Abstract

In classical mechanics there is a relation between integrability and equilibration, but this is not well understood in the quantum case. Closed quantum systems never equilibrate to a stationary state. However, in some circumstances, the system equilibrates locally (the reduced density matrix of a subsystem evolves to a stationary state). All finite-dimensional quantum systems are integrable, in the sense that solving its dynamics reduces to diagonalizing its hamiltonian. This procedure may need a large computational effort, which differs from system to system. In some sense, the lack of integrability of a quantum system can be quantified by the computational complexity of diagonalizing its hamiltonian. We show that, if this complexity is at least quadratic with the size of the system then local equilibration holds (for almost all hamiltonians); and if this complexity is sub-quadratic then local equilibration does not hold.