Anderson localization of matter waves in chaotic potentials

In the present paper we study Anderson localization of Bose-Einstein condensate with a weakly positive nonlinearity under the influence of chaotic potentials. We investigate the one-dimensional Gross-Pitaevskii equation numerically, in order to unveil the influence of the parameters that describe the potential and nonlinearity on the localization of the condensate. The results show that matter localization is possible, in certain regions in parameter space. Similarities to chaotically disordered photonic lattices suggest that the results are of direct interest to such photonic lattices as well.     

Zeroth-order phase transitions and Zipf law quantization

From the standpoint of thermodynamic averaging of fission microprocesses, we investigate the origin of radioactive release in an NPP after an accident or after resource depletion. The genesis of the NPP release is interpreted as a new thermodynamic phenomenon, a zeroth-order phase transition. This problem setting results in a problem in probabilistic number theory. We prove the corresponding theorem leading to quantization of the Zipf law for the frequency of a zeroth-order phase transition with different values of the jump of the Gibbs thermodynamic potential. We introduce the notion of hole dimension. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 118–142, January, 2007.     

Refinement of the Gibbs and Bose-Einstein Distributions

A rigorous derivation of the Gibbs and Bose-Einstein distributions on a finite set of energies is stated, in essence, as a theorem in number theory. If there are not very many particles, then the discussion of this question reduces to an exact theorem. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 433–436, December, 2005.     

Multiple-quantum-coherence dynamics of spin-1 Bose-Einstein condensate during quantum phase transitions

Multiple quantum coherences are often employed to describe quantum many-body dynamics in nuclear spin systems and recently,to characterize quantum phase transitions in trapped ions.Here we investigate the multiple-quantum-coherence dynamics of a spin-1 Bose-Einstein condensate.By adjusting the quadratic Zeeman shift,the condensate exhibits three quantum phases.Our numerical results show that the spectrum of multiple quantum coherence does indeed catch the quantum critical points.More importantly,with only a few low-order multiple quantum coherences,the spin-1 condensate exhibits rich signals of the many-body dynamics,beyond conventional observables.The experimental implementation of such multiple quantum coherence protocol is also discussed.