Talks

We consider a set of hardcore run and tumble particles on a 1d periodic lattice. The effect of external potential has been modeled as a special site where the tumbling probability is much larger than the rest of the system. We call it a ‘defect’ site and move its location along the ring lattice with speed u. When bulk tumbling rate is zero, in absence of any defect the system goes to a jammed state with no long range order. But introduction of the moving defect creates a strongly phase separated state where almost all active particles are present in a single large cluster, for small and moderate u. This striking effect is caused by the long-ranged velocity correlation of the active particles, induced by the moving defect. For large u, a single large cluster is no longer stable and breaks into multiple smaller clusters. When bulk tumbling rate is non-zero, a competition develops between the time-scales associated with tumbling and defect motion. While the moving defect attempts to create long ranged velocity order, bulk tumbling tends to randomize the velocity alignment. If the bulk tumbling rate is small enough such that relatively small number of tumbles take place during the time the moving defect travels through the entire system, the defect has enough time to restore the order in the system and our simulations show that the long range order in velocity and density survive. For larger tumbling rate, long range order is destroyed and the system develops multiple regions of high density and low density regions. We also propose possible experimental setup where our results can be verified.

In this talk, I present numerical results from a comprehensive Monte Carlo study in two dimensions of coarsening kinetics in the Coulomb glass (CG) model on a square lattice. The CG model is characterized by spin-spin interactions which are long-range Coulombic and antiferromagnetic. For the nonequilibrium properties we have studied spatial correlation functions and domain growth laws. At half filling and small disorders, we find that domain growth in the CG is analogous to that in the nearest-neighbor random-field Ising model. The domain length scale L(t ) shows a crossover from a regime of “power-law growth with a disorder-dependent exponent” [L(t ) ∼ t 1/z̄ ] to a regime of “logarithmic growth with a universal exponent” [L(t ) ∼ (ln t ) 1/ψ ]. We next look at the results for the asymmetric CG (slightly away from half filling) at zero disorder, where the ground state is checkerboard-like with excess holes distributed uniformly. We find that the evolution morphology is in the same dynamical universality class as the ordering ferromagnet. Further, the domain growth law is slightly slower than the Lifshitz-Cahn-Allen law, L(t ) ∼ t 1/2 , i.e., the growth exponent is underestimated. We speculate that this could be a signature of logarithmic growth in the asymptotic regime.

I will summarize some recent results on systems of dipole-conserving point particles, 'fractons'. These exhibit non-equilibrium dynamics characterized by attractors, that cannot be characterized by Gibbsean statistical mechanics. Fracton dynamics generically possess a 'Janus pont' of low complexity around which a bidirectional arrow of time naturally obtains. Its Boltzmann entropy is unbounded and thus the dynamics evades 'heat death' at late times, suggesting a surprisingly clean resolution of the arrow-of-time paradox in non-equilibrium dynamics.

The hippocampus supports two important functions: spatial navigation and the storage of episodic memories. Yet, how these two seemingly distinct roles converge in a single circuit remains an open question. In this talk, I will present a neural model that leverages the low-dimensional attractor dynamics of spatial "grid cells" to implement associative, spatial, and episodic memory, thus unifying these distinct functions. Our model, Vector-HaSH (Vector Hippocampal Scaffolded Heteroassociative Memory) operates through a factorization of the content of memories from dynamics that generate error-correcting stable states. This leads to a graceful trade-off between number of stored items and recall detail, unlike the abrupt capacity limits found in classical Hopfield-like memory models. We find that the usage of pre-structured low-dimensional representations also enables high-capacity sequence memorization by recasting the chaining problem of high-dimensional states into one of learning low-dimensional transitions. Further, our presented approach reproduces several hippocampal experiments on spatial mapping and context-dependent representations, and provides a circuit model of the 'memory palaces' used by memory athletes. Thus, this work provides a unified framework for understanding how the hippocampus simultaneously supports spatial mapping, associative memory, and episodic memory.

Exact solutions for excited states in non-integrable quantum Hamiltonians have revealed novel dynamical phenomena that can occur in quantum many-body systems. This work proposes a method to analytically construct a specific set of volume-law-entangled exact excited eigenstates in a large class of spin Hamiltonians. In particular, we show that all spin chains that satisfy a simple set of conditions host exact volume-law eigenstates in the middle of their spectra. Examples of physically relevant spin chains of this type include the transverse-field Ising model, PXP model, spin-S XY model, and spin-S Kitaev chain. Although these eigenstates are highly atypical in their structure, they are thermal with respect to local observables. Our framework also unifies many recent constructions of volume-law entangled eigenstates in the literature. Finally, we show that a similar construction also generalizes to spin models on graphs in arbitrary dimensions.

We introduce a rejection-free, flat histogram, cluster algorithm to determine the density of states of hardcore lattice gases. We show that the algorithm is able to efficiently sample low entropy states that are usually difficult to access, even when the excluded volume per particle is large. The algorithm is based on simultaneously evaporating all the particles in a strip and reoccupying these sites with a new appropriately chosen configuration. We implement the algorithm for the particular case of the hard-core lattice gas in which the first k next-nearest neighbors of a particle are excluded from being occupied. It is shown that the algorithm is able to reproduce the known results for k = 1, 2, 3 both on the square and cubic lattices. We also show that, in comparison, the corresponding flat histogram algorithms with either local moves or unbiased cluster moves are less accurate and do not converge as the system size increases.

Nonlinear dynamics aims to elucidate the basic mechanisms necessary to reflect the temporal behavior of a natural system. The data analysis and modeling techniques proposed by artificial intelligence (deep networks, computational reservoirs, recurrent networks, as examples), on the other hand, ostensibly resign the mechanistic vision for a data-oriented modeling paradigm.  In these lectures, these apparently antagonistic approaches will be analyzed in parallel, using as examples my work on the physics of birdsong production and vocal learning.

Small systems consisting of a few particles are increasingly technologically relevant. In such systems, an intense debate in microcanonical statistical mechanics has been about the correctness of Boltzmann’s surface entropy versus Gibbs’ volume entropy. While the former considers states within a fixed energy window centered around the energy of the system, the latter considers all states with energy lesser than or equal to the energy of the system. Both entropies have shortcomings─while Boltzmann entropy predicts unphysical negative/infinite absolute temperatures for small systems with an unbounded energy spectrum, Gibbs entropy entirely disallows negative absolute temperatures, in disagreement with experiments. We consider a relative energy window, motivated by the Heisenberg energy-time uncertainty principle and an eigenstate thermalization time inversely proportional to the system energy. The resulting entropy ensures positive, finite temperatures for systems without a maximum limit on their energy and allows negative absolute temperatures in bounded energy spectrum systems, e.g., with population inversion. It also closely matches canonical ensemble predictions for prototypical systems, for instance, correctly describing the zero-point energy of an isolated quantum harmonic oscillator. Overall, we enable accurate thermodynamic models for isolated systems with few degrees of freedom.