25,475 research outputs found
The quantum integrable system
The quantum integrable system is a 3D system with rational potential
related to the non-crystallographic root system . It is shown that the
gauge-rotated Hamiltonian as well as one of the integrals, when written
in terms of the invariants of the Coxeter group , is in algebraic form: it
has polynomial coefficients in front of derivatives. The Hamiltonian has
infinitely-many finite-dimensional invariant subspaces in polynomials, they
form the infinite flag with the characteristic vector \vec \al\ =\ (1,2,3).
One among possible integrals is found (of the second order) as well as its
algebraic form. A hidden algebra of the Hamiltonian is determined. It is
an infinite-dimensional, finitely-generated algebra of differential operators
possessing finite-dimensional representations characterized by a generalized
Gauss decomposition property. A quasi-exactly-solvable integrable
generalization of the model is obtained. A discrete integrable model on the
uniform lattice in a space of -invariants "polynomially"-isospectral to
the quantum model is defined.Comment: 32 pages, 3 figure
A model for conservative chaos constructed from multi-component Bose-Einstein condensates with a trap in 2 dimensions
To show a mechanism leading to the breakdown of a particle picture for the
multi-component Bose-Einstein condensates(BECs) with a harmonic trap in high
dimensions, we investigate the corresponding 2- nonlinear Schr{\"o}dinger
equation (Gross-Pitaevskii equation) with use of a modified variational
principle. A molecule of two identical Gaussian wavepackets has two degrees of
freedom(DFs), the separation of center-of-masses and the wavepacket width.
Without the inter-component interaction(ICI) these DFs show independent regular
oscillations with the degenerate eigen-frequencies. The inclusion of ICI
strongly mixes these DFs, generating a fat mode that breaks a particle picture,
which however can be recovered by introducing a time-periodic ICI with zero
average. In case of the molecule of three wavepackets for a three-component
BEC, the increase of amplitude of ICI yields a transition from regular to
chaotic oscillations in the wavepacket breathing.Comment: 5 pages, 4 figure
Is it possible to observe experimentally a metal-insulator transition in ultra cold atoms?
Kicked rotors with certain non-analytic potentials avoid dynamical
localization and undergo a metal-insulator transition. We show that typical
properties of this transition are still present as the non-analyticity is
progressively smoothed out provided that the smoothing is less than a certain
limiting value. We have identified a smoothing dependent time scale such that
full dynamical localization is absent and the quantum momentum distribution
develops power-law tails with anomalous decay exponents as in the case of a
conductor at the metal-insulator transition. We discuss under what conditions
these findings may be verified experimentally by using ultra cold atoms
techniques. It is found that ultra-cold atoms can indeed be utilized for the
experimental investigation of the metal-insulator transition.Comment: 7 pages, 3 figure
Nonlinear response of superparamagnets with finite damping: an analytical approach
The strongly damping-dependent nonlinear dynamical response of classical
superparamagnets is investigated by means of an analytical approach. Using
rigorous balance equations for the spin occupation numbers a simple approximate
expression is derived for the nonlinear susceptibility. The results are in good
agreement with those obtained from the exact (continued-fraction) solution of
the Fokker-Planck equation. The formula obtained could be of assistance in the
modelling of the experimental data and the determination of the damping
coefficient in superparamagnets.Comment: 7 PR pages, 2 figure
Higher order correction to the neutrino self-energy in a medium and its astrophysical applications
We have calculated the 1/M^4 (M the vector boson mass) order correction to
the neutrino self-energy in a medium. The possible application of this higher
order contribution to the neutrino effective potential is considered in the
context of the Early Universe hot plasma and of the cosmological Gamma Ray
Burst fireball. We found that, depending on the medium parameters and on the
neutrino properties (mixing angle and mass square difference) the resonant
oscillation of active to active neutrinos is possible.Comment: 10 pages, revtex style, uses axodraw.sty, 1 figur
Structural instability of vortices in Bose-Einstein condensates
In this paper we study a gaseous Bose-Einstein condensate (BEC) and show
that: (i) A minimum value of the interaction is needed for the existence of
stable persistent currents. (ii) Vorticity is not a fundamental invariant of
the system, as there exists a conservative mechanism which can destroy a vortex
and change its sign. (iii) This mechanism is suppressed by strong interactions.Comment: 4 pages with 3 figures. Submitted to Phys. Rev. Let
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