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arXiv:1106.4163 · Physical Review A

Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition

Pierfrancesco Buonsante, Vittorio Penna, A. Vezzani

Published Dec 2, 2011• 20 citations
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Abstract

We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding---inherently linear---quantum model, where, in a statistical-mechanics framework, the thermodynamic limit is realized by letting the particle population go to infinity at fixed size. We focus on lattice bosons described by the Bose-Hubbard (BH) model and discrete self-trapping (DST) equations at the quantum and semiclassical levels, respectively. After showing that the Gaussianity of the quantum ground states is broken at the phase transition, we evaluate finite-population effects by introducing a suitable scaling hypothesis; we work out the exact value of the critical exponents and provide numerical evidence confirming our hypothesis. Our analytical results rely on a general scheme obtained from a large-population expansion of the eigenvalue equation of the BH model. In this approach the DST equations resurface as solutions of the zeroth-order problem.

DOI
10.1103/physreva.84.061601

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Abstract Mean field and beyond mean field model calculations of Bose–Einstein condensates trapped in optical lattices have shown that initially homogeneous condensates can evolve into self-trapped, strongly localized states in the presence of weak boundary dissipation, a phenomenon called self-localization . A dynamical phase transition from extended to localized states can be observed when the effective nonlinearity exceeds a critical threshold Λ eff c . We investigate this phase transition to self-localization in the mean field approximation of the discrete nonlinear Schrödinger equation. We quantitatively characterize the properties of the discrete breathers , i.e. the nonlinear localized solutions, at the phase transition. This leads us to propose and numerically verify an analytical lower bound Λ eff L for the critical nonlinearity based on the idea of self-induced Anderson localization.