Mathematical and Theoretical Physics Seminar (MTPS)

Alexander Hartmann (University of Oldenburg)

I want it all and I want it now: large-deviation simulations in statistical physics

Abstract: For every random process, all measurable quantities are described comprehensively through their probability distributions. In the ideal but rare case they can be obtained analytically, i.e., completely. Most physical models are not accessible analytically thus one has to perform numerical simulations. Usually this means one does many independent runs and obtains estimates of the probability distributions by the measured histograms. Since the number of repetitions is limited, maybe 10 million, correspondingly the distributions can be estimated in a range down to probabilities like $10^{-10}$. But what if one wants to obtain the full distribution, in the spirit of obtaining all information? This means one desires to get the distribution down to the rare events, but without waiting forever by performing an almost infinite number of simulation runs. Here, we study rare events numerically using a very general black-box method. It is based on sampling vectors of random numbers within an artificial finite-temperature (Boltzmann) ensemble to access rare events and large deviations for almost arbitrary equilibrium and non-equilibrium processes. In this way, we obtain probabilities as small as 10^-500 and smaller, hence (almost) the full distribution can be obtained in a reasonable amount of time. Examples are presented for selected applications from random graphs, work in stochastic thermodynamics, perolation, particle diffusion, sequence alignment or traffic flow models etc.

Michael A. Sentef (Institute for Theoretical Physics and BCCMS, University of Bremen, and MPI for the Structure and Dynamics of Matter, Hamburg)

Designing Quantum Materials with Light

Abstract: In recent years, light-driven quantum materials science has undergone a fundamental transformation. What was once a theoretical vision—the ability to control and manipulate emergent properties of materials on ultrafast timescales—has now become a reality [1]. This progress has been enabled by rapid advancements in shaping laser pulses, probing nonequilibrium dynamics with femtosecond resolution, and developing sophisticated theoretical approaches to describe light-driven many-body systems [2]. As a result, we are now entering an era in which quantum materials can be actively “designed” and controlled using tailored light fields.

A cornerstone of this approach is Floquet engineering, which exploits periodic driving to coherently modify electronic states and induce novel phases of matter. I will briefly review key developments in realizing Floquet states in quantum materials and discuss their implications for controlling competing orders. However, despite its promise, Floquet engineering also faces intrinsic limitations, particularly due to heating effects and decoherence, which can constrain its applicability as a general tuning mechanism.

Moving beyond conventional Floquet approaches, a new frontier is emerging: cavity quantum materials [3]. By embedding materials in tailored quantum-electrodynamical environments, such as optical cavities, it is possible to enhance light-matter interactions and create hybrid light-matter states with fundamentally new properties. Unlike classical laser-driven schemes, cavity-mediated interactions can modify quantum fluctuations and collective excitations even in thermal equilibrium, offering a novel route to control material properties without direct external driving. I will highlight recent advances in this field, both from theoretical [4] and experimental [5,6] perspectives, and specifically discuss how strong correlations in cavity quantum materials provide new opportunities for engineering competing electronic orders through light-matter hybridization. Importantly, this relies on a generalization of the “cavity paradigm” beyond optical resonators into the realm of “polaritonic quantum matter” in order to structure fluctuations in cavity quantum materials [7]. This may open pathways toward controlling superconductivity, charge density waves, and other ordered phases in a fundamentally new way.

References:
[1] A. de la Torre et al., Nonthermal pathways towards ultrafast control in quantum materials, Rev. Mod. Phys. 93, 041002 (2021).
[2] F. Caruso, MAS, et al., The 2025 Roadmap to Ultrafast Dynamics: Frontiers of Theoretical and Computational Modeling, JPhys Materials (2025), arXiv:2501.06752.
[3] F. Schlawin, D. M. Kennes, MAS, Cavity quantum materials, Applied Physics Reviews 9, 011312 (2022).
[4] MAS et al., Quantum to classical crossover of Floquet engineering in correlated quantum systems, Phys. Rev. Research 2, 033033 (2020).
[5] G. Kipp, H. Bretscher, et al., Cavity electrodynamics of van der Waals heterostructures, Nature Physics (2025). https://www.nature.com/articles/s41567-025-03064-8
[6] I. Keren, T. Webb, et al., Cavity-altered superconductivity, arXiv:2505.17378, Nature (2026).
[7] H. M. Bretscher et al., Structuring fluctuations in cavity quantum materials, forthcoming review article.