3,703 research outputs found
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
Tunable Wigner States with Dipolar Atoms and Molecules
We study the few-body physics of trapped atoms or molecules with electric or
magnetic dipole moments aligned by an external field. Using exact numerical
diagonalization appropriate for the strongly correlated regime, as well as a
classical analysis, we show how Wigner localization emerges with increasing
coupling strength. The Wigner states exhibit non-trivial geometries due to the
anisotropy of the interaction. This leads to transitions between different
Wigner states as the tilt angle of the dipoles with the confining plane is
changed. Intriguingly, while the individual Wigner states are well described by
a classical analysis, the transitions between different Wigner states are
strongly affected by quantum statistics. This can be understood by considering
the interplay between quantum-mechanical and spatial symmetry properties.
Finally, we demonstrate that our results are relevant to experimentally
realistic systems.Comment: 4 pages, 6 figure
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