Talks

We present results of construction of the ground states of a paradigmatic strongly interacting quantum system namely the square lattice quantum dimer model as a group equivariant convolutional neural network variational state. The network is trained by minimizing, using stochastic gradient descent, the Monte Carlo estimated energy expectation value. We show comparison with exact diagonalization for small systems (size = 8x8) and with quantum Monte Carlo for larger systems up to 48x48.

In this work, I explore the topological features of aggregation patterns in the Vicsek Model, a widely used framework for describing the collective dynamics of active matter. By varying the three key parameters—population size N, interaction radius R, and noise η, different point sets of self- organising agents are generated. To analyse the emergent structures, I employ topological tools, namely the Euler characteristic and Betti numbers, in both spatial and temporal domains. The Euler characteristic, a fundamental topological invariant, provides insights into system connectivity, while Betti numbers characterise features such as connected components, loops, and voids. Three-dimensional Euler Characteristic Surfaces (ECS) are constructed that carry the summary of the spatio-temporal evolution of the Euler Characteristic. Further, a metric distance, which we name the Euler Metric (EM), is estimated between these surfaces to investigate how system parameters influence aggregation dynamics. Additionally, I analyse order parameters to distinguish between ordered and chaotic regimes, further contextualising the topological findings.

Statistical physics deals with the large amount of heterogeneous population, nonequilibrium systems and have facilitated the studies of complex systems dynamics. Now with the help of volumes of data available it is possible to understand the dynamical processes ongoing on complex systems through nonlinearity, feedback loops, emergence and in some instances  critical transitions via data driven approaches, computational modeling and complex networks.  In addition to this there are wicked problems, characterized by their complexity and interconnectedness. These are referred to as social, economical, environmental or cultural issues that defy simple solutions due to their inherent ambiguity, multiple variable interactions and  lack of a clear convergent solution. The complex systems approach provides a framework for understanding and addressing such problems by emphasizing interconnectedness and feedback loops, which can help to identify and mitigate unintended consequences of policy interventions. Wicked problems involve multiple, interconnected factors, making it difficult to pinpoint through single cause or effect. Complex systems thinking involves interconnectedness of various factors and actors, helping to understand how different elements influence each other & drives the feedback loops and recognizing how actions and interventions can lead to unintended consequences through feedback loops and path dependencies which is crucial for detailed understanding and  effective policy design. In this talk I will discuss some wicked problems and their complexity inspired solutions.

Keywords: Interaction, Interconnectedness, Complex networks, Random Matrices, Ecological Flourishing

Glassy systems are ubiquitous in nature, appearing in materials ranging from window glass to biological matter. These systems are non-crystalline solids that structurally resemble liquids but exhibit extremely slow dynamics. In this talk, I will focus on a particular class of glassy materials known as topological glass formers—systems composed of ring polymers. We investigate how aging influences the dynamics of these systems and explore how their behavior changes across the temperature–stiffness phase space. Interestingly, we find a nonlinear relationship between the glass transition temperature and the stiffness of the rings. A central role is played by threading interactions—entanglement-like constraints unique to ring polymers, which become increasingly long-lived as the system ages. Together, these features give rise to a distinct form of glassy dynamics that emerges purely from the system’s topology.

In this talk, I will present findings from our recent work (Phys. Rev. B 108, 024203 (2023)), where we propose a Monte Carlo simulation to understand electron transport in a non-equilibrium steady state (NESS) for the lattice Coulomb Glass model, created by continuous excitation of single electrons to high energies followed by relaxation of the system. Around the Fermi level, the NESS state roughly obeys the Fermi-Dirac statistics, with an effective temperature (Teff) greater than the bath temperature of the system (T). Teff is a function of T and the rate of photon absorption by the system. Furthermore, we find that the change in conductivity is only a function of relaxation times and is almost independent of the bath temperature. Our results indicate that the conductivity of the NESS state can still be characterized by the Efros-Shklovskii law with an effective temperature of Teff > T. Additionally, the dominance of phononless hopping over phonon-assisted hopping is used to explain the hot electron model's relevance to the conductivity of the NESS state.

When do mucus films plug lung airways? Using reduced-order simulations of a large ensemble of randomly perturbed films, we show that the answer is not determined by just the film’s volume. While very thin films always stay open and very thick films always plug, we find a range of intermediate films for which plugging is uncertain. The fastest-growing linear mode of the Rayleigh-Plateau instability ensures that the film’s volume is divided among multiple humps. However, the nonlinear growth of these humps can occur unevenly, due to spontaneous axial sliding—a lucky hump can sweep up a disproportionate share of the film’s volume and so form a plug. This sliding-induced plugging is robust and prevails with or without gravitational and ciliary transport.

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.