146 research outputs found
Trace of broken integrability in stationary correlation properties
We show that the breaking of integrability in the fundamental one-dimensional
model of bosons with contact interactions has consequences on the stationary
correlation properties of the system. We calculate the energies and correlation
functions of the integrable Lieb-Liniger case, comparing the exact Bethe-ansatz
solution with a corresponding Jastrow ansatz. Then we examine the
non-integrable case of different interaction strengths between each pair of
atoms by means of a variationally optimized Jastrow ansatz, proposed in analogy
to the Laughlin ansatz. We show that properties of the integrable state are
more stable close to the Tonks-Girardeau regime than for weak interactions. All
energies and correlation functions are given in terms of explicit analytical
expressions enabled by the Jastrow ansatz. We finally compare the correlations
of the integrable and non-integrable cases and show that apart from symmetry
breaking the behavior changes dramatically, with additional and more pronounced
maxima and minima interference peaks appearing.Comment: 19 pages, 5 figures. Published with minor change
Universality and quantum criticality of the one-dimensional spinor Bose gas
We investigate the universal thermodynamics of the two-component
one-dimensional Bose gas with contact interactions in the vicinity of the
quantum critical point separating the vacuum and the ferromagnetic liquid
regime. We find that the quantum critical region belongs to the universality
class of the spin-degenerate impenetrable particle gas which, surprisingly, is
very different from the single-component case and identify its boundaries with
the peaks of the specific heat. In addition, we show that the compressibility
Wilson ratio, which quantifies the relative strength of thermal and quantum
fluctuations, serves as a good discriminator of the quantum regimes near the
quantum critical point. Remarkably, in the Tonks-Girardeau regime the universal
contact develops a pronounced minimum, reflected in a counterintuitive
narrowing of the momentum distribution as we increase the temperature. This
momentum reconstruction, also present at low and intermediate momenta, signals
the transition from the ferromagnetic to the spin-incoherent Luttinger liquid
phase and can be detected in current experiments with ultracold atomic gases in
optical lattices.Comment: 5+2 pages, RevTeX 4.
The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz
The purpose of the ''bootstrap program'' for integrable quantum field
theories in 1+1 dimensions is to construct explicitly a model in terms of its
Wightman functions. In this article, this program is mainly illustrated in
terms of the sinh-Gordon model and the SU(N) Gross-Neveu model. The nested
off-shell Bethe ansatz for an SU(N) factorizing S-matrix is constructed. We
review some previous results on sinh-Gordon form factors and the quantum
operator field equation. The problem of how to sum over intermediate states is
considered in the short distance limit of the two point Wightman function for
the sinh-Gordon model.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Emergence of junction dynamics in a strongly interacting Bose mixture
We study the dynamics of a one-dimensional system composed of a bosonic
background and one impurity in single- and double-well trapping geometries. In
the limit of strong interactions, this system can be modeled by a spin chain
where the exchange coefficients are determined by the geometry of the trap. We
observe non-trivial dynamics when the repulsion between the impurity and the
background is dominant. In this regime, the system exhibits oscillations that
resemble the dynamics of a Josephson junction. Furthermore, the double-well
geometry allows for an enhancement in the tunneling as compared to the
single-well case.Comment: 20 pages, 9 figure
Dynamical realization of magnetic states in a strongly interacting Bose mixture
We describe the dynamical preparation of magnetic states in a strongly
interacting two-component Bose gas in a harmonic trap. By mapping this system
to an effective spin chain model, we obtain the dynamical spin densities and
the fidelities for a few-body system. We show that the spatial profiles transit
between ferromagnetic and antiferromagnetic states as the intraspecies
interaction parameter is slowly increased.Comment: 6 pages, 7 figure
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