123 research outputs found
Lowest Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap
A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional
trap can be described with the lowest Landau-level set of states. In this case,
the condensate wave function psi(x,y) is a Gaussian function of r^2 = x^2 +
y^2, multiplied by an analytic function P(z) of the single complex variable z=
x+ i y; the zeros of P(z) denote the positions of the vortices. Here, a similar
description is used for a rapidly rotating anisotropic two-dimensional trap
with arbitrary anisotropy (omega_x/omega_y le 1). The corresponding condensate
wave function psi(x,y) has the form of a complex anisotropic Gaussian with a
phase proportional to xy, multiplied by an analytic function P(zeta), where
zeta is proportional to x + i beta_- y and 0 le beta_- le 1 is a real parameter
that depends on the trap anisotropy and the rotation frequency. The zeros of
P(zeta) again fix the locations of the vortices. Within the set of lowest
Landau-level states at zero temperature, an anisotropic parabolic density
profile provides an absolute minimum for the energy, with the vortex density
decreasing slowly and anisotropically away from the trap center.Comment: 13 pages, 1 figur
Inequivalent representations of commutator or anticommutator rings of field operators and their applications
Hamiltonian of a system in quantum field theory can give rise to infinitely
many partition functions which correspond to infinitely many inequivalent
representations of the canonical commutator or anticommutator rings of field
operators. This implies that the system can theoretically exist in infinitely
many Gibbs states. The system resides in the Gibbs state which corresponds to
its minimal Helmholtz free energy at a given range of the thermodynamic
variables. Individual inequivalent representations are associated with
different thermodynamic phases of the system. The BCS Hamiltonian of
superconductivity is chosen to be an explicit example for the demonstration of
the important role of inequivalent representations in practical applications.
Its analysis from the inequivalent representations' point of view has led to a
recognition of a novel type of the superconducting phase transition.Comment: 25 pages, 6 figure
Density and spin response functions in ultracold fermionic atom gases
We propose a new method of detecting the onset of superfluidity in a
two-component ultracold fermionic gas of atoms governed by an attractive
short-range interaction. By studying the two-body correlation functions we find
that a measurement of the momentum distribution of the density and spin
response functions allows one to access separately the normal and anomalous
densities. The change in sign at low momentum transfer of the density response
function signals the transition between a BEC and a BCS regimes, characterized
by small and large pairs, respectively. This change in sign of the density
response function represents an unambiguous signature of the BEC to BCS
crossover. Also, we predict spin rotational symmetry-breaking in this system
Four-particle condensate in strongly coupled fermion systems
Four-particle correlations in fermion systems at finite temperatures are
investigated with special attention to the formation of a condensate. Instead
of the instability of the normal state with respect to the onset of pairing
described by the Gorkov equation, a new equation is obtained which describes
the onset of quartetting. Within a model calculation for symmetric nuclear
matter, we find that below a critical density, the four-particle condensation
(alpha-like quartetting) is favored over deuteron condensation (triplet
pairing). This pairing-quartetting competition is expected to be a general
feature of interacting fermion systems, such as the excition-biexciton system
in excited semiconductors. Possible experimental consequences are pointed out.Comment: LaTeX, 11 pages, 2 figures, uses psfig.sty (included), to be
published in Phys. Rev. Lett., tentatively scheduled for 13 April 1998
(Volume 80, Number 15
A New Interpretation of Flux Quantization
We study the effect of Aharonov-Bohm flux on the superconducting state in
metallic cylinders. Although Byers and Yang attributed flux quantization to the
flux-dependent minimum of kinetic energies of the Cooper pairs, it is shown
that kinetic energies do not produce any discernible oscillations in the free
energy of the superconducting state (relative to that of normal state) as a
function of the flux. This result is indeed anticipated by the observation of
persistent current in normal metal rings at low temperature. Instead, we have
found that pairing interaction depends on the flux, leading to flux
quantization. When the flux ) is given by (with
integer n), the pairing interaction and the free energy become unchanged (even
n) or almost unchanged (odd n), due to degenerate-state pairing resulting from
the energy level crossing. As a result, flux quantization and Little-Parks
oscillations follow.Comment: Revtex, 10 pages, 6 figures, For more information, send me an e-mail
at [email protected]
Dynamical moment of inertia and quadrupole vibrations in rotating nuclei
The contribution of quantum shape fluctuations to inertial properties of
rotating nuclei has been analysed within the self-consistent one-dimensional
cranking oscillator model. It is shown that in even-even nuclei the dynamical
moment of inertia calculated in the mean field approximation is equivalent to
the Thouless-Valatin moment of inertia calculated in the random phase
approximation if and only if the self-consistent conditions for the mean field
are fulfilled.Comment: 4 pages, 2 figure
Two-particle pairing and phase separation in a two-dimensional Bose-gas with one or two sorts of bosons
We present a phase diagram for a dilute two-dimensional Bose-gas on a
lattice. For one sort of boson we consider a realistic case of the van der
Waals interaction between particles with a strong hard-core repulsion and a
van der Waals attractive tail . For , being a hopping
amplitude, the phase diagram of the system contains regions of the usual
one-particle Bose-Einstein condensation (BEC). However for we have total
phase separation on a Mott-Hubbard Bose solid and a dilute Bose gas. For two
sorts of structureless bosons described by the two band Hubbard model an s-wave
pairing of the two bosons of different sort is possible.
