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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 11: Many-body Theory II

MP 11.1: Talk

Thursday, March 21, 2024, 09:30–09:50, HL 102

Double or nothing: a Kolmogorov extension theorem for (bi)probabilities in quantum mechanics — •Davide Lonigro — Department of Mathematics, Università degli Studi di Bari Aldo Moro, Bari, Italy — Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

The family of multitime probability distributions obtained by repeatedly probing a quantum system generally violates Kolmogorov's consistency property, thus preventing us from interpreting such distributions as the result of the sampling of a single trajectory. We argue that, nonetheless, a pair of trajectories is sufficient. To this purpose, we prove a generalization of Kolmogorov extension theorem that applies to families of complex-valued bi-probability distributions (that is, defined on pairs of elements of the original sample spaces), and we employ this result in the quantum mechanical scenario. In this sense, rather than give up on trajectories, quantum mechanics requires to ``double down" on them.

Joint work with D. Chruściński, Ł. Cywiński, F. Sakuldee, and P. Szańkowski.

Keywords: Quantum multitime probabilities; Kolmogorov extension theorem; Stochastic processes; Quantum classicality