In this talk I will present some recent results about the connection between heat fluctuation in the two-time measurement framework and ultraviolet regularity, and I will sketch what we expect to happen for (toy)-models that can be renormalized through self-energy extraction.
To put the result in context, in the first part of the talk I will review the celebrated fluctuation theorem in statistical mechanics and the two-time measurement framework. 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 the second part of the talk, I will present our recent results. We show that the description of heat fluctuation differs considerably from its classical counterpart, in particular a crucial role is played by ultraviolet regularity conditions. 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.
I will conclude with some conjectures for models that can be renormalized through self-energy extraction.
(Joint work with T. Benoist, R. Raquépas)
This talk is part of series of talks affiliated with the virtual Mittag-Leffler workshop "Scattering, microlocal analysis and renormalization", organized by Claudio Dappiaggi, Jacob Schach Møller and Michal Wrochna. The full schedule can be found at: