Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition

Anno: 2011

Autori: Buonsante P., Penna V., Vezzani A.

Affiliazione autori: Dipartimento di Fisica, Università degli Studi di Parma, Viale G.P. Usberti 7/A, I-43100 Parma, Italy; Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy; Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia, UdR Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy; Centro S3, Consiglio Nazionale delle Ricerche, Istituto di Nanoscienze, Via Campi 213/a, I-41100 Modena, Italy

Abstract: We illustrate howdynamical 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.

Giornale/Rivista: PHYSICAL REVIEW A

Volume: 84 (6)      Da Pagina: 061601  A: 061601

Maggiori informazioni: Rapid Communication
Parole chiavi: quantum phase transition; bosons; lattice; nonlinear;
DOI: 10.1103/PhysRevA.84.061601

Citazioni: 18
dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2025-05-18
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