In absence of connection to a thermal bath, isolated quantum systems do not equilibrate to the low-energy state in the long run. Nevertheless, typical isolated quantum systems show thermalization, because a local subsystem effectively sees the remainder as a thermal bath. This behaviour is understood in terms of the eigenstate thermalization hypothesis (ETH), which states that the eigenstates of the Hamiltonian are effectively so random that fluctuations of local observables after a quench average out to a thermal value. In contrast, integrable systems lack fully random states due to the conserved quantities, and thus equilibration to the Gibbs ensemble does not occur. In this talk, I will address several properties of the eigenstates that can be studied numerically in finite systems. First, I discuss the finite-size scaling of the fluctuations of the eigenstate expectation values, relevant for the long-time average in thermalization after a quench. Secondly, I address the structure of the coefficients of the eigenstates, in particular through the participation ratio and the entanglement entropy. Thirdly, I study off-diagonal matrix elements relevant for the strength of the temporal fluctuations after a quench.

These quantities have been studied for different families of models with tunable integrability breaking, as to uncover the profound differences in behaviour between integrable and nonintegrable systems.

Seminar, December 16, 2014, 12:00. Seminar Room

Hosted by Dr. Andy Ferris