Quantum-classical correspondence for a non-Hermitian Bose-Hubbard dimer

Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.013629· OSTI ID:21442978

Graefe, Eva-Maria ^[1]; Korsch, Hans Juergen ^[2]; Niederle, Astrid Elisa ^[2]

---

1. School of Mathematics, University of Bristol, Bristol BS8 1TW (United Kingdom)
2. FB Physik, TU Kaiserslautern, D-67653 Kaiserslautern (Germany)

We investigate the many-particle and mean-field correspondence for a non-Hermitian N-particle Bose-Hubbard dimer where a complex on-site 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 Schroedinger 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.

• OSTI ID: 21442978
• Journal Information: Physical Review. A, Vol. 82, Issue 1; Other Information: DOI: 10.1103/PhysRevA.82.013629; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BOSE-EINSTEIN GAS
DAMPING
DIMERS
HUBBARD MODEL
MEAN-FIELD THEORY
METRICS
NONLINEAR PROBLEMS
OSCILLATIONS
SCHROEDINGER EQUATION
TRAPPING
TUNNEL EFFECT
CALCULATION METHODS
CRYSTAL MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS