Condensed Matter Theory

Abstract:

Fluctuation theorems specify the non-zero probability to observe negative entropy production, contrary to a naive expectation from the second law of thermodynamics. For closed particle trajectories in a fluid, Stokes theorem can be used to give a geometric characterization of the entropy production. Building on this picture, we formulate a topological fluctuation theorem that depends only by the winding number around each vortex core and is insensitive to other aspects of the force. The probability is robust to local deformations of the particle trajectory, reminiscent of topologically protected modes in various classical and quantum systems. We demonstrate that entropy production is quantized in these strongly fluctuating systems, and it is controlled by a topological invariant. We demonstrate that the theorem holds even when the probability distributions are non-Gaussian functions of the generated heat.

Abstract:

This thesis investigates the conformation and dynamics of active polymers driven tangentially along their backbone in complex environments, including porous structures, granular media, and aqueous settings. Active polymers, in contrast to passive systems, are self-driven entities capable of converting energy into mechanical motion, a characteristic observed in both biological and synthetic systems. Through advanced computer simulations, this research examines the interplay between polymer flexibility, self-propulsion strength, and environmental features such as fluid-mediated interactions and obstacle arrangements in porous media. The findings reveal how conformational transitions, such as coil-stretch and spiral formations, influence polymers' transport. By elucidating the influence of activity on both conformational and dynamical properties, this thesis enhances the understanding of transport phenomena in active matter. The results have broad implications for biological processes, such as intracellular transport and active motion of polymer-like worms, and for the development of synthetic active materials

Abstract:

We investigate the full doping and strain-dependent phase diagram of the normal state of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all nonzero integer fillings of the moiré unit cell, is found to be ubiquitous for noninteger doping as well. We demonstrate that the corresponding electronic compressibility and Fermi surface structure are consistent with the “cascade” physics and Landau fans observed experimentally. This suggests a unified picture of the phase diagram of TBG in terms of IKS order.