2,824 research outputs found
Dynamic Density Functional theory for steady currents: Application to colloidal particles in narrow channels
We present the theoretical analysis of the steady state currents and density
distributions of particles moving with Langevin dynamics, under the effects of
an external potential displaced at constant rate. The Dynamic Density
Functional (DDF) formalism is used to introduce the effects of the molecular
interactions, from the equilibrium Helmholtz free energy density functional. We
analyzed the generic form of the DDF for one-dimensional external potentials
and the limits of strong and weak potential barriers. The ideal gas case is
solved in a closed form for generic potentials and compared with the numerical
results for hard-rods, with the exact equilibrium free energy. The results may
be of relevance for microfluidic devices, with colloidal particles moving along
narrow channels, if external driving forces have to compete with the brownian
fluctuations and the interaction forces of the particles
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
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
Persistence of mean-field features in the energy spectrum of small arrays of Bose-Einstein condensates
The Bose-Hubbard Hamiltonian capturing the essential physics of the arrays of
interacting Bose-Einstein condensates is addressed, focusing on arrays
consisting of two (dimer) and three (trimer) sites. In the former case, some
results concerning the persistence of mean-field features in the energy
spectrum of the symmetric dimer are extended to the asymmetric version of the
system, where the two sites are characterized by different on-site energies.
Based on a previous systematic study of the mean-field limit of the trimer,
where the dynamics is exhaustively described in terms of its fixed points for
every choice of the significant parameters, an interesting mapping between the
dimer and the trimer is emphasized and used as a guide in investigating the
persistence of mean-field features in the rather complex energy spectrum of the
trimer. These results form the basis for the systematic investigation of the
purely quantum trimer extending and completing the existing mean-field
analysis. In this respect we recall that, similar to larger arrays, the trimer
is characterized by a non-integrable mean-field dynamics featuring chaotic
trajectories. Hence, the correspondence between mean-field fixed points and
quantum energy levels emphasized in the present work may provide a key to
investigate the quantum counterpart of classical instability.Comment: 12 pages, 6 figures, to appear on Journal of Physics B (Special
Issue: Levico BEC workshop). Publication status update
Efficient Monte Carlo Simulation of Biological Aging
A bit-string model of biological life-histories is parallelized, with
hundreds of millions of individuals. It gives the desired drastic decay of
survival probabilities with increasing age for 32 age intervals.Comment: PostScript file to appear in Int.J.Mod.Phys.
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
Mean-field phase diagram for Bose-Hubbard Hamiltonians with random hopping
The zero-temperature phase diagram for ultracold Bosons in a random 1D
potential is obtained through a site-decoupling mean-field scheme performed
over a Bose-Hubbard (BH) Hamiltonian whose hopping term is considered as a
random variable. As for the model with random on-site potential, the presence
of disorder leads to the appearance of a Bose-glass phase. The different phases
-i.e. Mott insulator, superfluid, Bose-glass- are characterized in terms of
condensate fraction and superfluid fraction. Furthermore, the boundary of the
Mott lobes are related to an off-diagonal Anderson model featuring the same
disorder distribution as the original BH Hamiltonian.Comment: 7 pages, 6 figures. Submitted to Laser Physic
Gutzwiller approach to the Bose-Hubbard model with random local impurities
Recently it has been suggested that fermions whose hopping amplitude is
quenched to extremely low values provide a convenient source of local disorder
for lattice bosonic systems realized in current experiment on ultracold atoms.
Here we investigate the phase diagram of such systems, which provide the
experimental realization of a Bose-Hubbard model whose local potentials are
randomly extracted from a binary distribution. Adopting a site-dependent
Gutzwiller description of the state of the system, we address one- and
two-dimensional lattices and obtain results agreeing with previous findings, as
far as the compressibility of the system is concerned. We discuss the expected
peaks in the experimental excitation spectrum of the system, related to the
incompressible phases, and the superfluid character of the {\it partially
compressible phases} characterizing the phase diagram of systems with binary
disorder. In our investigation we make use of several analytical results whose
derivation is described in the appendices, and whose validity is not limited to
the system under concern.Comment: 12 pages, 5 figures. Some adjustments made to the manuscript and to
figures. A few relevant observations added throughout the manuscript.
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