The quantum H3H_3 integrable system

The quantum $H_3$ integrable system is a 3D system with rational potential related to the non-crystallographic root system $H_3$. It is shown that the gauge-rotated $H_3$ Hamiltonian as well as one of the integrals, when written in terms of the invariants of the Coxeter group $H_3$, 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 $H_3$ 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 $H_3$-invariants "polynomially"-isospectral to the quantum $H_3$ 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-$d$ 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