Condensed Matter Theory

Abstract:

Due to their remarkable properties, systems that exhibit self-organization of their components resulting from intrinsic microscopic activity have been extensively studied in the last two decades. In a generic class of active matter, the interactions between the active components are represented via an effective density-dependent diffusivity in a mean-field single-particle description. Here, a class of scalar active matter is proposed by incorporating a diffusivity edge into the dynamics: when the local density of the system surpasses a critical threshold, the diffusivity vanishes. The effect of the diffusivity edge is studied under the influence of an external potential, which introduces the ability to control the behavior of the system by changing an effective temperature, which is defined in terms of the single-particle diffusivity and mobility. At a critical effective temperature, a system that is trapped by a harmonic potential is found to undergo a condensation transition, which manifests formal similarities to Bose-Einstein condensation.

Abstract:

A walker is a droplet of liquid that self-propels on the free surface of an oscillating bath of the same liquid through feedback between the droplet and its wave field. We have studied walking droplets in the presence of two driving frequencies and have observed a new class of walking droplets, which we coin superwalkers. Superwalkers may be more than double the size of the largest walkers, may travel at more than triple the speed of the fastest ones, and enable a plethora of novel multidroplet behaviors.

Abstract:

We construct and solve a classical percolation model with a phase transition that we argue acts as a proxy for the quantum many-body localization transition. The classical model is defined on a graph in the Fock space of a disordered, interacting quantum spin chain, using a convenient choice of basis. Edges of the graph represent matrix elements of the spin Hamiltonian between pairs of basis states that are expected to hybridize strongly. At weak disorder, all nodes are connected, forming a single cluster. Many separate clusters appear above a critical disorder strength, each typically having a size that is exponentially large in the number of spins but a vanishing fraction of the Fock-space dimension. We formulate a transfer matrix approach that yields an exact value ν = 2 for the localization length exponent, and also use complete enumeration of clusters to study the transition numerically in finite-sized systems.