Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-06-21
Phys. Rev. A. 84, 061601 (2011)
Physics
Condensed Matter
Statistical Mechanics
4 pages, 3 figures; a few changes made in the layout of equations; improved visibility of some figures; added some references
Scientific paper
10.1103/PhysRevA.84.061601
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.
Buonsante Pierfrancesco
Penna Vittorio
Vezzani Alessandro
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