Vorträge in der Woche 13.11.2023 bis 19.11.2023

Donnerstag, 16.11.2023: Dissipation-enabled bosonic Hamiltonian learning via new information-propagation bounds

Andreas Bluhm (Grenoble)

Hamiltonian learning is the problem of characterizing and benchmarking quantum devices or experiments in continuous time. In contrast to multi-qubit systems, learning guarantees for the dynamics of bosonic systems have hitherto remained mostly unexplored. In this talk, we will discuss how to extend the ideas from the finite-dimensional setting to bosonic Hamiltonians given as polynomials of bounded degree in annihilation and creation operators. As a crucial step in our analysis, we add photon-driven dissipation to the time evolution of the unknown Hamiltoian and we prove a new Lieb-Robinson type bound for such a combined evolution.

Donnerstag, 16.11.2023: On the initial value problem for the Einstein inequalities

Jonathan Glöckle (Universität Regensburg)

The Einstein field equations relate the curvature of a Lorentzian spacetime with the energy-momentum tensor determined by the matter distribution. Since the latter is hard to describe for a universe as ours, cosmological arguments usually just use that the energy-momentum tensor satisfies the dominant energy condition (=dec). The Einstein field equations then turn into a curvature condition for which A. Rendall coined the term “Einstein inequalities”. In this talk, we want to discuss the Cauchy problem for these partial differential inequalities. Initial data sets for this problem necessarily satisfy a condition that is also called dec. We review for which initial data sets a solution is known to exist and rigidity phenomena that lead to local uniqueness. The main result, however, is a negative one: We construct dec initial data sets that cannot be embedded into dec spacetimes.

Donnerstag, 16.11.2023: Bosonic Trotter-Kato Product Formula

Tim Möbus (TU München)

In bosonic systems, generators of quantum Markov semigroups are often unbounded due to the intrinsic infinite-dimensional Fock space. A major difficulty in the perturbation theory of such semigroups arises from the fact that, for example, the Duhamel equation is not always well-defined. One workaround is to assume the existence of a reference operator that defines an admissible subspace of the semigroup. In bosonic systems, this corresponds to the number operator, and the assumption that the evolved moments can be bounded with the help of the input moment. This method can be used to establish a generalized Trotter-Kato product formula as well as the Zeno effect. A possible application is to introduce dissipation into a closed quantum system, which can compel the entire system to exhibit the mentioned stability assumption on the moments, thereby enabling the learning of the Hamiltonian.

Donnerstag, 16.11.2023: Operator Norm Bounds on the Correlation Matrix of the SK Model

Prof. Dr. Christian Brennecke (Universität Bonn)

In this talk I will review basic predictions for the high temperature regime, the so called replica symmetric regime, of the Sherrington-Kirkpatrick mean field spin glass. I will recall the TAP equations, their derivation and their validity in connection with the decay of the two point correlation functions. For the simplified case of vanishing external field, I will present some details on recent results that characterize the susceptibility of the model as a resolvent of the interaction matrix, which predicts in a simple way the (well-known) RS-RSB transition temperature. The talk is based on joint work with Adrien Schertzer, Changji Xu and Horng-Tzer Yau.

Freitag, 17.11.2023: Was ist ein Physics Informed Neural Network (PINN)?

Dr. Jonas Ziefle (Uni Tübingen)