Condensed Matter Theory

Abstract:

Living systems are intrinsically out of equilibrium, which makes their physical description challenging. This has led to the emergence, over the past thirty years, of a new field of physics, active matter, which studies collectives whose components dissipate energy to perform work. Two common features of biological and artificial active matter systems are their ability to respond to environmental stimuli through gradient-following behavior, and to affect the fields whose gradients they respond to. The interplay between these two phenomena lead to the emergence of intrinsically out-of-equilibrium field-mediated interactions, which are long-ranged and potentially non-reciprocal, and can lead to spectacular self-organization behavior. Field-mediated interactions are relevant to many biological systems, for instance populations of bacteria and mixtures of catalytic enzymes, and are likely to be involved in intracellular organization processes. Previous studies on the collective behavior of non-reciprocally interacting agents have focused on short-range interactions. The effect of long-range, intrinsically out-of-equilibrium interactions at the collective level is meanwhile still not fully understood. In this thesis, we thus study the self-organization of catalytic systems which exhibit field-mediated non-reciprocal interactions using analytical and numerical tools. We begin with an overview of the concepts approached in this thesis. We describe the mechanisms through which active particles can interact with, create and respond to field gradients, explain how these two abilities lead to effective interactions between active particles and their relevance to intracellular behavior. Throughout this introduction, we introduce minimal models describing the self-organization of catalytic particles, which serve as a starting point for the rest of the thesis. We then characterize the consequences of using a detailed description of the catalytically active particles under study. We do so by adding a Michaelis-Menten-like substrate concentration dependence to the catalytic activity, and by taking into account the effect of size dispersity. Our analytical calculations show that these two ingredients strongly enrich the phenomenology of catalytic phase separation. In the second part, we switch our focus to the study of catalytically active particles involved in model metabolic cycles, in which the product of a given catalytic species is the substrate of the next. We analytically and numerically characterize the behavior of a metabolic cycle involving an arbitrary number of catalytically active and chemotactic particles with identical parameters. We find that cycles with an even number and an odd number of catalytic species show a qualitatively different behavior, with the latter being able to develop oscillatory steady states. We then study metabolic cycles of three species with arbitrary parameters. We discover that the resulting network effects can give rise to clustering of active species which are all self-repelling, the conditions for which we calculate analytically and confirm numerically. Going beyond this result, we perform a classification of all the three-species metabolic networks depending on their ability to self-organize. Coarse-graining the interactions between the active species leads to the identification of the inter-species interaction motifs which tend to stabilize or destabilize a metabolic cycle. Generic cycles can be mapped to a small subset of elementary cycles, whose stability is obtained based on the decomposition into single-species and pair interaction motifs. Finally, we summarize in detail the results obtained in this thesis, and propose some directions for future research.2023-08-2

Abstract:

We consider magic-angle twisted bilayer graphene (TBG) at filling $\nu=+3$, where experiments have observed a robust quantized anomalous Hall effect. This has been attributed to the formation of a valley- and spin-polarized Chern insulating ground state that spontaneously breaks time-reversal symmetry, and is stabilized by a hexagonal boron nitride (hBN) substrate. We identify three different types of domain wall, and study their properties and energetic selection mechanisms via theoretical arguments and Hartree-Fock calculations adapted to deal with inhomogeneous moir\'e systems. We comment on the implications of these results for transport and scanning probe experiments.

Abstract:

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.