Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics

We discuss the localization of wavefunctions along planes containing the shortest periodic orbits in a three-dimensional billiard system with axial symmetry. This model mimicks the self-consistent mean field of a heavy nucleus at deformations that occur characteristically during the fission process [1,2]. Many actinide nuclei become unstable against left-right asymmetric deformations, which results in asymmetric fragment mass distributions. Recently we have shown [3,4] that the onset of this asymmetry can be explained in the semiclassical periodic orbit theory by a few short periodic orbits lying in planes perpendicular to the symmetry axis. Presently we show that these orbits are surrounded by small islands of stability in an otherwise chaotic phase space, and that the wavefunctions of the diabatic quantum states that are most sensitive to the left-right asymmetry have their extrema in the same planes. An EBK quantization of the classical motion near these planes reproduces the exact eigenenergies of the diabatic quantum states surprisingly well.Comment: 4 pages, 5 figures, contribution to the Nobel Symposium on Quantum Chao

Exact diagonalization results for an anharmonically trapped Bose-Einstein condensate

We consider bosonic atoms that rotate in an anharmonic trapping potential. Using numerical diagonalization of the Hamiltonian, we identify the various phases of the gas as the rotational frequency of the trap and the coupling between the atoms are varied.Comment: 7 pages, RevTex, 10 figure

Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consists of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.Comment: 4 pages, 1 figure; revised version explains exact solutions in terms of isospin symmetry and Hund's rul

Few-body precursor of the Higgs mode in a superfluid Fermi gas

We demonstrate that an undamped few-body precursor of the Higgs mode can be investigated in a harmonically trapped Fermi gas. Using exact diagonalisation, the lowest monopole mode frequency is shown to depend non-monotonically on the interaction strength, having a minimum in a crossover region. The minimum deepens with increasing particle number, reflecting that the mode is the few-body analogue of a many-body Higgs mode in the superfluid phase, which has a vanishing frequency at the quantum phase transition point to the normal phase. We show that this mode mainly consists of coherent excitations of time-reversed pairs, and that it can be selectively excited by modulating the interaction strength, using for instance a Feshbach resonance in cold atomic gases.Comment: 9 pages, 7 figure

Comment on ``Fragmented Condensate Ground State of Trapped Weakly Interacting Bosons in Two Dimensions"

Recently Liu et al. [PRL 87, 030404 (2001)] examined the lowest state of a weakly-interacting Bose-Einstein condensate. In addition to other interesting results, using the method of the pair correlation function, they questioned the validity of the mean-field picture of the formation of vortices and stated that the vortices are generated at the center of the cloud. This is in apparent contradiction to the Gross-Pitaevskii approach, which predicts that the vortices successively enter the cloud from its outer parts as L/N (where N is the number of atoms in the trap and hbar(L) is the angular momentum of the system) increases. We have managed to reproduce the results of Liu et al. however a more careful analysis presented below confirms the validity of the mean-field approach.Comment: 1 page, RevTex, 2 figure

Mixtures of Bose gases under rotation

We examine the rotational properties of a mixture of two Bose gases. Considering the limit of weak interactions between the atoms, we investigate the behavior of the system under a fixed angular momentum. We demonstrate a number of exact results in this many-body system.Comment: 4 pages, RevTex, 6 figure

Persistent currents in Bose gases confined in annular traps

We examine the problem of stability of persistent currents in a mixture of two Bose gases trapped in an annular potential. We evaluate the critical coupling for metastability in the transition from quasi-one to two-dimensional motion. We also evaluate the critical coupling for metastability in a mixture of two species as function of the population imbalance. The stability of the currents is shown to be sensitive to the deviation from one-dimensional motion.Comment: 6 pages, 4 figure