Date/heure
2 octobre 2019
09:00 - 10:00
Oratrice ou orateur
Annalisa Panati
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
(Joint work with T.Benoist, R. Raquépas) Since Kurchan’s seminal work (2000), two-time measurement statistics (also known as full counting statistics) has been shown to have an important theoretical role in the context of quantum statistical mechanics, as they allow for an extension of the celebrated fluctuation relation to the quantum setting. In this contribution, we consider heat two-time measurement statistics for a locally perturbed system. We translate the problem into the analysis of the spectral measure of an auxiliary operator (a perturbed Liouvillean), which allow us to tackle consider infinitely extended reservoir. Through the analysis of this spectral measure momenta, we show heat fluctuation description differs considerably form its classical counterpart, in particular a crucial role is played by ultraviolet regularity conditions. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat variation to be uniformly bounded in time, and for the Fourier transform of the heat variation distribution to be analytic and uniformly bounded in time in a complex neighborhood of 0. On a set of canonical examples, with bounded and unbounded perturbations, we show that our ultraviolet conditions are essentially necessary. If the form factor of the perturbation does not meet our assumptions, the heat variation distribution exhibits heavy tails. The tails can be as heavy as preventing the existence of a fourth moment of the heat variation. This phenomenon has no classical analogue.