title: Classical analysis of quantum phase transitions in a bilayer model.
abstract: In this Brief Report we extend the classical analysis performed on the schematic model proposed in [T. Moreira, G. Q. Pellegrino, J. G. Peixoto de Faria, M. C. Nemes, F. Camargo, and A. F. R. Toledo Piza, Phys. Rev. E 77, 051102 (2008)] concerning quantum phase transitions in a bilayer system. We show that appropriate integrations along the classical periodic orbits reproduce with excellent agreement both the quantum spectrum and the expected mean value for the number of excitons in the system, quantities which are directly related to the observed boson-fermion quantum phase transition.
authors.affiliation: Departamento de Engenharia Elétrica, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG, Brazil.
authors.forename: Mariane Camargos
authors.initials: MC
authors.lastname: Figueiredo
authors.forename: Tathiana Moreira
authors.initials: TM
authors.lastname: Cotta
authors.forename: Giancarlo Queiroz
authors.initials: GQ
authors.lastname: Pellegrino