Quantum Quenches with Random Matrix Hamiltonians and Disordered Potentials. Issue 12 (10th October 2017)

• Record Type: Journal Article
• Authors: Kolley, Fabian; Bohigas, Oriol; Fine, Boris V.
• Is Part Of: Annalen der Physik. Volume 529:Issue 12(2017)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-10-10
• Subjects: Quantum quenches -- random matrices -- disordered lattices; Physics -- Periodicals; Chemistry -- Periodicals; 530.05
• DOI: 10.1002/andp.201700009
• Languages: English
• ISSNs: 0003-3804

Abstract

Abstract: We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered lattices. In the former case, the quench consists of sudden switching‐on the off‐diagonal elements of the Hamiltonian. In the latter case, it is sudden switching‐on of the hopping between adjacent lattice sites. The quench‐induced ensembles are compared with the so‐called "quantum micro‐canonical" (QMC) ensemble describing quantum superpositions with fixed energy expectation values. Our main finding is that quantum quenches with sparse random matrices having one special diagonal element lead to the condensation phenomenon predicted for the QMC ensemble. Away from the QMC condensation regime, the overall agreement with the QMC predictions is only qualitative for both random matrices and disordered lattices but with some cases of a very good quantitative agreement. In the case of disordered lattices, the QMC ensemble can be used to estimate the probability of finding a particle in a localized or delocalized eigenstate. Abstract : The authors numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered lattices. The quench‐induced ensembles are compared with the so‐called "quantum micro‐canonical" (QMC) ensemble describing quantum superpositions with fixed energy expectation values. The authors find that quantum quenches with sparse random matrices can lead to the condensation phenomenon predicted for the QMC ensemble. In the case of disordered lattices, the QMC ensemble can be used to estimate the probability of finding a particle in a localized or delocalized eigenstate.