Seminars

Noether's theorem is familiar to most physicists due its fundamental role in linking the existence of conservation laws to the underlying symmetries of a physical system. In this talk I will present how Noether's reasoning also applies within statistical mechanics to thermal systems, where fluctuations are paramount. Exact identities ("sum rules") follow thereby from functional symmetries determining well-known relations (such as the force balance) as well as previously unknown identities, relating different correlations in many-body systems. The identification of the underlying Noether concept enables their systematic derivation. The generalization to arbitrary thermodynamic observables yields sum rules for hyperforces, i.e. the mean product between the considered observable and the relevant forces that act in the system. Simulations of a range of simple and complex liquids demonstrate the fundamental role of these correlation functions in the characterization of spatial structure, such as quantifying spatially inhomogeneous self-organization.
Finally, I will briefly introduce the intensity countoscope which is another statistical method based on correlations for studying particle suspensions. By leveraging temporal intensity fluctuations in microscopy images, we can access dynamical information such as diffusion coefficents directly.

Understanding how large ecological communities remain stable despite intricate interaction networks is a long-standing challenge in theoretical ecology. While the fully connected limit of the generalized Lotka–Volterra (gLV) dynamics has been thoroughly analyzed, the sparse case—where each species interacts only with a few others—remains largely unexplored due to the combined effects of network heterogeneity, nonlinearity, and stochastic fluctuations.

In this talk, I will present a new analytical framework based on a small-coupling expansion of the dynamic cavity method, which provides a self-consistent description of the stationary state of sparse random ecosystems in terms of effective single-species stochastic processes with memory and colored noise. Solving the resulting distributional fixed-point equations via population dynamics reveals a remarkably rich phase diagram. Even in the absence of disorder, sparse competitive interactions induce a topological phase, where a finite fraction of species go extinct while the survivors form a percolating subgraph that eventually fragments at a percolation-like transition. When heterogeneity in the couplings is introduced, these geometric transitions intertwine with the multiple-equilibria phase known from fully connected models, producing novel mixed regimes and reshaping the boundaries of stability and diversity. Our results show that network sparseness alone can generate complex ecological organization, offering new insights into the interplay between structure, stability, and function in high-dimensional ecosystems.

Active systems, such as living cells, are traditionally modelled via self-propelled particles driven by internal forces. It is however often assumed that these internal forces do not depend on the environment which is questionable from a biological perspective. Here we use the framework of Generalized Langevin Equations (GLE) to go beyond this paradigm by incorporating internal state dynamics and environmental sensing into active particle models. We show that when the self-propulsion of a particle depends on internal variables themselves depending on the environment, qualitatively new behaviours emerge. These include memory-induced responses, controllable localization in complex landscapes, and suppression of motility-induced phase separation or enhanced jamming transitions. Our results demonstrate how minimal information processing capabilities, intrinsic to nonequilibrium systems like living cells, can profoundly influence both individual and collective behaviours. This framework bridges cell-scale activity and large-scale intelligent motion of active agents and offers insights relevant to systems ranging from synthetic colloids to biological collectives or robotic swarms.

Phenomenological rules that govern the collective behaviour of complex physical systems are powerful tools because they can make concrete predictions about their universality class based on generic considerations, such as symmetries, conservation laws, and dimensionality. While in most cases such considerations are manifestly ingrained in the constituents, novel phenomenology can emerge when composite units associated with emergent symmetries dominate the behaviour of the system. I will present the study of a generic class of active matter systems with non-reciprocal interactions where we demonstrate the existence of true long-range polar order in two dimensions and above, both at the linear level and by including all relevant nonlinearities in the Renormalization Group sense. We achieve this by uncovering a mapping of our scalar active mixture theory to the Toner-Tu theory of dry polar active matter by employing a suitably defined polar order parameter. I will then show that the complete effective field theory of fluctuations -- which includes all the soft modes and the relevant nonlinear terms -- belongs to the (Burgers-) Kardar-Parisi-Zhang universality class. This classification allows us to prove the stability of the emergent polar long-range order in scalar non-reciprocal mixtures in two dimensions, and hence a conclusive violation of the Mermin-Wagner theorem. Finally, I will briefly show how to extend this dry system to a wet case, where hydrodynamic interactions are taken into consideration in the presence of a momentum-conserving fluid. The mapping to a polar active fluid is again crucial to uncover a fluid mediated linear instability for traveling waves.

This talk will describe recent attempts at building quantitative theories of active nematics guided by experimental data.  Two examples will be considered - a confined 3D flow aligned fluid and a 2D bulk fluid. Further, some ongoing work on optimal control theory for control of active flows will be discussed.

In this talk, I will provide an overview of my recent research. The first part focuses on the main line of my thesis project, exploring network theory issues using the formalism of statistical mechanics. 

The recent Laplacian renormalization group [1] has introduced a new perspective on treating networks within this framework, opening up several research avenues. Notably, we developed a community detection method that resolves information aggregation in networks at various resolutions [2]. We also investigated nodes that act as bottlenecks for temporal diffusion, proposing an alternative centrality measure. This measure connects with the fluctuation dissipation theorem, analogized with the Laplacian formalism. 

Additionally, we identified new methods for detecting spectral dimensions, which under certain conditions, are related to the specific heat of graphs. 

The second part briefly covers part of my research on dynamical systems. The project I would like to share aims to describe the dynamical effects of feed-forward and cyclic coupling structures in a modified Wilson-Cowan model.

[1] Villegas, P., Gili, T., Caldarelli, G. et al. Laplacian renormalization group for heterogeneous networks. Nat. Phys. 19, 445–450 (2023)

[2] arXiv:2301.04514

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