title: Complexity and instability of quantum motion near a quantum phase transition.
abstract: We show that the number of harmonics of the Wigner function, recently proposed as a measure of quantum complexity, can also be used to characterize quantum phase transitions. The nonanalytic behavior of this quantity in the neighborhood of a quantum phase transition is illustrated by means of the Dicke model and is compared to two well-known measures of the (in)stability of quantum motion: the quantum Loschmidt echo and fidelity.
authors.affiliation: Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.
authors.forename: Pinquan
authors.initials: P
authors.lastname: Qin
authors.affiliation: Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.
authors.forename: Wen-ge
authors.initials: WG
authors.lastname: Wang
authors.affiliation: CNISM and Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy.
authors.forename: Giuliano
authors.initials: G
authors.lastname: Benenti
authors.affiliation: CNISM and Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy.
authors.forename: Giulio
authors.initials: G
authors.lastname: Casati