Mathematical and Theoretical Physics Seminar (MTPS)

Mikhail Katsnelson (Nijmegen University)

Frustrations, memory, and complexity in classical and quantum spin systems

Abstract: The origin of complexity remains one of the most important and, at the same time, the most controversial scientific problems. Earlier attempts were based on theory of dynamical systems but did not lead to a satisfactory solution of the problem. I believe that a deeper understanding is possible based on a recent development of statistical physics, combining it with relevant ideas from evolutionary biology and machine learning. Using patterns in magnetic materials as the main example, I discuss some general problems such as a formal definition of pattern complexity, self-induced spin glassiness due to competing interactions as a way to interpret chaotic patterns, multi-well states intermediate between glasses and ordinary ordered states, and complexity of frustrated quantum spin systems studied via generalization properties of neural networks used to find the ground state.

Mikhail Katsnelson is also the author of several poem books. He will read from them (in Russian with English translation) after a coffee break on Thursday 7.11.2024 16:00-17:00 in the IRC Seminar Room III which will be hosted by Irina.

Tuan Minh Pham (University of Amsterdam)

Irreversibility in Non-reciprocal Chaotic Neural Networks: An exact microscopic approach

Abstract: How is entropy production, a measure of time irreversibility, of a complex system with emergent chaotic behaviour controlled by the heterogeneity in the non-reciprocal interactions among its elements? Despite the challenge in computing entropy production within a microscopic theory, the importance of entropy production for the brain’s cognition as recently demonstrated, greatly motivates theoretical work on this question. In this talk, we address this question using a classic model of random recurrent neural networks that undergoes a dynamical transition from quiescence to chaos at a critical heterogeneity level. By obtaining an exact analytical expression for the averaged entropy production rate, we show how this quantity becomes a constant at the onset of chaos while changing its functional form upon crossing this point. Our work provides the first step to understand not only non-equilibrium phase transitions without broken symmetry but also the intriguing connection between dynamics and thermodynamics of complex living systems such as the brain.