The results we obtained should be important for different Bose systems,
including submonolayers of He, excitons in semiconductors, Schwinger bosons
in magnetic systems and holons in HTSC. In the HTSC case a possibility of
two-holon pairing in the slave-bosons theories of superconductivity can restore
a required charge of a Cooper pair.Comment: 10 pages, 2 figure
Resonance superfluidity in a quantum degenerate Fermi gas
We consider the superfluid phase transition that arises when a Feshbach
resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider
a specific resonance in potassium-40, and find that for achievable experimental
conditions, the transition to a superfluid phase is possible at the high
critical temperature of about 0.5 T_F. Observation of superfluidity in this
regime would provide the opportunity to experimentally study the crossover from
the superfluid phase of weakly-coupled fermions to the Bose-Einstein
condensation of strongly-bound composite bosons.Comment: 4 pages, 3 figure
Vortex stabilization in a small rotating asymmetric Bose-Einstein condensate
We use a variational method to investigate the ground-state phase diagram of
a small, asymmetric Bose-Einstein condensate with respect to the dimensionless
interparticle interaction strength and the applied external rotation
speed . For a given , the transition lines between no-vortex
and vortex states are shifted toward higher relative to those for the
symmetric case. We also find a re-entrant behavior, where the number of vortex
cores can decrease for large . In addition, stabilizing a vortex in a
rotating asymmetric trap requires a minimum interaction strength. For a given
asymmetry, the evolution of the variational parameters with increasing
shows two different types of transitions (sharp or continuous), depending on
the strength of the interaction. We also investigate transitions to states with
higher vorticity; the corresponding angular momentum increases continuously as
a function of
Single Spin Superconductivity: Formulation and Ginzburg-Landau Theory
We describe a novel superconducting phase that arises due to a pairing
instability of the half-metallic antiferromagnetic (HM AFM) normal state. This
single spin superconducting (SSS) phase contains broken time reversal symmetry
in addition to broken gauge symmetry, the former due to the underlying magnetic
order in the normal state. A classification of normal state symmetries leads to
the conclusion that the HM AFM normal phase whose point group contains the
inversion operator contains the least symmetry possible which still allows for
a zero momentum pairing instability. The Ginzburg-Landau free energy for the
superconducting order parameter is constructed consistent with the symmetry of
the normal phase, electromagnetic gauge invariance and the crystallographic
point group symmetry including inversion. For cubic, hexagonal and tetragonal
point groups, the possible symmetries of the superconducting phase are
classified, and the free energy is used to construct a generalized phase
diagram. We identify the leading candidate out of the possible SSS phases for
each point group. The symmetry of the superconducting phase is used to
determine the cases where the gap function has generic zeros (point or line
nodes) on the Fermi surface. Such nodes always occur, hence thermodynamic
properties will have power-law behavior at low temperature.Comment: 39 pages, RevTeX, 4 PostScript figures included, submitted to Phys.
Rev.
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