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Mean-field approximation for a Bose-Hubbard dimer with complex interaction strength

Eva-Maria Graefe, Chiara Liverani

A generalised mean-field approximation for non-Hermitian many-particle systems has been introduced recently for a Bose-Hubbard dimer with complex on-site energies. Here we apply this approximation to a Bose-Hubbard dimer with a complex particle interaction term, modelling losses due to interactions in a two mode Bose-Einstein condensate. We derive the mean-field equations of motion leading to nonlinear dissipative Bloch dynamics, related to a nontrivial complex generalisation of the nonlinear Schrodinger equation. It is shown that depending on the parameter values there can be up to six stationary states. Further, for small values of the interaction strength the dynamics shows limit cycles.

http://arxiv.org/abs/1305.7160
Quantum Physics (quant-ph); Mathematical Physics (math-ph)

Twofold Transition in PT-Symmetric Coupled Oscillators

Carl M. Bender, Mariagiovanna Gianfreda

The inspiration for this theoretical paper comes from recent experiments on a PT-symmetric system of two coupled optical whispering galleries (optical resonators). The optical system can be modeled as a pair of coupled linear oscillators, one with gain and the other with loss. If the coupled oscillators have a balanced loss and gain, the system is described by a Hamiltonian and the energy is conserved. This theoretical model exhibits two PT transitions depending on the size of the coupling parameter \epsilon. For small \epsilon the PT symmetry is broken and the system is not in equilibrium, but when \epsilon becomes sufficiently large, the system undergoes a transition to an equilibrium phase in which the PT symmetry is unbroken. For very large $$\epsilon$$ the system undergoes a second transition and is no longer in equilibrium. The classical and the quantized versions of the system exhibit transitions at exactly the same values of $$\epsilon$$.

http://arxiv.org/abs/1305.7107
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)