4,248 research outputs found

### 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

### 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

### 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

### Turbulent flow in graphene

We demonstrate the possibility of a turbulent flow of electrons in graphene
in the hydrodynamic region, by calculating the corresponding turbulent
probability density function. This is used to calculate the contribution of the
turbulent flow to the conductivity within a quantum Boltzmann approach. The
dependence of the conductivity on the system parameters arising from the
turbulent flow is very different from that due to scattering.Comment: 4 pages, Latex file, Journal versio

### 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

### 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

### On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields

It was shown recently that Frobenius reduction of the matrix fields reveals
interesting relations among the nonlinear Partial Differential Equations (PDEs)
integrable by the Inverse Spectral Transform Method ($S$-integrable PDEs),
linearizable by the
Hoph-Cole substitution ($C$-integrable PDEs) and integrable by the method of
characteristics ($Ch$-integrable PDEs). However, only two classes of
$S$-integrable PDEs have been involved: soliton equations like Korteweg-de
Vries, Nonlinear Shr\"odinger, Kadomtsev-Petviashvili and Davey-Stewartson
equations, and GL(N,\CC) Self-dual type PDEs, like Yang-Mills equation. In
this paper we consider the simple five-dimensional nonlinear PDE from another
class of $S$-integrable PDEs, namely, scalar nonlinear PDE which is
commutativity condition of the pair of vector fields. We show its origin from
the (1+1)-dimensional hierarchy of $Ch$-integrable PDEs after certain
composition of Frobenius type and differential reductions imposed on the matrix
fields. Matrix generalization of the above scalar nonlinear PDE will be derived
as well.Comment: 14 pages, 1 figur

### Observation of nonlinear dispersion relation and spatial statistics of wave turbulence on the surface of a fluid

We report experiments on gravity-capillary wave turbulence on the surface of
a fluid. The wave amplitudes are measured simultaneously in time and space
using an optical method. The full space-time power spectrum shows that the wave
energy is localized on several branches in the wave-vector-frequency space. The
number of branches depend on the power injected within the waves. The
measurement of the nonlinear dispersion relation is found to be well described
by a law suggesting that the energy transfer mechanisms involved in wave
turbulence are not only restricted to purely resonant interaction between
nonlinear waves. The power-law scaling of the spatial spectrum and the
probability distribution of the wave amplitudes at a given wave number are also
measured and compared to the theoretical predictions.Comment: accepted to Phys. Rev. Lett

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