4 research outputs found
Dynamics of a many-particle Landau-Zener model: inverse sweep
We consider dynamics of a slowly time-dependent Dicke model, which represents
a many-body generalization of the Landau-Zener model. In particular, the model
describes narrow Feshbach resonance passage in an ultracold gas of Fermi atoms.
Adiabaticity is destroyed when a parameter crosses a critical value, even at
very slow sweeping rates of a parameter. The dynamics crucially depends on
direction of the sweep. We apply our recent analysis [A.P. Itin, P. Torma,
arXiv:0901.4778v1] to the "inverse" sweep through the resonance, corresponding
(in a context of Feshbach resonance passage) to dissociation of molecules. On a
level of the mean-field approximation, the dynamics is equivalent to a
molecular condensate formation from Bose atoms within a two-mode model. Mapping
the system to a Painlev\'e equation allows us to calculate deviation from
adiabaticity at very slow sweeps analytically.Comment: 3 pages. Submitted to CEWQO 2009 on 14th Februar
Near-adiabatic parameter changes in correlated systems: Influence of the ramp protocol on the excitation energy
We study the excitation energy for slow changes of the hopping parameter in
the Falicov-Kimball model with nonequilibrium dynamical mean-field theory. The
excitation energy vanishes algebraically for long ramp times with an exponent
that depends on whether the ramp takes place within the metallic phase, within
the insulating phase, or across the Mott transition line. For ramps within
metallic or insulating phase the exponents are in agreement with a perturbative
analysis for small ramps. The perturbative expression quite generally shows
that the exponent depends explicitly on the spectrum of the system in the
initial state and on the smoothness of the ramp protocol. This explains the
qualitatively different behavior of gapless (e.g., metallic) and gapped (e.g.,
Mott insulating) systems. For gapped systems the asymptotic behavior of the
excitation energy depends only on the ramp protocol and its decay becomes
faster for smoother ramps. For gapless systems and sufficiently smooth ramps
the asymptotics are ramp-independent and depend only on the intrinsic spectrum
of the system. However, the intrinsic behavior is unobservable if the ramp is
not smooth enough. This is relevant for ramps to small interaction in the
fermionic Hubbard model, where the intrinsic cubic fall-off of the excitation
energy cannot be observed for a linear ramp due to its kinks at the beginning
and the end.Comment: 24 pages, 6 figure
On quantum mean-field models and their quantum annealing
This paper deals with fully-connected mean-field models of quantum spins with
p-body ferromagnetic interactions and a transverse field. For p=2 this
corresponds to the quantum Curie-Weiss model (a special case of the
Lipkin-Meshkov-Glick model) which exhibits a second-order phase transition,
while for p>2 the transition is first order. We provide a refined analytical
description both of the static and of the dynamic properties of these models.
In particular we obtain analytically the exponential rate of decay of the gap
at the first-order transition. We also study the slow annealing from the pure
transverse field to the pure ferromagnet (and vice versa) and discuss the
effect of the first-order transition and of the spinodal limit of metastability
on the residual excitation energy, both for finite and exponentially divergent
annealing times. In the quantum computation perspective this quantity would
assess the efficiency of the quantum adiabatic procedure as an approximation
algorithm.Comment: 44 pages, 23 figure