2,701 research outputs found
Fermionization and fractional statistics in the strongly interacting one-dimensional Bose gas
We discuss recent results on the relation between the strongly interacting
one-dimensional Bose gas and a gas of ideal particles obeying nonmutual
generalized exclusion statistics (GES). The thermodynamic properties considered
include the statistical profiles, the specific heat and local pair
correlations. In the strong coupling limit , the
Tonks-Girardeau gas, the equivalence is with Fermi statistics. The deviation
from Fermi statistics during boson fermionization for finite but large
interaction strength is described by the relation , where is a measure of the GES. This gives a quantitative
description of the fermionization process. In this sense the recent
experimental measurement of local pair correlations in a 1D Bose gas of
Rb atoms also provides a measure of the deviation of the GES parameter
away from the pure Fermi statistics value . Other
thermodynamic properties, such as the distribution profiles and the specific
heat, are also sensitive to the statistics. They also thus provide a way of
exploring fractional statistics in the strongly interacting 1D Bose gas.Comment: 7 pages, 4 figure
Ferromagnetic behaviour in the strongly interacting two-component Bose gas
We investigate the low temperature behaviour of the integrable 1D
two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find
that for strong coupling the characteristics of the thermodynamics at low
temperatures are quantitatively affected by the spin ferromagnetic states,
which are described by an effective ferromagnetic Heisenberg chain. The free
energy, specific heat, susceptibility and local pair correlation function are
calculated for various physical regimes in terms of temperature and interaction
strength. These thermodynamic properties reveal spin effects which are
significantly different than those of the spinless Bose gas. The zero-field
susceptibility for finite strong repulsion exceeds that of a free spin
paramagnet. The critical exponents of the specific heat and
the susceptibility are indicative of the ferromagnetic
signature of the two-component spinor Bose gas. Our analytic results are
consistent with general arguments by Eisenberg and Lieb for polarized spinor
bosons.Comment: 15 pages, 6 figures, revised version, references added, minor
correction
Yang-Yang method for the thermodynamics of one-dimensional multi-component interacting fermions
Using Yang and Yang's particle-hole description, we present a thorough
derivation of the thermodynamic Bethe ansatz equations for a general
fermionic system in one-dimension for both the repulsive and
attractive regimes under the presence of an external magnetic field. These
equations are derived from Sutherland's Bethe ansatz equations by using the
spin-string hypothesis. The Bethe ansatz root patterns for the attractive case
are discussed in detail. The relationship between the various phases of the
magnetic phase diagrams and the external magnetic fields is given for the
attractive case. We also give a quantitative description of the ground state
energies for both strongly repulsive and strongly attractive regimes.Comment: 22 pages, 2 figures, slight improvements, some extra reference
Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases
We investigate pairing and quantum phase transitions in the one-dimensional
two-component Fermi atomic gas in an external field. The phase diagram,
critical fields, magnetization and local pairing correlation are obtained
analytically via the exact thermodynamic Bethe ansatz solution. At zero
temperature, bound pairs of fermions with opposite spin states form a singlet
ground state when the external field . A completely ferromagnetic
phase without pairing occurs when the external field . In the
region we observe a mixed phase of matter in which paired
and unpaired atoms coexist. The phase diagram is reminiscent of that of type II
superconductors. For temperatures below the degenerate temperature and in the
absence of an external field, the bound pairs of fermions form hard-core bosons
obeying generalized exclusion statistics.Comment: 9 pages, 5 figures, expanded version with additional text, references
and figure
Generalized exclusion statistics and degenerate signature of strongly interacting anyons
We show that below the degenerate temperature the distribution profiles of
strongly interacting anyons in one dimension coincide with the most probable
distributions of ideal particles obeying generalized exclusion statistics
(GES). In the strongly interacting regime the thermodynamics and the local
two-particle correlation function derived from the GES are seen to agree for
low temperatures with the results derived for the anyon model using the
thermodynamic Bethe Ansatz. The anyonic and dynamical interactions implement a
continuous range of GES, providing a signature of strongly interacting anyons,
including the strongly interacting one-dimensional Bose gas.Comment: 7 pages, 3 figures, expanded versio
The 1D interacting Bose gas in a hard wall box
We consider the integrable one-dimensional delta-function interacting Bose
gas in a hard wall box which is exactly solved via the coordinate Bethe Ansatz.
The ground state energy, including the surface energy, is derived from the
Lieb-Liniger type integral equations. The leading and correction terms are
obtained in the weak coupling and strong coupling regimes from both the
discrete Bethe equations and the integral equations. This allows the
investigation of both finite-size and boundary effects in the integrable model.
We also study the Luttinger liquid behaviour by calculating Luttinger
parameters and correlations. The hard wall boundary conditions are seen to have
a strong effect on the ground state energy and phase correlations in the weak
coupling regime. Enhancement of the local two-body correlations is shown by
application of the Hellmann-Feynman theorem.Comment: 23 pages, 7 figures. Improved version. Extra figure added for the
weak coupling regime. New expression for the interaction-dependent cloud size
and additional reference
Collective dispersion relations for the 1D interacting two-component Bose and Fermi gases
We investigate the elementary excitations of charge and spin degrees for the
1D interacting two-component Bose and Fermi gases by means of the discrete
Bethe ansatz equations. Analytic results in the limiting cases of strong and
weak interactions are derived, where the Bosons are treated in the repulsive
and the fermions in the strongly attractive regime. We confirm and complement
results obtained previously from the Bethe ansatz equations in the
thermodynamic limit.Comment: 12 pages, 1 figur
Exact solution for random walks on the triangular lattice with absorbing boundaries
The problem of a random walk on a finite triangular lattice with a single
interior source point and zig-zag absorbing boundaries is solved exactly. This
problem has been previously considered intractable.Comment: 10 pages, Latex, IOP macro
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