our case) scattering length.Comment: 6 pages, 6 figures, 1 tabl

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

Symmetry Induced 4-Wave Capillary Wave Turbulence

We report theoretical and experimental results on 4-wave capillary wave turbulence. A system consisting of two inmiscible and incompressible fluids of the same density can be written in a Hamiltonian way for the conjugated pair $(\eta,\Psi)$. When given the symmetry $z\to-z$, the set of weakly non-linear interacting waves display a Kolmogorov-Zakharov (KZ) spectrum $n_k\sim k^{-4}$ in wave vector space. The wave system was studied experimentally with two inmiscible fluids of almost equal densities (water and silicon oil) where the capillary surface waves are excited by a low frequency random forcing. The power spectral density (PSD) and probability density function (PDF) of the local wave amplitude are studied. Both theoretical and experimental results are in fairly good agreement with each other.Comment: 6 pages, 2 figure

On the infrared limit of Horava's gravity with the global Hamiltonian constraint

We show that Horava's theory of gravitation with the global Hamiltonian constraint does not reproduce General Relativity in the infrared domain. There is one extra propagating degree of freedom, besides those two associated with the massless graviton, which does not decouple.Comment: 7 pages, typos corrected, to be published in PR

New multidimensional partially integrable generalization of S-integrable N-wave equation

This paper develops a modification of the dressing method based on the inhomogeneous linear integral equation with integral operator having nonempty kernel. Method allows one to construct the systems of multidimensional Partial Differential Equations (PDEs) having the differential polynomial forms in any dimension n. Associated solution space is not full, although it is parametrized by a certain number of arbitrary functions of (n-1)-variables. We consider 4-dimensional generalization of the classical (2+1)-dimensional S-integrable N-wave equation as an example.Comment: 38 page

Nonperturbative physics at short distances

There is accumulating evidence in lattice QCD that attempts to locate confining fields in vacuum configurations bring results explicitly depending on tha lattice spacing (that is, ultraviolet cut off). Generically, one deals with low-dimensional vacuum defects which occupy a vanishing fraction of the total four-dimensional space. We review briefly existing data on the vacuum defects and their significance for confinement and other nonperturbative phenomena. We introduce the notion of `quantum numbers' of the defects and draw an analogy, rather formal one, to developments which took place about 50 years ago and were triggered by creation of the Sakata model.Comment: 15 pages, contributed to International Symposium on the Jubilee of the Sakata Model (pnLambda50), Nagoya, Japan, Nov. 200

From confining fields on the lattice to higher dimensions in the continuum

We discuss relation between lattice phenomenology of confining fields in the vacuum state of Yang-Mills theories (mostly SU(2) case) and continuum theories. In the continuum, understanding of the confinement is most straightforward in the dual formulation which involves higher dimensions. We try to bridge these two approaches to the confinement, let it be on a rudimentary level. We review lattice data on low-dimensional defects, that is monopoles, center vortices, topological defects. There is certain resemblance to dual strings, domain walls, introduced in large-N Yang-Mills theories.Comment: 21 pages; based on three lectures given at the Conference ``Infrared QCD in Rio'', Rio de Janeiro, Brazil, 5-0 June 200

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