2019/06/29 by Samy Mailoud, Mailoud, Samy, F. Borgonovi +3
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum many-body systems #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.1907.01893
As recently manifested , the quench dynamics of isolated quantum systems\nconsisting of a finite number of particles, is characterized by an exponential\nspreading of wave packets in the many-body Hilbert space. This happens when the\ninter-particle interaction is strong enough, thus resulting in a chaotic\nstructure of the many-body eigenstates considered in an unperturbed basis. The\nsemi-analytical approach used here, allows one to estimate the rate of the\nexponential growth as well as the relaxation time, after which the\nequilibration (thermalization) emerges. The key ingredient parameter in the\ndescription of this process is the width \Γ of the Local Density of\nStates (LDoS) defined by the initially excited state, the number of particles\nand the interaction strength. In this paper we show that apart from the meaning\nof \Γ as the decay rate of survival probability, the width of the LDoS is\ndirectly related to the diagonal entropy and the latter can be linked to the\nthermodynamic entropy of a system equilibrium state emerging after the complete\nrelaxation. The analytical expression relating the two entropies is derived\nphenomenologically and numerically confirmed in a model of bosons with random\ntwo-body interaction, as well as in a deterministic model which becomes\ncompletely integrable in the continuous limit.\n