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WIP Seminar

Detailed balance for finite-dimensional quantum Markov semigroups

Erik Amorim, Rutgers University

Location:  Hill 423
Date & time: Wednesday, 09 October 2019 at 11:00AM - 12:20PM

Abstract: A quantum Markov semigroup (QMS) is a one-parameter family of linear maps on some operator algebra satisfying certain continuity, positivity and normalization properties. They model the non-unitary quantum evolution of a system coupled with an external environment. The notion of detailed balance (DB) with respect to a steady-state has an interpretation of reversibility of the QMS when the system is in that state. But it turns out that there are many inequivalent ways to define DB in a noncommutative setting. I will present current work in progress (joint with Eric Carlen) towards a general classification of the QMS's that satisfy different notions of DB. If time permits I will mention why it is useful to have such a classification, which recently allowed Carlen and Mass to obtain entropy inequalities for a QMS satisfying DB of a certain kind. It is worth noting that the entire scope of this talk is within the space of n by n complex matrices, with linear algebra being the only prerequisite. Everything will be very concrete and elementary!