Symmetries and Symmetry Breaking in Open Qubit Systems

The theory of quantum open systems is far reaching having applications in physics spanning many scales, from condensed matter to cosmology. Although, only for a limited number of models can the infinitesimal time evolution (i.e. equation of motion) of open systems be explicitly determined. But the presence of symmetries in an open system should give a handle on the equations of motion.

Thus to address the construction of equations of motion in open quantum systems, we consider the reduced dynamics generated from interacting qubits that has a global symmetry, as well as a phase covariance/time translation symmetry. We show how the 1-qubit reduced dynamics is constrained by these symmetries, and how in conjunction with the initial environment state, one can construct effective equations of motion.

To more closely connect with open cosmological systems, we also consider interactions with a third qubit which explicitly breaks the time translation symmetry present. We calculate the post time translation symmetry breaking dynamical map, and determine how it differs from the time translation symmetric map.