Anomalous Thermalization in Quantum Collective Models

Abstract

We show that apparently thermalised states still store relevant amounts of information about their past, information that can be tracked by experiments involving non-equilibrium processes. We provide a condition for the microcanonical quantum Crook's theorem, and we test it by means of numerical experiments. In the Lipkin-Meshkov-Glick model, two different procedures leading to the same equilibrium states give rise to different statistics of work in non-equilibrium processes. In the Dicke model, two different trajectories for the same non-equilibrium protocol produce different statistics of work. Microcanonical averages provide the correct results for the expectation values of physical observables in all the cases; the microcanonical quantum Crook's theorem fails, in some of them. We conclude that testing quantum fluctuation theorems is mandatory to verify if a system is properly thermalised.

Fluctuations of work in realistic equilibrium states of quantum systems with conserved quantities

“…[22] were obtained assuming that the system is initially equilibrated, and hence perfectly described by either a Gibbs, with inverse temperature β, or a GGE density matrix, with two generalised temperatures, β and β M . A recent work by one of us [38] shows that the usual concept of thermalisation -the equivalence between microcanonical ensemble and long-time averages of physical observables-is not always enough to guarantee the applicability of standard quantum fluctuation relations. Here, we show that our generalised QFRs are robust and provide a good description of non-equilibrium processes starting from real equilibrium states in integrable systems.…”

“…( 12) we have introduced g, the coupling strength between two-level systems and the boson field, and the parameter 0 ≤ α ≤ 1. When α = 0 or α = 1, the Dicke Hamiltonian reduces to the Tavis-Cummings model, which is integrable and has an additional conserved quantity, the total number of excitations in the system, Mk = Ĵ + Ĵz + b † b, see; otherwise, for 0 < α < 1, the model is in the chaotic regime [22,[34][35][36]38]. Thus, we can analyse the behaviour of this system in the integrable and non-integrable limits simply by considering cases with α ∈ {0, 1} and α ∈ {0, 1}, respectively.…”

Can we retrieve information from quantum thermalized states?

“…That is, this equilibrium state is really closer to the GGE than to the standard canonical or microcanonical ensembles, although it lays within a highly chaotic region. The eigenstate thermalization hypothesis, the mechanism explaining thermalization in isolated quantum systems, entails that this fact bears no consequences in the equilibrium values of physical observables, but non-equilibrium processes might not be oblivious to it and might give rise to anomalous work statistics [46,55].…”

Quantum quenches in the Dicke model: Thermalization and failure of the generalized Gibbs ensemble*

“…The nonequilibrium dynamics of the Dicke model have been studied by many authors. [46][47][48][49][50][51][52] The statistics of the work in the quench process were calculated, [47,48] and used to verify the anomalous thermalization, [48] and the dynamics of the total occupation of the bosonic modes were obtained. Reference [49] focused on the post quench dynamics of the survival probability and the strength function which denotes the local density of states, and discussed the connection with the excited state quantum phase transitions.…”