64 research outputs found
Some exact results for a trapped quantum gas at finite temperature
We present closed analytical expressions for the particle and kinetic energy
spatial densities at finite temperatures for a system of noninteracting
fermions (bosons) trapped in a d-dimensional harmonic oscillator potential. For
d=2 and 3, exact expressions for the N-particle densities are used to calculate
perturbatively the temperature dependence of the splittings of the energy
levels in a given shell due to a very weak interparticle interaction in a
dilute Fermi gas. In two dimensions, we obtain analytically the surprising
result that the |l|-degeneracy in a harmonic oscillator shell is not lifted in
the lowest order even when the exact, rather than the Thomas-Fermi expression
for the particle density is used. We also demonstrate rigorously (in two
dimensions) the reduction of the exact zero-temperature fermionic expressions
to the Thomas-Fermi form in the large-N limit.Comment: 14 pages, 4 figures include
Strongly correlated phases in rapidly rotating Bose gases
We consider a system of trapped spinless bosons interacting with a repulsive
potential and subject to rotation. In the limit of rapid rotation and small
scattering length, we rigorously show that the ground state energy converges to
that of a simplified model Hamiltonian with contact interaction projected onto
the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue
of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles,
we also prove convergence of states; in particular, in a certain regime we show
convergence towards the bosonic Laughlin wavefunction. This is the first
rigorous justification of the effective FQHE Hamiltonian for rapidly rotating
Bose gases. We review previous results on this effective Hamiltonian and
outline open problems.Comment: AMSLaTeX, 23 page
Entanglement in the Quantum Heisenberg XY model
We study the entanglement in the quantum Heisenberg XY model in which the
so-called W entangled states can be generated for 3 or 4 qubits. By the concept
of concurrence, we study the entanglement in the time evolution of the XY
model. We investigate the thermal entanglement in the two-qubit isotropic XY
model with a magnetic field and in the anisotropic XY model, and find that the
thermal entanglement exists for both ferromagnetic and antiferromagnetic cases.
Some evidences of the quantum phase transition also appear in these simple
models.Comment: 7 pages, 6 figs, revised version submitted to Phys. Rev.
A short proof of stability of topological order under local perturbations
Recently, the stability of certain topological phases of matter under weak
perturbations was proven. Here, we present a short, alternate proof of the same
result. We consider models of topological quantum order for which the
unperturbed Hamiltonian can be written as a sum of local pairwise
commuting projectors on a -dimensional lattice. We consider a perturbed
Hamiltonian involving a generic perturbation that can be written
as a sum of short-range bounded-norm interactions. We prove that if the
strength of is below a constant threshold value then has well-defined
spectral bands originating from the low-lying eigenvalues of . These bands
are separated from the rest of the spectrum and from each other by a constant
gap. The width of the band originating from the smallest eigenvalue of
decays faster than any power of the lattice size.Comment: 15 page
Geometric effects on T-breaking in p+ip and d+id superconductors
Superconducting order parameters that change phase around the Fermi surface
modify Josephson tunneling behavior, as in the phase-sensitive measurements
that confirmed order in the cuprates. This paper studies Josephson coupling
when the individual grains break time-reversal symmetry; the specific cases
considered are and , which may appear in SrRuO and
NaCoO(HO) respectively. -breaking order parameters
lead to frustrating phases when not all grains have the same sign of
time-reversal symmetry breaking, and the effects of these frustrating phases
depend sensitively on geometry for 2D arrays of coupled grains. These systems
can show perfect superconducting order with or without macroscopic
-breaking. The honeycomb lattice of superconducting grains has a
superconducting phase with no spontaneous breaking of but instead power-law
correlations. The superconducting transition in this case is driven by binding
of fractional vortices, and the zero-temperature criticality realizes a
generalization of Baxter's three-color model.Comment: 8 page
The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin
We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in
the absence of an external field. Spin wave theory suggests that in a suitable
temperature regime the system behaves effectively as a system of
non-interacting bosons (magnons). We prove this fact at the level of the
specific free energy: if and the inverse temperature in such a way that stays constant, we rigorously show that
the free energy per unit volume converges to the one suggested by spin wave
theory. The proof is based on the localization of the system in small boxes and
on upper and lower bounds on the local free energy, and it also provides
explicit error bounds on the remainder.Comment: 11 pages, pdfLate
Ising Spins on Thin Graphs
The Ising model on ``thin'' graphs (standard Feynman diagrams) displays
several interesting properties. For ferromagnetic couplings there is a mean
field phase transition at the corresponding Bethe lattice transition point. For
antiferromagnetic couplings the replica trick gives some evidence for a spin
glass phase. In this paper we investigate both the ferromagnetic and
antiferromagnetic models with the aid of simulations. We confirm the Bethe
lattice values of the critical points for the ferromagnetic model on
and graphs and examine the putative spin glass phase in the
antiferromagnetic model by looking at the overlap between replicas in a
quenched ensemble of graphs. We also compare the Ising results with those for
higher state Potts models and Ising models on ``fat'' graphs, such as those
used in 2D gravity simulations.Comment: LaTeX 13 pages + 9 postscript figures, COLO-HEP-340,
LPTHE-Orsay-94-6
Spin-dependent thermoelectric transport coefficients in near-perfect quantum wires
Thermoelectric transport coefficients are determined for semiconductor
quantum wires with weak thickness fluctuations. Such systems exhibit anomalies
in conductance near 1/4 and 3/4 of 2e^2/h on the rising edge to the first
conductance plateau, explained by singlet and triplet resonances of conducting
electrons with a single weakly bound electron in the wire [T. Rejec, A. Ramsak,
and J.H. Jefferson, Phys. Rev. B 62, 12985 (2000)]. We extend this work to
study the Seebeck thermopower coefficient and linear thermal conductance within
the framework of the Landauer-Buettiker formalism, which also exhibit anomalous
structures. These features are generic and robust, surviving to temperatures of
a few degrees. It is shown quantitatively how at elevated temperatures thermal
conductance progressively deviates from the Wiedemann-Franz law.Comment: To appear in Phys. Rev. B 2002; 3 figure
Disorder Induced Phase Transition in a Random Quantum Antiferromagnet
A two-dimensional Heisenberg model with random antiferromagnetic
nearest-neighbor exchange is studied using quantum Monte Carlo techniques. As
the strength of the randomness is increased, the system undergoes a transition
from an antiferromagnetically ordered ground state to a gapless disordered
state. The finite-size scaling of the staggered structure factor and
susceptibility is consistent with a dynamic exponent .Comment: Revtex 3.0, 10 pages + 5 postscript figures available upon request,
UCSBTH-94-1
Testing one-body density functionals on a solvable model
There are several physically motivated density matrix functionals in the
literature, built from the knowledge of the natural orbitals and the occupation
numbers of the one-body reduced density matrix. With the help of the equivalent
phase-space formalism, we thoroughly test some of the most popular of those
functionals on a completely solvable model.Comment: Latex, 16 pages, 4 figure
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