arXiv subjects
Publications and source records attributed to Hagar Veksler.
Edge localization is a fascinating quantum phenomenon. In this paper, the underlying mechanism generating it is presented analytically and verified numerically for a weakly kicked three-dimensional rotor. Analogy to tight binding model in solid state physics is used. The edge states result of the edge at zero angular momentum of the three-dimensional kicked rotor.
The effect of quantum collapse and revival is a fascinating interference phenomenon. In this paper the phenomenon is demonstrated analytically and numerically for a simple system, a slightly anharmonic Hamiltonian. The initial wave-function is a displaced ground state of a harmonic oscillator. Possible experimental realizations for cold atoms are discussed in detail.
Ultracold atoms placed in a tight cigar-shaped trap are usually described in terms of the Lieb-Liniger model. We study the extensions of this model which arise when van der Waals interaction between atoms is taken into account. We find that the corrections induced by the finite range of interactions can become especially important in the vicinity of narrow Feshbach resonances and suggest realistic schemes of their experimental detection. The interplay of confinement and interactions can lead to effective transparency where the one-dimensional interactions are weak in a wide range of parameters.
In 1963, Lieb and Liniger solved exactly a one dimensional model of bosons interacting by a repulsive δ-potential and calculated the ground state in the thermodynamic limit. In the present work, we extend this model to a potential of three δ-functions, one of them is repulsive and the other two are attractive, modeling some aspects of the interaction between atoms, and present an approximate solution for a dilute gas. In this limit, for low energy states, the results are found to be reduced to the ones of an effective Lieb Liniger model with an effective δ-function of strength $c_{eff}$ and the regime of stability is identified. This may shed light on some aspects of interacting bosons.
Quantum collapses and revivals are fascinating manifestations of interference. Of particular interest in recent years are macroscopic quantum interference effects in Bose-Einstein condensates. In this letter such effects will be studied for the two site Bose-Hubbard model that is a standard model for exploration of Bose-Einstein condensates. An analytic expression that is valid in the weak coupling limit for the difference in the occupation of the two sites is developed and tested numerically. It describes correctly the collapses and revivals. Moreover, it is demonstrated that a calculation to the first order in the interparticle interaction is required for the prediction of the collapse and revival times while the second order is required for the evaluation of the shape of the revival peaks. We believe that the result is relevant for a variety of situations where collapses and revivals are found.
In this work the two site Bose-Hubbard model is studied analytically in the limit of weak coupling u and large number of particles N . The semiclassical approximation where \frac{1}{N} plays the role of Planck's constant was used and perturbation theory to order u^{2} was applied. In particular, the difference in the occupation between the two sites, where initially all particles are at one site was calculated analytically. Excellent agreement with the exact numerical solution was found. This quantity exhibits collapses and revivals that superimpose rapid oscillations. The occupation difference was calculated also for the case where initially both sites are occupied provided that the difference in occupation is sufficiently large. It provides an analytical description of results that were so far found only numerically. Similar behavior and analysis are expected for a large variety of physical situations in optics, atom optics and quantum dynamics of electrons in Rydberg atoms.
One of the assumptions leading to the Gross-Pitaevskii Equation (GPE) is that the interaction between atom pairs can be written effectively as a δ-function so that the interaction range of the particles is assumed to vanish. A simple model that takes into account the extension of the inter-particle potential is introduced. The correction to the GPE predictions for the energy of a condensate confined by a harmonic trap in the Thomas-Fermi (TF) regime is estimated. Although it is found to be small, we believe that in some situations it can be measured using its dependance on the frequency of the confining trap. Due to the simplicity of the model, it may have a wide range of applications.
The role of double humped states in spreading of wave packets for the nonlinear Schroedinger equation (NLSE) with a random potential is explored and the spreading mechanism is unraveled. Comparison with an NLSE with a double-well potential is made. There are two independent affects of the nonlinearity on the double humped states for the NLSE: coupling to other states and destruction. The interplay between these effects is discussed.
The dynamics of an initially localized wavepacket is studied for the generalized nonlinear Schroedinger Equation with a random potential, where the nonlinearity term is |ψ|^p*ψand "p" is arbitrary. Mainly short times for which the numerical calculations can be performed accurately are considered. Long time calculations are presented as well. In particular the subdiffusive behavior where the average second moment of the wavepacket is of the form ~t^a is computed. Contrary to former heuristic arguments, no evidence for any critical behavior as function of "p" is found. The properties of α(t) are explored.