Typical fast thermalization processes in closed many-body systems

Abstract

The lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a very successful general framework to cope with this problem. However, far from equilibrium, only very few quantitative and comparably universal results are known. Here a quantum mechanical prediction of this type is derived and verified against various experimental and numerical data from the literature. It quantitatively describes the entire temporal relaxation towards thermal equilibrium for a large class (in a mathematically precisely defined sense) of closed many-body systems, whose initial state may be arbitrarily far from equilibrium.

Real-time dynamics of typical and untypical states in nonintegrable systems

“…Consequently, we proceed also in a different way and analyze the generalized diffusion coefficient D q (t), as introduced in Eq. (21).…”

“…The concept of typicality [10][11][12][13][14][15][16][17][18][19][20][21] states that a single pure state can have the same "properties" as the full statistical ensemble. Remarkably, this concept does not require eigenstate thermalization [22][23][24] and also applies to the dynamics of expectation values.…”

“…While this question has a long and fertile history, it has attracted continuously increasing attention in the last decade [1,2]. This upsurge of interest is also related to the advent of novel materials and cold atomic gases [3,4], the discovery of new states of matter such as many-body localized phases [5][6][7], the invention of powerful numerical techniques such as density-matrix renormalization group [8,9], as well as the emergence of fresh key concepts, with typicality of pure states [10][11][12][13][14][15][16][17][18][19][20][21] and eigenstate thermalization hypothesis [22][23][24] as prime examples. Although clarifying the mere existence of equilibration and thermalization in isolated systems has seen substantial progress [25,26], rigorously deriving the macroscopic phenomena of (exponential) relaxation and (diffusive) transport from truly microscopic principles is still a major challenge [27,28].…”

Real-time broadening of nonequilibrium density profiles and the role of the specific initial-state realization

“…In particular, the theoretical understanding has seen substantial progress by the fascinating concepts of eigenstate thermalization [4][5][6] and typicality of pure quantum states [7][8][9][10][11][12][13][14] as well as by the invention of powerful numerical methods such as density-matrix renormalization group [15]. Much less is known on the route to equilibrium as such [16] and still the derivation of the conventional laws of (exponential) relaxation and (diffusive) transport on the basis of truly microscopic principles is a challenge to theory [17].…”

Total correlations of the diagonal ensemble as a generic indicator for ergodicity breaking in quantum systems

“…In addition to the above, in recent years dynamical equilibration of expectation values and density matrices of subsystems under unitary dynamics has been studied extensively [32][33][34][35][36][37] (see also 8 for a review). Such equilibration can be rigorously shown to happen if the spectrum of the Hamiltonian fulfills certain non-resonance conditions, and the initial state has overlap with many energy eigenstates or the second most populated eigenstates is occupied with only a small probability (a arXiv:1611.02046v3 [cond-mat.dis-nn] 30 Jan 2017 weaker requirement).…”