03/08/2024
By Joris Roos

The Department of Mathematics & Statistics invites you to attend a colloquium lecture by Jeff Schenker, Professor of Mathematics at Michigan State University.

The talk will be delivered in person, but it is also possible to attend via Zoom: https://uml.zoom.us/j/96299486791

Everyone is welcome.

Title: Theory of Ergodic Quantum Processes
Date: Wednesday, March 13
Time: 11 a.m. to noon
Room: Southwick 350W

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 system is described by completely positive, trace preserving maps on the mixed states, represented by density matrices. In this talk, we will review the background of open quantum systems and their description and 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-Frobenius theorem. Finally, we will "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. Applications and extensions to repeated measurement of quantum systems will be discussed if time permits.

For future events in this colloquium series, visit the Math website.