1,289 research outputs found
Analytical mean-field approach to the phase-diagram of ultracold bosons in optical superlattices
We report a multiple-site mean-field analysis of the zero-temperature phase
diagram for ultracold bosons in realistic optical superlattices. The system of
interacting bosons is described by a Bose-Hubbard model whose site-dependent
parameters reflect the nontrivial periodicity of the optical superlattice. An
analytic approach is formulated based on the analysis of the stability of a
fixed-point of the map defined by the self-consistency condition inherent in
the mean-field approximation. The experimentally relevant case of the period-2
one-dimensional superlattice is briefly discussed. In particular, it is shown
that, for a special choice of the superlattice parameters, the half-filling
insulator domain features an unusual loophole shape that the single-site
mean-field approach fails to capture.Comment: 7 pages, 1 figur
Complex phase-ordering of the one-dimensional Heisenberg model with conserved order parameter
We study the phase-ordering kinetics of the one-dimensional Heisenberg model
with conserved order parameter, by means of scaling arguments and numerical
simulations. We find a rich dynamical pattern with a regime characterized by
two distinct growing lengths. Spins are found to be coplanar over regions of a
typical size , while inside these regions smooth rotations associated
to a smaller length are observed. Two different and coexisting
ordering mechanisms are associated to these lengths, leading to different
growth laws and violating dynamical
scaling.Comment: 14 pages, 8 figures. To appear on Phys. Rev. E (2009
Strong-coupling expansions for the topologically inhomogeneous Bose-Hubbard model
We consider a Bose-Hubbard model with an arbitrary hopping term and provide
the boundary of the insulating phase thereof in terms of third-order strong
coupling perturbative expansions for the ground state energy. In the general
case two previously unreported terms occur, arising from triangular loops and
hopping inhomogeneities, respectively. Quite interestingly the latter involves
the entire spectrum of the hopping matrix rather than its maximal eigenpair,
like the remaining perturbative terms. We also show that hopping
inhomogeneities produce a first order correction in the local density of
bosons. Our results apply to ultracold bosons trapped in confining potentials
with arbitrary topology, including the realistic case of optical superlattices
with uneven hopping amplitudes. Significant examples are provided. Furthermore,
our results can be extented to magnetically tuned transitions in Josephson
junction arrays.Comment: 5 pages, 2 figures,final versio
The inverse Mermin-Wagner theorem for classical spin models on graphs
In this letter we present the inversion of the Mermin-Wagner theorem on
graphs, by proving the existence of spontaneous magnetization at finite
temperature for classical spin models on transient on the average (TOA) graphs,
i.e. graphs where a random walker returns to its starting point with an average
probability . This result, which is here proven for models with
O(n) symmetry, includes as a particular case , providing a very general
condition for spontaneous symmetry breaking on inhomogeneous structures even
for the Ising model.Comment: 4 Pages, to appear on PR
Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
We analyze the quantum phase transition in the Bose-Hubbard model borrowing
two tools from quantum-information theory, i.e. the ground-state fidelity and
entanglement measures. We consider systems at unitary filling comprising up to
50 sites and show for the first time that a finite-size scaling analysis of
these quantities provides excellent estimates for the quantum critical point.We
conclude that fidelity is particularly suited for revealing a quantum phase
transition and pinning down the critical point thereof, while the success of
entanglement measures depends on the mechanisms governing the transition.Comment: 7 pages, 5 figures (endfloats used due to problems with figures and
latex. Sorry about that); final version, similar to the published on
The Type-problem on the Average for random walks on graphs
When averages over all starting points are considered, the Type Problem for
the recurrence or transience of a simple random walk on an inhomogeneous
network in general differs from the usual "local" Type Problem. This difference
leads to a new classification of inhomogeneous discrete structures in terms of
{\it recurrence} and {\it transience} {\it on the average}, describing their
large scale topology from a "statistical" point of view. In this paper we
analyze this classification and the properties connected to it, showing how the
average behavior affects the thermodynamic properties of statistical models on
graphs.Comment: 10 pages, 3 figures. to appear on EPJ
Rare events and scaling properties in field-induced anomalous dynamics
We show that, in a broad class of continuous time random walks (CTRW), a
small external field can turn diffusion from standard into anomalous. We
illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in
disordered and glassy materials, and in the L\'evy walk process, which
describes superdiffusion within inhomogeneous media. For both models, in the
presence of an external field, rare events induce a singular behavior in the
originally Gaussian displacements distribution, giving rise to power-law tails.
Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating
waiting times and of a drift yields a non-Gaussian distribution characterized
by long spatial tails and strong anomalous superdiffusion.Comment: 11 pages, 3 figure
Quantum signatures of self-trapping transition in attractive lattice bosons
We consider the Bose-Hubbard model describing attractive bosonic particles
hopping across the sites of a translation-invariant lattice, and compare the
relevant ground-state properties with those of the corresponding
symmetry-breaking semiclassical nonlinear theory. The introduction of a
suitable measure allows us to highlight many correspondences between the
nonlinear theory and the inherently linear quantum theory, characterized by the
well-known self-trapping phenomenon. In particular we demonstrate that the
localization properties and bifurcation pattern of the semiclassical
ground-state can be clearly recognized at the quantum level. Our analysis
highlights a finite-number effect.Comment: 9 pages, 8 figure
Scaling properties of field-induced superdiffusion in Continous Time Random Walks
We consider a broad class of Continuous Time Random Walks with large
fluctuations effects in space and time distributions: a random walk with
trapping, describing subdiffusion in disordered and glassy materials, and a
L\'evy walk process, often used to model superdiffusive effects in
inhomogeneous materials. We derive the scaling form of the probability
distributions and the asymptotic properties of all its moments in the presence
of a field by two powerful techniques, based on matching conditions and on the
estimate of the contribution of rare events to power-law tails in a field.Comment: 17 pages, 8 figures, Proceedings of the Conference "Small system
nonequilibrium fluctuations, dynamics and stochastics, and anomalous
behavior", KITPC, Beijing, Chin
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