Theory of Ergodic Quantum Processes
A talk in the Mathematisches Kolloquium & Mathematisches Kolloquium (SFB 1283) series by
Jeffrey Schenker from Michigan State University
| Abstract: | An "open" quantum system has non-trivial interactions with its environment. In an open system, states are no longer represented by vectors in a Hilbert space and the nature of the dynamical evolution of the changes dramatically. In place of the unitary dynamics of a closed system, the evolution of an open quantum systems is described by completely positive, trace preserving maps on the mixed states, represented by density matrices. In this talk, we will first review the background of open quantum systems and their description and then introduce the notion of a "quantum process," as a sequence of quantum channels. If the process is given by repetition of a single channel with decoherence, it drives the system to a unique equilibrium state, a result which follows from a generalization of the Perron-Frobenious theorem. Finally, we will consider "ergodic quantum processes" composed of stochastic channels with arbitrary correlations and non-negligible decoherence and present a recent theorem which shows that such a process drives the system to a unique fluctuating equilibrium with ergodic time dependence. The implications of these results for the structure of Matrix Product States will also be discussed. (Joint work with Ramis Movassagh). Zoom Meeting ID: 687 2256 4221 Passcode: 937351 $\href{https://uni-bielefeld.zoom.us/j/68722564221?pwd=bTM5YWlDMnJGUW13YnpiNjh6ajJkQT09 }{\textbf{Join Zoom Meeting}}$ |