41,372 research outputs found
Soliton localization in Bose-Einstein condensates with time-dependent harmonic potential and scattering length
We derive exact solitonic solutions of a class of Gross-Pitaevskii equations
with time-dependent harmonic trapping potential and interatomic interaction. We
find families of exact single-solitonic, multi-solitonic, and solitary wave
solutions. We show that, with the special case of an oscillating trapping
potential and interatomic interaction, a soliton can be localized indefinitely
at an arbitrary position. The localization is shown to be experimentally
possible for sufficiently long time even with only an oscillating trapping
potential and a constant interatomic interaction.Comment: 19 pages, 11 figures, accepted for publication in J.Phys.
Directional flow of solitons with asymmetric potential wells: Soliton diode
We study the flow of bright solitons through two asymmetric potential wells.
The scattering of a soliton by certain type of single potential wells, e.g.,
Gaussian or Rosen-Morse, is distinguished by a critical velocity above which
solitons can transmit almost completely and below which solitons can reflect
nearly perfectly. For two such wells in series with certain parameter
combinations, we find that there is an appreciable velocity range for which
solitons can propagate in one direction only. Our study shows that this
directional propagation or diode behavior is due to a combined effect of the
sharp transition in the transport coefficients at the critical velocity and a
slight reduction in the center-of-mass speed of the soliton while it travels
across a potential well.Comment: 7 pages, 5 figure
Nonlinear coupling between scissors modes of a Bose-Einstein condensate
We explore the nonlinear coupling of the three scissors modes of an
anisotropic Bose-Einstein condensate. We show that only when the frequency of
one of the scissors modes is twice the frequency of another scissors mode,
these two modes can be resonantly coupled and a down conversion can occur. We
perform the calculation variationally using a gaussian trial wave function.
This enables us to obtain simple analytical results that describe the
oscillation and resonance behaviour of the two coupled modes.Comment: 12 pages, 3 figures, submitted to Phys. Rev.
Self-adjoint Extensions for Confined Electrons:from a Particle in a Spherical Cavity to the Hydrogen Atom in a Sphere and on a Cone
In a recent study of the self-adjoint extensions of the Hamiltonian of a
particle confined to a finite region of space, in which we generalized the
Heisenberg uncertainty relation to a finite volume, we encountered bound states
localized at the wall of the cavity. In this paper, we study this situation in
detail both for a free particle and for a hydrogen atom centered in a spherical
cavity. For appropriate values of the self-adjoint extension parameter, the
bound states lo calized at the wall resonate with the standard hydrogen bound
states. We also examine the accidental symmetry generated by the Runge-Lenz
vector, which is explicitly broken in a spherical cavity with general Robin
boundary conditions. However, for specific radii of the confining sphere, a
remnant of the accidental symmetry persists. The same is true for an electron
moving on the surface of a finite circular cone, bound to its tip by a 1/r
potential.Comment: 22 pages, 9 Figure
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