| A fundamental question of statistical mechanics is how macroscopic equations of motion (such as e.g. the Navier-Stokes equation) arise from the microscopic interactions between the particles in the underlying many-body systems. There is a considerable body of work on classical systems, particularly stochastic interacting particles systems, that illuminates this phenomenon of emergence for many fundamentally
important systems, but very little has been achieved for systems with genuine quantum mechanical dynamics, i.e., where no classical description is known or possible on intermediate scales. Taking the quantum XX-spin chain as an example for an open
system kept at low temperatures we propose a hydrodynamic
limit for the large-scale dynamics of the conserved local order parameter. We verify this description by investigating the same system in contact not with a surrounding heat bath, but with an infinite quantum XX-reservoir at its boundaries. |
