Non-equilibrium quantum mechanics

Background: thermalisation in quantum mechanics

Time evolution in quantum mechanics is unitary and therefore completely deterministic. Naively, one would, therefore, expect that quantum systems never thermalise. However, in experiments we only have access to a very small number of degrees of freedom of a quantum system and the question is whether that small subset sees thermalisation.

Two scenarios are possible:

  1. Thermalisation occurs: eigenstate thermalisation hypothesis (ETH) holds, eigenstates tend to thermal states at long times, observables tend to their prediction from microcanonical ensemble. Information about initial conditions is long at long times. Entanglement entropy has extensive (volume law) behaviour.
  2. Thermalisation does not occur: ETH does not hold, information is held indefinitely within locally accessible observables. Entanglement entropy behaves sub-extensively (area law).
Figure 1. A diagram of thermalisation in classical physics.
Figure 2. Two scenarios: thermalisation occurs and the information is washed out throughout the whole system, or thermalisation does not occur and the wavefunction is localised (picture adapted from A. Aspect, M. Inguscio, Physics Today 62, 8, 30 2009).