540 research outputs found
Nash Equilibria in the Response Strategy of Correlated Games
In nature and society problems arise when different interests are difficult
to reconcile, which are modeled in game theory. While most applications assume
uncorrelated games, a more detailed modeling is necessary to consider the
correlations that influence the decisions of the players. The current theory
for correlated games, however, enforces the players to obey the instructions
from a third party or "correlation device" to reach equilibrium, but this
cannot be achieved for all initial correlations. We extend here the existing
framework of correlated games and find that there are other interesting and
previously unknown Nash equilibria that make use of correlations to obtain the
best payoff. This is achieved by allowing the players the freedom to follow or
not to follow the suggestions of the correlation device. By assigning
independent probabilities to follow every possible suggestion, the players
engage in a response game that turns out to have a rich structure of Nash
equilibria that goes beyond the correlated equilibrium and mixed-strategy
solutions. We determine the Nash equilibria for all possible correlated
Snowdrift games, which we find to be describable by Ising Models in thermal
equilibrium. We believe that our approach paves the way to a study of
correlations in games that uncovers the existence of interesting underlying
interaction mechanisms, without compromising the independence of the players
Feshbach molecules in a one-dimensional Fermi gas
We consider the binding energy and the wave function of Feshbach molecules
confined in a one-dimensional matter waveguide. We compare the binding energy
with the experiment of Moritz et al. and find excellent agreement for the full
magnetic field range explored experimentally.Comment: Extended original comment to article form. Replaced original figure
with 2 new figures. 1 page + 2 figure
Quantum phases in a resonantly-interacting Bose-Fermi mixture
We consider a resonantly-interacting Bose-Fermi mixture of K and
Rb atoms in an optical lattice. We show that by using a red-detuned
optical lattice the mixture can be accurately described by a generalized
Hubbard model for K and Rb atoms, and K-Rb
molecules. The microscopic parameters of this model are fully determined by the
details of the optical lattice and the interspecies Feshbach resonance in the
absence of the lattice. We predict a quantum phase transition to occur in this
system already at low atomic filling fraction, and present the phase diagram as
a function of the temperature and the applied magnetic field.Comment: 4 pages, 3 figure
Low-dimensional Bose gases
We present an improved many-body T-matrix theory for partially Bose-Einstein
condensed atomic gases by treating the phase fluctuations exactly. The
resulting mean-field theory is valid in arbitrary dimensions and able to
describe the low-temperature crossover between three, two and one-dimensional
Bose gases. When applied to a degenerate two-dimensional atomic hydrogen gas,
we obtain a reduction of the three-body recombination rate which compares
favorably with experiment. Supplementing the mean-field theory with a
renormalization-group approach to treat the critical fluctuations, we also
incorporate into the theory the Kosterlitz-Thouless transition that occurs in a
homogeneous Bose gas in two dimensions. In particular, we calculate the
critical conditions for the Kosterlitz-Thouless phase transition as a function
of the microscopic parameters of the theory. The proposed theory is further
applied to a trapped one-dimensional Bose gas, where we find good agreement
with exact numerical results obtained by solving a nonlinear Langevin field
equation.Comment: 14 pages, 13 figures, revte
BEC-BCS crossover in an optical lattice
We present the microscopic theory for the BEC-BCS crossover of an atomic
Fermi gas in an optical lattice, showing that the Feshbach resonance underlying
the crossover in principle induces strong multiband effects. Nevertheless, the
BEC-BCS crossover itself can be described by a single-band model since it
occurs at magnetic fields that are relatively far away from the Feshbach
resonance. A criterion is proposed for the latter, which is obeyed by most
known Feshbach resonances in ultracold atomic gases.Comment: 4 pages, 3 figure
Inelastic light scattering from a Mott insulator
We propose to use Bragg spectroscopy to measure the excitation spectrum of
the Mott insulator state of an atomic Bose gas in an optical lattice. We
calculate the structure factor of the Mott insulator taking into account both
the selfenergy corrections of the atoms and the corresponding dressing of the
atom-photon interaction. We determine the scattering rate of photons in the
stimulated Raman transition and show that by measuring this scattering rate in
an experiment, in particular the excitation gap of the Mott insulator can be
determined.Comment: 4 pages, 7 figures, LaTeX, submitted to PR
Pairing of a trapped resonantly-interacting fermion mixture with unequal spin populations
We consider the phase separation of a trapped atomic mixture of fermions with
unequal spin populations near a Feshbach resonance. In particular, we determine
the density profile of the two spin states and compare with the recent
experiments of Partridge et al. (cond-mat/0511752). Overall we find quite good
agreement. We identify the remaining discrepancies and pose them as open
problems.Comment: 4 figures, 4+ pages, revtex
The bosonic Kondo effect
The Kondo effect is associated with the formation of a many-body ground state
that contains a quantum-mechanical entanglement between a (localized) fermion
and the free fermions. We show that a bosonic version of the Kondo effect can
occur in degenerate atomic Fermi gases near the Feshbach resonance. We also
discuss how this bosonic Kondo effect can be observed experimentally.Comment: 4 pages, 2 figures, some references added, some removed. More
comments adde
Cooper pair formation in trapped atomic Fermi gases
We apply the closed time-path formalism to evaluate the dynamics of the BCS
transition to the superfluid state in trapped atomic Li. We find that the
Fokker-Planck equation for the probability distribution of the order parameter
is, sufficiently close to the critical temperature, identical to the equation
that describes the switching on of a single-mode laser.Comment: 4 pages revtex including 1 figur
Phase coherence in quasicondensate experiments: an ab initio analysis via the stochastic Gross-Pitaevskii equation
We perform an ab initio analysis of the temperature dependence of the phase
coherence length of finite temperature, quasi-one-dimensional Bose gases
measured in the experiments of Richard et al. (Phys. Rev. Lett. 91, 010405
(2003)) and Hugbart et al. (Eur. Phys. J. D 35, 155-163 (2005)), finding very
good agreement across the entire observed temperature range
(). Our analysis is based on the one-dimensional stochastic
Gross-Pitaevskii equation, modified to self-consistently account for
transverse, quasi-one-dimensional effects, thus making it a valid model in the
regime . We also numerically implement an
alternative identification of , based on direct analysis of the
distribution of phases in a stochastic treatment.Comment: Amended manuscript with improved agreement to experiment, following
some additional clarifications by Mathilde Hugbart and Fabrice Gerbier and
useful comments by the reviewer; accepted for publication in Physical Review
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