3,085 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 (Rb -K in
our case) scattering length.Comment: 6 pages, 6 figures, 1 tabl
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 and arbitrary angular dependence. It is
shown exactly that collapse of Bose-Einstein condensate without contact
interactions is possible only for . Case 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 is supercritical with expected weak collapse which traps rapidly
decreasing number of particles during approach to collapse. For
singularity at is not strong enough to allow collapse but attractive
interaction admits stable self-trapping even in absence of external
trapping potential
Symmetry Breaking and Enhanced Condensate Fraction in a Matter-Wave Bright Soliton
An exact diagonalization study reveals that a matter-wave bright soliton and
the Goldstone mode are simultaneously created in a quasi-one-dimensional
attractive Bose-Einstein condensate by superpositions of quasi-degenerate
low-lying many-body states. Upon formation of the soliton the maximum
eigenvalue of the single-particle density matrix increases dramatically,
indicating that a fragmented condensate converts into a single condensate as a
consequence of the breaking of translation symmetry.Comment: 4 pages, 4 figures, revised 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
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 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 dimensions (), possessing a manifold of analytic
solutions of dimension (), which includes one largely arbitrary relation
among the fields. These nonlinear equations can also contain an arbitrary
forcing.Comment: 21 page
Collinear Photon Emission from the Quark-Gluon Plasma: The Light-Cone Path Integral Formulation
We give a simple physical derivation of the photon emission rate from the
weakly coupled quark-gluon plasma connected with the collinear processes and . The analysis is based on the light-cone
path integral approach to the induced radiation. Our results agree with that by
Arnold, Moore and Yaffe obtained using the real-time thermal perturbation
theory. It is demonstrated that the solution of the AMY integral equation is
nothing but the time-integrated Green's function of the light-cone path
integral approach written in the momentum representation.Comment: 12 pages, 2 figure
Cosmology and the Korteweg-de Vries Equation
The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has
played a fundamental role in diverse branches of mathematical and theoretical
physics. In the present paper, we consider its significance to cosmology. It is
found that the KdV equation arises in a number of important scenarios,
including inflationary cosmology, the cyclic universe, loop quantum cosmology
and braneworld models. Analogies can be drawn between cosmic dynamics and the
propagation of the solitonic wave solution to the equation, whereby quantities
such as the speed and amplitude profile of the wave can be identified with
cosmological parameters such as the spectral index of the density perturbation
spectrum and the energy density of the universe. The unique mathematical
properties of the Schwarzian derivative operator are important to the analysis.
A connection with dark solitons in Bose-Einstein condensates is briefly
discussed.Comment: 7 pages; References adde
Dressing method based on homogeneous Fredholm equation: quasilinear PDEs in multidimensions
In this paper we develop a dressing method for constructing and solving some
classes of matrix quasi-linear Partial Differential Equations (PDEs) in
arbitrary dimensions. This method is based on a homogeneous integral equation
with a nontrivial kernel, which allows one to reduce the nonlinear PDEs to
systems of non-differential (algebraic or transcendental) equations for the
unknown fields. In the simplest examples, the above dressing scheme captures
matrix equations integrated by the characteristics method and nonlinear PDEs
associated with matrix Hopf-Cole transformations.Comment: 31 page
Modulated wavepackets associated with longitudinal dust grain oscillations in a dusty plasma crystal
The nonlinear amplitude modulation of longitudinal dust lattice waves (LDLWs)
propagating in a dusty plasma crystal is investigated in a continuum
approximation. It is shown that long wavelength LDLWs are modulationally
stable, while shorter wavelengths may be unstable. The possibility for the
formation and propagation of different envelope localized excitations is
discussed. It is shown that the total grain displacement bears a (weak)
constant displacement (zeroth harmonic mode), due to the asymmetric form of the
nonlinear interaction potential. The existence of asymmetric envelope localized
modes is predicted. The types and characteristics of these coherent nonlinear
structures are discussed.Comment: 18 pages, 7 figures, to appear in Physics of Plasma
Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation
We apply a version of the dressing method to a system of four dimensional
nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer
equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform
Method) and nonlinear matrix PDE integrable by the method of characteristics as
particular reductions. Some other reductions are suggested.Comment: 12 page
- …