We identify the many-body counterpart of flat bands, which we call many-body cages, as a general mechanism for non-
equilibrium phenomena such as a novel type of glassy eigenspectrum order and many-body Rabi oscillations in the time
domain. We focus on constrained systems of current interest in the context of Rydberg atoms and synthetic or
emergent gauge theories. We find that their state graphs host motifs which produce flat bands in the many-body spectrum
at a particular set of energies. Basis states in Fock space exhibit an order parameter based on band overlap in the absence of
quenched disorder, with an intricate, possibly fractal, distribution over Fock space which is reflected in a distinctive
structure of a non-vanishing post-quench long-time Loschmidt echo. In general,
phenomena familiar from single-particle flat bands manifest themselves in characteristic many-body incarnations, such as
a reentrant `Anderson' delocalisation, offering a rich ensemble of experimental signatures in the abovementioned
quantum simulators.
Cells are by definition the smallest units of life, but in contrast to the hydrogen atom, i.e., the smallest unit of chemistry that we can fully describe using the laws of physics, there is no chance for their coherent fundamental understanding. The reason is that more than 3 billions of years of evolution have thoroughly complexified living systems to the point that today, only computers and AI may be able to comprehend them in their entirety. In the quest to define more quantitatively approachable living systems, we are designing minimal cells from the bottom-up. We have particularly focused on the phenomenon of cell division, aiming at membrane compartments that are able to orchestrate their own division through energy dissipation. I will present our latest results and explain why obtaining simplicity can be challenging if the role models - living cells - are so complex.
The majority of cells in our body do not move around—but when they do, it is for an important reason: single and collectively migrating cells shape us during development, they protect us during immune response but can also harm us during cancer progression. Yet, the underlying dynamics of how cells move and interact with each other and their environment remains unclear. I will discuss how data-driven theoretical approaches can be used to learn the dynamical laws underlying cell movement, morphology and interactions of cells in controlled artificial environments. By inferring a stochastic equation of motion directly from experimental data, we show that cells exhibit intricate non-linear deterministic dynamics that adapt to the geometry of confinement. We extend this approach to interacting systems, by tracking how trajectories of colliding pairs of cells scatter. This allows us to develop and constrain a phenomenological theory of contact-interactions between cells. Finally, I will discuss how our approach can be generalized to identify the interactions rules underlying the many-body stochastic dynamics that controls collective migration in multicellular systems.
