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.

Thomas La Cour Jansen (University of Groningen)

Energy Transfer in Photosynthetic Systems

Abstract: Energy transfer in photosynthetic systems can be described using a range of quantum dynamical theories, each applicable at different length and time scales. In this talk, I will discuss these different levels of theory and outline the regimes in which common approximations are valid. Particular attention will be given to the transition between coherent and incoherent energy transfer.
In addition, I will present examples of energy transfer in photosynthetic supercomplexes [1]. Specifically, I will show how exciton transport between two-dimensional lamellar structures can be strongly influenced by quantum interference effects. These insights provide guidance for the design of artificial materials, where energy transfer can be selectively enhanced or suppressed through structural control [2].
[1] Blankenship, R. E. Molecular Mechanisms of Photosynthesis, Third Edition.; Wiley: Oxfort, U.K., 2021.
[2] Park, Y.; Ten Hoven, G. A. H.; Jansen, T. L. C. Energy Transfer between Two-Dimensional Sheets: An Investigation of Chlorosome Lamella. J. Phys. Chem. Lett. 2025, 12507–12513. https://doi.org/10.1021/acs.jpclett.5c02725.

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.

Vishnu Sanjay (Gran Sasso Science Institute)

On the weak coupling limit for the periodic quantum Lorentz gas

Abstract: The quantum Lorentz gas is a fundamental model in kinetic theory, where one studies the effective behaviour of a single quantum particle interacting with its environment. In mathematical terms, the particle evolves according to a linear Schrödinger equation with a potential term representing the environment. In the weak coupling scaling, the particle interacts weakly with the potential, but spacetime is rescaled in such a way that the cumulative effect of the potential becomes significant. For Gaussian random potentials, it is known that under this scaling the rescaled Wigner transform of the wavefunction (which plays the role of a phase space density) converges weakly, on average, to the solution of a linear Boltzmann equation with an energy-preserving collision kernel determined by the covariance of the field.

In this talk, we consider instead a smooth deterministic potential that is periodic on the unit lattice in d space dimensions. Using Wigner series representations and rough path techniques, we show that for a certain class of observables the weak coupling limit yields free transport. For others, we show that the existence of the limit hinges on the continuity of a certain generalized phase-space object at energy band crossings of the free Hamiltonian. This is work done under the supervision of Prof. Massimiliano Gubinelli.

Alexander Lichtenstein (Inst. of Theoretical Physics, University of Hamburg)

Monte Carlo Sign Problem and Superconductivity of Bad Fermions

Abstract: Quantum Monte Carlo schemes for fermions suffer from the infamous sign problem. There is still much debate about the mathematical complexity class to which it belongs: NP-complete [1] or merely polynomial [2]. Possible solutions to the sign problem would greatly facilitate numerically exact studies of high-temperature superconductivity in cuprates.

We introduce a strong-coupling perturbation scheme starting from an optimally chosen reference system free of the sign problem [3]. The approach is based on a lattice QMC method for the general t-t' Hubbard model, expanded around the half-filled particle-hole symmetric state with the same Coulomb interaction.

First-order perturbation in the chemical-potential shift and long-range hopping gives reasonable accuracy for parameters corresponding to optimal cuprate systems at pseudogap temperatures. The calculated spectral function of the doped Hubbard model for cuprate parameters shows pseudogap formation. The formalism was extended to superconductivity with a small external d-wave field [4]. The formation of a two-gap structure related to the pseudogap and the d-wave superconducting gap will be discussed.

References:
[1] M. Troyer et al., PRL 94, 170201 (2005).
[2] R. Rossi, et al,, EPL 118 (2017) 10004.
[3] S. Iskakov, et al., npj Comput. Mater. 10, 36 (2024).
[4] E. Stepanov, et al., Comm. Physics 9, 91 (2026)