Noise-driven dynamics and phase transitions in fermionic systems

Abstract

We study abrupt changes in the dynamics and/or steady state of fermionic noise-driven systems produced by small changes in the system parameters. Specifically,we consider fermionic systems whose dynamics is described by master equations that are quadratic (and, under certain conditions, quartic) in creation and annihilation operators. We analyze phase transitions in the steady state as well as “dynamical transitions.” The latter are characterized by abrupt changes in the rate at which the system asymptotically approaches the steady state. We illustrate our general findings with relevant examples of fermionic (and, equivalently, spin) systems and show that they can be realized in ion chains.