Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

Abstract

This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian. We discuss several aspects of the slow dynamics in driven systems and emphasize the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions. We also review recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis and discuss relaxation in integrable systems. Finally we overview key experiments probing quantum dynamics in cold atom systems and put them in the context of our current theoretical understanding.

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

“…Finally, we believe that our results point the way to future explorations of quantum many-body spin systems, including thermalization and ergodicity crossing a quantum phase transition 34,35 , investigations of Hamiltonian monodromy 28 and other non-linear phenomena, finite temperature effects and dynamic stability. The combination of an exactly solvable Hamiltonian with a quantum phase transition together with demonstrated dynamics in the quantum regime should provide unique insights to these important topics.…”

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

“…Among the various quantities that one can focus on in order to define an effective temperature, a special role is expected to be played by the energy of the system [1,[29][30][31]33]: indeed the average energy E(t) ≡ ψ(t)|Ĥ(Γ)|ψ(t) = ψ 0 |Ĥ(Γ)|ψ 0 = E(t = 0) is conserved because the dynamics after the quench is unitary. Rather generally, one can define the density matrixρ possibly describing the asymptotic state of the system as the one which maximizes the von Neumann entropy S[ρ] = −Tr[ρ logρ], subject to the constraint of having the correct expectation value of the energy.…”

“…Basic questions as to whether a stationary state is reached and how this state could be characterized have been addressed in a number of simple models, including the one-dimensional systems reviewed in Refs. [1,16]. The first picture which emerged was the following: non-integrable systems are expected to reach a thermal stationary state characterized by a Gibbs distribution with a single temperature.…”

“…The lack of thermalization to a Gibbs ensemble becomes apparent within this approach. Motivated by recent experimental advances in the field of cold atoms, the theoretical study of the non-equilibrium dynamics of isolated interacting many-body quantum systems is currently receiving increasing attention [1][2][3][4]. Among the several questions that have been addressed, a central one concerns the way in which a macroscopically large isolated system evolving with unitary quantum dynamics from a generic initial state approaches equilibrium.…”

Quench dynamics of the topological quantum phase transition in the Wen-plaquette model

“…These explorations mainly focus on nonequilibrium dynamics in quantum systems which undergo a quantum phase transition when a system parameter is varied (quantum quench) [1]. These experimental and theoretical studies can potentially help to pave the way for future technologies and provide a deeper understanding of quantum many-body physics, particularly the universal scaling behavior in quench dynamics.…”