19th Colloquium on Mathematics and Foundations of Quantum Theory, October 1st, 2024

About

This event is organized alternately each semester by the groups of Dirk - André Deckert (LMU), Wojciech Dybalski (U Poznań), Felix Finster (U Regensburg), and Peter Pickl (U Tübingen).

Venue: The colloquium takes place in room number 2033, Auf der Morgenstelle 15, 72076 Tübingen

Program

Abstracts

Alessandro Pizzo: A Theory of Quantum Jumps

Starting from the so-called ETH-Approach to Quantum Mechanics we describe fluorescence and the phenomenon of “quantum jumps” in idealized models of atoms coupled to the quantized electromagnetic field. In a limiting regime where the orbital motion of the atoms is neglected and the velocity of light tends to ∞ we derive explicit non-linear stochastic differential equations describing the effective time evolution of states of individual atoms. These equations give rise to a measure on state trajectories exhibiting quantum jumps. This measure is a quantum- mechanical analogue of the Wiener measure on Brownian paths encountered in the theory of diffusion. Joint work with J. Fröhlich and Z. Gang

Roderich Tumulka: The Ghirardi-Rimini-Weber Theory of Wave Function Collapse: Principles and Recent Developments

The Ghirardi-Rimini-Weber (GRW) theory hypothesizes that wave function collapse is a real physical process and proposes explicit equations for it, thereby providing a way of solving the foundational paradoxes of quantum mechanics. I will give an overview of how this theory works, including the case of relativistic space-time. For that case, it was non-trivial to construct versions of the theory that allow for interaction (it was easier without) and for identical particles (it was easier for distinguishable ones). As I will elucidate, both have been achieved, the former in 2019 and the latter in 2024.

Felix Finster: Causal Fermion Systems as a Dynamical Collapse Theory

The theory of causal fermion systems is an approach to fundamental physics. It gives quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. The dynamics of causal fermion systems is described by a variational principle called the causal action principle. After a short general introduction, I will explain how, in the non-relativistic limit, the causal action principle gives rise to an effective collapse theory. The effective model has similarities with the continuous spontaneous localization model, but differs from it by a conservation law for the probability integral as well as a non-locality in time on a microscopic scale.

I am reporting on recent work with Johannes Kleiner and Claudio Paganini.

Jago Silberbauer: Markov Decision Problems - Introduction to Reinforcement Learning

We take a look at 'Markov Decision Problems', a part of probability theory used to describe the setting of Reinforcement Learning.