Condensed Matter Theory

Abstract:

Active particles are nonequilibrium entities that uptake energy and convert it into self-propulsion. A dynamically rich class of inertial active particles having features of wave-particle coupling and wave memory are walking/superwalking droplets. Such classical, active wave-particle entities (WPEs) have previously been shown to exhibit hydrodynamic analogs of many single-particle quantum systems. Inspired by the rich dynamics of strongly interacting superwalking droplets in experiments, we numerically investigate the dynamics of WPE clusters using a stroboscopic model. We find that several interacting WPEs self-organize into a stable bound cluster, reminiscent of an atomic nucleus. This active cluster exhibits a rich spectrum of collective excitations, including shape oscillations and chiral rotating modes, akin to vibrational and rotational modes of nuclear excitations, as the spatial extent of the waves and their temporal decay rate (memory) are varied. Dynamically distinct excitation modes create a common time-averaged collective wave field potential, bearing qualitative similarities with the nuclear shell model and the bag model of hadrons. For high memory and rapid spatial decay of waves, the active cluster becomes unstable and disintegrates; however, within a narrow regime of the parameter space, the cluster ejects single particles whose decay statistics follow exponential laws, reminiscent of radioactive nuclear decay. Our study uncovers a rich spectrum of dynamical behaviors in clusters of active particles, opening new avenues for exploring hydrodynamic quantum analogs in active matter systems.

Abstract:

The Boltzmann distribution encodes our subjective knowledge of the configuration in a classical lattice model, given only its Hamiltonian. If we acquire further information about the configuration from measurement, our knowledge is updated according to Bayes' theorem. We examine the resulting “conditioned ensembles,” finding that they show many new phase transitions and new renormalization-group fixed points. (Similar conditioned ensembles also describe “partial quenches” in which some of the system's degrees of freedom are instantaneously frozen, while the others continue to evolve.) After describing general features of the replica field theories for these problems, we analyze the effect of measurement on illustrative critical systems, including: critical Ising and Potts models, which show surprisingly rich phase diagrams, with RG fixed points at weak, intermediate, and infinite measurement strength; various models involving free fields, XY spins, or flux lines in 2D or 3D; and geometrical models such as polymers or clusters. We also give a formalism for measurement of classical stochastic processes. We use this to make connections with quantum dynamics, in particular with “charge sharpening” in 1D, for which we give a purely hydrodynamic derivation of the known effective field theory. We discuss qualitative differences between RG flows for the above measured systems, described by $N\to 1$ replica limits, and those for disordered systems, described by $N\to 0$ limits. In addition to discussing measurement of critical states, we give a unifying treatment of a family of inference problems for noncritical states. These are related to the Nishimori line in the phase diagram of the random-bond Ising model, and are relevant to various quantum error correction problems. We describe distinct physical interpretations of conditioned ensembles and note interesting open questions.

Abstract:

We link the presence of “unnecessary” quantum critical surfaces within a single gapped phase of matter to the nontrivial topology of of gapped Hamiltonians that encircle the critical surface. We study a specific set of one-dimensional spin models where each such family forms a one-parameter loop in a two-dimensional phase diagram. Foliating the noncritical region by such loops identifies “radial” and “angular” coordinates in the phase diagram that respectively parametrize different families and different members of a single family. We show that each one-parameter family is a generalized Thouless charge pump, all with the same topological index, and hence the gapped phase undergoes one or more nontrivial boundary phase transitions as we vary the angular coordinate in a loop through members of one family. Tuning the radial coordinate generates loci of boundary critical points that terminate at the end points of the bulk unnecessary critical line within the gapped phase. We discuss broader implications of our results and possible extensions to higher dimensions.

Abstract:

A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [D. Müller , ] and quasiperiodically [D. Müller-Bender and G. Radons, ] time-varying delay. Compared to high-dimensional turbulent chaos that is typically found in such systems with large constant delay, laminar chaos is a very low-dimensional phenomenon. It is characterized by a time series with nearly constant laminar phases that are interrupted by irregular bursts, where the intensity level of the laminar phases varies chaotically from phase to phase. In this paper, we demonstrate that laminar chaos, and its generalizations, can also be observed in systems with random and chaotically time-varying delay. Moreover, while for periodic and quasiperiodic delays the appearance of (generalized) laminar chaos and turbulent chaos depends in a fractal manner on the delay parameters, it turns out that short-time correlated random and chaotic delays lead to (generalized) laminar chaos in almost the whole delay parameter space, where the properties of circle maps with quenched disorder play a crucial role. It follows that introducing such a delay variation typically leads to a drastic reduction of the dimension of the chaotic attractor of the considered systems. We investigate the dynamical properties and generalize the known methods for detecting laminar chaos in experimental time series to random and chaotically time-varying delay.

Abstract:

The study of active solids offers a window into the mechanics and thermodynamics of dense living matter. A key aspect of the nonequilibrium dynamics of such active systems is a mechanistic description of how the underlying mechanochemical couplings arise, which cannot be resolved in models that are phenomenologically constructed. Here, we follow a bottom-up theoretical approach to develop a thermodynamically consistent active solid model and uncover a nontrivial crosstalk that naturally ensues between mechanical response and dissipation. In particular, we show that dissipation reaches a maximum at finite stresses, while it is inhibited under large stresses, effectively reverting the system to a passive state. Our findings establish a generic mechanism plausibly responsible for the nonmonotonic behavior observed in recent experimental measurements of entropy production rate in an actomyosin material and enzymatic activity in crowded condensates.