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Mathematical Physics Seminar

Krzysztof Gawedzki - Full counting statistics of energy transfers in nonequilibrium CFT and conformal welding

Krzysztof Gawedzki

Location:  Webinar
Date & time: Thursday, 13 August 2020 at 11:00AM - 12:00PM

Krzysztof Gawedzki – École Normale Supérieure de Lyon

Thursday, August 13, 11:00AM

Title
“Full counting statistics of energy transfers in nonequilibrium CFT and conformal welding"

I shall discuss heat transport in simple nonequilibrium states of (1+1)D Conformal Field Theory that interpolate smoothly between two equilibria with different temperatures. Such states can be described using the representation theory of the group Diff(S^1) of circle diffeomorphisms. In particular, I shall present an exact expression for the Full Counting Statistics (FCS) governing the fluctuations of heat transfers in such states. Our FCS expression is based on an extended character formula for unitary positive-energy representations of Diff(S^1) that was obtained using the conformal welding technique. In the thermodynamic limit, the FCS expression takes a universal form depending on the CFT only through its central charge. We proved that for large transfer times, the infinite- volume FCS exhibits large deviations with a rate function of the form predicted by D. Bernard and B. Doyon in 2012. The proof required a nontrivial asymptotic control of a nonlocal Riemann-Hilbert problem of noncompact type. Based on joint works with K. K. Kozlowski.