Mathematical and Theoretical Physics Seminar (MTPS)

Stephan Haas (Physics & Astronomy, University of Southern California, United States and Jacobs University, Bremen)

Emulating Quantum Dynamics with Neural Networks via Knowledge Distillation

Abstract: I will introduce an efficient training framework for constructing machine learning-based emulators and demonstrate its capability of training an artificial neural network to predict the time evolution of quantum wave packets propagating through a potential landscape. This approach is based on the idea of knowledge distillation and uses elements of curriculum learning. It works by constructing a set of simple, but rich-in-physics training examples (a curriculum). These examples are used by the emulator to learn the general rules describing the time evolution of a quantum system (knowledge distillation). I discuss how this emulator is capable of learning the rules of quantum dynamics from a curriculum of simple training examples (wave packet interacting with a single rectangular potential barrier) and subsequently generalizes this knowledge to solve more challenging cases (propagation through an arbitrarily complex potential landscape). Furthermore, I discuss how by using this framework we can not only make high-fidelity predictions, but we can also learn new facts about the underlying physical system, detect symmetries, and measure the relative importance of the contributing physical processes.

Shahnaz Farhat (Université de Rennes 1)

Classical-Quantum motion of charged particles in interaction with scalar field

Abstract: This talk explores the quantum-classical transition in particle-field dynamics where a finite and fixed number of non-relativistic or semi-relativistic quantum particles interact with a quantized scalar field in the scaling limit of small value of Planck constant $\hbar\to 0$. Such topic aims to rigorously derive effective equations from fundamental first principles of quantum mechanics. In our case, the interaction between the wave and the particles are sufficiently singular to prevent us from using a standard fixed point argument. So that, when analyzing the quantum-classical transition, we crucially use the transferring of some a priori quantum regularizing effects to the classical equation in such a way that we are able to establish the global well-posedness for the particle-field equation while studying the transition by means of Wigner measures. And, we also establish the Bohr's correspondence principle for the Nelson model.

Denis Périce (ENS de Lyon)

Multiple Landau level filling for a mean field limit of 2D fermions

Abstract: Motivated by the quantum hall effect, we study N two dimensional interacting fermions in a large magnetic field limit. We work in a bounded domain, ensuring finite degeneracy of the Landau levels. In our regime, several levels are fully filled and inert: the density in these levels is constant. We derive a limiting mean-field and semi classical description of the physics in the last, partially filled Landau level.

Arman Babakhani (Department of Physics, University of Southern California)

Non-Abelian Eigenstate Thermalization Hypothesis

Abstract: The eigenstate thermalization hypothesis (ETH) explains why nonintegrable quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization within a charge sector—in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local operators' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.140402