14 research outputs found
Initial value representation for the SU(n) semiclassical propagator
The semiclassical propagator in the representation of SU(n) coherent states
is characterized by isolated classical trajectories subjected to boundary
conditions in a doubled phase space. In this paper we recast this expression in
terms of an integral over a set of initial-valued trajectories. These
trajectories are monitored by a filter that collects only the appropriate
contributions to the semiclassical approximation. This framework is suitable
for the study of bosonic dynamics in n modes with fixed total number of
particles. We exemplify the method for a Bose-Einstein condensate trapped in a
triple-well potential, providing a detailed discussion on the accuracy and
efficiency of the procedure.Comment: 24 pages, 6 figure
Coherent state approach to the cross collisional effects in the population dynamics of a two-mode Bose-Einstein condensate
We reanalyze the non-linear population dynamics of a Bose-Einstein Condensate
(BEC) in a double well trap considering a semiclassical approach based on a
time dependent variational principle applied to coherent states associated to
SU(2) group. Employing a two-mode local approximation and hard sphere type
interaction, we show in the Schwinger's pseudo-spin language the occurrence of
a fixed point bifurcation that originates a separatrix of motion on a sphere.
This separatrix corresponds to the borderline between two dynamical regimes of
Josephson oscillations and mesoscopic self-trapping. We also consider the
effects of interaction between particles in different wells, known as cross
collisions. Such terms are usually neglected for traps sufficiently far apart,
but recently it has been shown that they contribute to the effective tunneling
constant with a factor growing linearly with the particle number. This effect
changes considerably the effective tunneling of the system for sufficiently
large number of trapped atoms, in perfect accord with experimental data.
Finally, we identify analytically the transition parameter associated to the
bifurcation in the generalized phase space of the model with cross-collision
terms, and show how the dynamical regime depends on the initial conditions of
the system and the collisional parameters values.Comment: 19 pages, 8 figures. Added some references, remarks on LMG model and
acknowledgment
Dynamics of a Bose-Einstein condensate in a symmetric triple-well trap
We present a complete analysis of the dynamics of a Bose-Einstein condensate
trapped in a symmetric triple-well potential. Our classical analogue treatment,
based on a time-dependent variational method using SU(3) coherent states,
includes the parameter dependence analysis of the equilibrium points and their
local stability, which is closely related to the condensate collective
behaviour. We also consider the effects of off-site interactions, and how these
"cross-collisions" may become relevant for a large number of trapped bosons.
Besides, we have shown analytically, by means of a simple basis transformation
in the single-particle space, that an integrable sub-regime, known as
twin-condensate dynamics, corresponds in the classical phase space to invariant
surfaces isomorphic to the unit sphere. However, the quantum dynamics preserves
the twin-condensate defining characteristics only partially, thus breaking the
invariance of the associated quantum subspace. Moreover, the periodic geometry
of the trapping potential allowed us to investigate the dynamics of finite
angular momentum collective excitations, which can be suppressed by the
emergence of chaos. Finally, using the generalized purity associated to the
su(3) algebra, we were able to quantify the dynamical classicality of a quantum
evolved system, as compared to the corresponding classical trajectory.Comment: 22 pages, 10 figure
Multiconfigurational quantum propagation with trajectory-guided generalized coherent states
A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability. The approach is illustrated with simple models for interacting bosons trapped in double- and triple-well potentials, most adequately described in terms of SU(2) and SU(3) bosonic coherent states, respectively1449CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPsem informação2008/09491-9; 2011/20065-4; 2012/20452-0; 2014/04036-