Quantum quench influenced by an excited-state phase transition

We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear cut evidence of the ESQPT effects is presented in integrable models, while in the nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.P.C. acknowledges useful discussions with M. Kastner and J. Hirsch. This work has been partially supported by the Czech Science Foundation (Grant No. 202/09/0084), by the Czech Ministry of Education (Grant No. MSM 0021620859), by the Spanish Ministerio de Educacion y Ciencia and the European regional development fund FEDER (Grants No. FIS2009-07277, No. FIS2008-04189, No. FIS2006-12783-C03-01, No. FPA2006-13807-C02-02, No. FPA2007-63074, and No. FIS2009-11621-C02-01), by CPAN-Ingenio (Grant No. CSPD-2007-00042-Ingenio), by Junta de Andalucia (Grants No. FQM160, No. FQM318, No. P05-FQM437, and No. P07-FQM-02962), and by the Universidad Complutense de Madrid (Grant No. UCM-910059). P.P-F. is supported by a FPU grant of the Spanish Ministerio de Educacion y Ciencia. A.R. is supported by the Spanish program CPAN Consolider-ingenio