Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
File(s)
Accepted version
Author(s)
Graefe, E
Korsch, HJ
Niederle, AE
Type
Journal Article
Abstract
We investigate the many-particle and mean-field correspondence for a
non-Hermitian N-particle Bose-Hubbard dimer where a complex onsite energy
describes an effective decay from one of the modes. Recently a generalized
mean-field approximation for this non-Hermitian many-particle system yielding
an alternative complex nonlinear Schr\"odinger equation was introduced. Here we
give details of this mean-field approximation and show that the resulting
dynamics can be expressed in a generalized canonical form that includes a
metric gradient flow. The interplay of nonlinearity and non-Hermiticity
introduces a qualitatively new behavior to the mean-field dynamics: The
presence of the non-Hermiticity promotes the self-trapping transition, while
damping the self-trapping oscillations, and the nonlinearity introduces a
strong sensitivity to the initial conditions in the decay of the normalization.
Here we present a complete characterization of the mean-field dynamics and the
fixed point structure. We also investigate the full many-particle dynamics,
which shows a rich variety of breakdown and revival as well as tunneling
phenomena on top of the mean-field structure.
non-Hermitian N-particle Bose-Hubbard dimer where a complex onsite energy
describes an effective decay from one of the modes. Recently a generalized
mean-field approximation for this non-Hermitian many-particle system yielding
an alternative complex nonlinear Schr\"odinger equation was introduced. Here we
give details of this mean-field approximation and show that the resulting
dynamics can be expressed in a generalized canonical form that includes a
metric gradient flow. The interplay of nonlinearity and non-Hermiticity
introduces a qualitatively new behavior to the mean-field dynamics: The
presence of the non-Hermiticity promotes the self-trapping transition, while
damping the self-trapping oscillations, and the nonlinearity introduces a
strong sensitivity to the initial conditions in the decay of the normalization.
Here we present a complete characterization of the mean-field dynamics and the
fixed point structure. We also investigate the full many-particle dynamics,
which shows a rich variety of breakdown and revival as well as tunneling
phenomena on top of the mean-field structure.
Date Issued
2010
Citation
Phys. Rev. A, 2010, 82
ISSN
1050-2947
Publisher
AMER PHYSICAL SOC
Journal / Book Title
Phys. Rev. A
Volume
82
Issue
1
Copyright Statement
© 2010 The American Physical Society
Identifier
http://arxiv.org/abs/1003.3355v2
Publication Status
Published
Article Number
013629