Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition

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 level, respectively. After showing that the gaussianity of the quantum ground states is broken at the phase transition, we evaluate finite populations effects introducing a suitable scaling hypothesis; we work out the exact value of the critical exponents and we provide numerical evidences 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.

4 pages, 3 figures; a few changes made in the layout of equations; improved visibility of some figures; added some references and endnotes

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• The phase-separation mechanism of a binary mixture in a ring trimer
• Ehrenfest breakdown of the mean-field dynamics of Bose gases
• Dynamics of the central-depleted-well regime in the open Bose-Hubbard trimer
• A continuous-variable approach to the spectral properties and quantum states of the two-component Bose-Hubbard dimer
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• Quantum-granularity effect in the formation of supermixed solitons in ring lattices
• Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
• Localization-delocalization transition of dipolar bosons in a four-well potential
• Quantum phase transition in an effective three-mode model of interacting bosons