ICTS

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.

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.

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.

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

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.

We uncover activity-driven crossover from phase separation to a new turbulent state in a two- dimensional system of counter-rotating spinners. We study the statistical properties of this active- rotor turbulence using the active-rotor Cahn-Hilliard-Navier-Stokes model, and show that the vor- ticity ω ∝ ϕ, the scalar field that distinguishes regions with different rotating states. We explain this intriguing proportionality theoretically, and we characterize power-law energy and concentra- tion spectra, intermittency, and flow-topology statistics. We suggest biological implications of such turbulence. This work has been done with Biswajit Maji and Nadia Bihari Padhan. https://arxiv.org/abs/2503.03843

Hard-core lattice-gas models serve as minimal yet powerful models to explore entropy-driven phase transitions. In these models, particles are restricted from occupying neighboring sites up to a specified kth next-nearest neighbor, effectively bridging the behavior from simple nearest-neighbor exclusion to the continuum hard-sphere gas. While most prior studies have examined cases up to k = 3, this talk presents a detailed investigation of the lattice-gas model on a triangular lattice up to k = 7, using a rejection free flat histogram algorithm enhanced with cluster moves. Our findings reveal that for k = 3 to k = 7, the system exhibits a single, discontinuous phase transition from a low-density disordered fluid to a high-density sublattice-ordered phase. This conclusion is supported by the analysis of partition function zeros and the nonconvexity of entropy.

We study the dynamics of an athermal inertial active particle moving in a shear-thinning medium in $d=1$. The viscosity of the medium is modeled using a Coulomb-tanh function, while the activity is represented by an asymmetric dichotomous noise with strengths $-\Delta$ and $\mu\Delta$, transitioning between these states at a rate $\lambda$. Starting from the Fokker-Planck~(FP) equation for the time-dependent probability distributions $P(v,-\Delta,t)$ and $P(v,\mu\Delta,t)$ of the particle's velocity $v$ at time $t$, moving under the influence of active forces $-\Delta$ and $\mu\Delta$ respectively, we analytically derive the steady-state velocity distribution function $P_s(v)$, explicitly dependent on $\mu$. Also, we obtain a quadrature expression for the effective diffusion coefficient $D_e$ for the symmetric active force case~($\mu=1$). For a given $\Delta$ and $\mu$, we show that $P_s(v)$ exhibits multiple transitions as $\lambda$ is varied. Subsequently, we numerically compute $P_s(v)$, the mean-squared velocity $\langle v^2\rangle(t)$, and the diffusion coefficient $D_e$ by solving the particle's equation of motion, all of which show excellent agreement with the analytical results in the steady-state. Finally, we examine the universal nature of the transitions in $P_s(v)$ by considering an alternative functional form of medium's viscosity that also capture the shear-thinning behavior.

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.

Legendre transform between thermodynamic quantities such as the Helmholtz free energy and entropy plays a key role in the formulation of the canonical ensemble. In the standard treatment, the transform exchanges the independent variable from the system’s internal energy to its conjugate variable—the inverse temperature of the heat reservoir. In this article, we formulate a microscopic version of the trans- form between the free energy and Shannon entropy of the system, where the conju- gate variables are the microstate probabilities and the energies (scaled by the inverse temperature). The present approach gives a non-conventional perspective on the connection between information-theoretic measure of entropy and thermodynamic entropy. We focus on the exact differential property of Shannon entropy, utilizing it to derive central relations within the canonical ensemble. Thermodynamics of a system in contact with the heat reservoir is discussed in this framework. Other approaches, in particular, Jaynes’ maximum entropy principle is compared with the present approach. Ref: R.S. Johal, Microscopic Legendre Transform, Canonical Ensemble and Jaynes’ Maximum Entropy Principle, Foundations of Physics, 55:12 (2025). https://doi.org/10.1007/s10701-025-00824-7

TBA

We study the nonequilibrium stationary state (NESS) induced by quantum resetting of a system of N noninteracting bosons in a harmonic trap. Under repeated resetting, the system reaches a NESS where the positions of bosons get strongly correlated due to simultaneous resetting induced by the trap. We fully characterize the steady state by analytically computing several physical observables such as the average density, extreme value statistics, order and gap statistics, and also the distribution of the number of particles in a region [−L,L], known as the full counting statistics (FCS). This is a rare example of a strongly correlated quantum many-body NESS where various observables can be exactly computed.

We present PIC-VIC, a novel computational framework for simulating collective behavior of self-propelled particles on curved surfaces. Building upon the Particle-in-Cell (PIC) method, widely used in plasma physics, we track individual particles (Lagrangian description) while employing a static Eulerian mesh for interaction calculations. Using mesh with arbitrary geometries we extend the Vicsek model to study flocking dynamics on curved manifolds. Crucially, we incorporate Laplace-Beltrami based vector diffusion to ensure geometrically consistent averaging of particle velocities, effectively implementing parallel transport on the curved surface. This particle-based PIC-VIC method complements continuum active-hydrodynamics approaches and allows for the investigation of curvature-induced fluctuations. We demonstrate the capabilities of PIC-VIC and discuss its potential for uncovering novel collective phenomena, emergent patterns, and geometry-driven interactions in biological, physical, and artificial systems constrained to non-Euclidean spaces.

Two dimensional elastic tethered membranes (ball-and-spring model) with finite bending rigidity and no self-avoidance are known to exist in a flat/crumpled phase for small/large temperatures. The change in phase is mediated by a second order phase transition. Once self-avoidance is introduced, the tethered membranes do not exhibit a crumpled phase and remain flat for all temperatures. By considering the nodes of the membrane as active Brownian particles, we observe that membranes without self-avoidance retain the crumpling transition with activity as the tuning parameter. We find evidence of a crumpled phase with Flory dimensions of 2.4 in spherical self-avoiding active membranes.

In this talk, I will describe a method that rigorously transforms the toric code model into independent emergent qubits, which enables us to construct the toric code eigenstates exactly and devise precise quantum circuits for their implementation on quantum processors.

Introducing a single hole in a strongly repulsive Hubbard model at half filling switches the ground state from an antiferromagnet to a ferromagnet on bipartite lattices. However, there is no general understanding of how the magnetic order is affected by odd loops which cause kinetic frustration. We find that local frustration strongly affects global magnetization by binding singlets in general networks.

We study extreme events of avalanche activities in finite-size two-dimensional self- organized critical (SOC) models, specifically the stochastic Manna model (SMM) and Bak-Tang-Weisenfeld (BTW) sandpile model. Employing the approach of block maxima, the study numerically reveals that the distributions for extreme avalanche size and area follow the generalized extreme value (GEV) distribution. The extreme avalanche size follows the Gumbel distribution with shape parameter $\xi=0$ while in case of the extreme avalanche area, we report $\xi>0$. We propose scaling functions for extreme avalanche activities that connect the activities on different length scales. With the help of data collapse, we estimate the precise values of these critical exponents. The scaling functions provide an understanding of the intricate dynamics for different variants of the sandpile model, shedding light on the relationship between system size and extreme event characteristics. Our findings give insight into the extreme behavior of SOC models and offer a framework to understand the statistical properties of extreme events.

Effect on arrangement of motors on cargo surface and collective transport by a team of motor proteins

The diversity of diffusive systems exhibiting long-range correlations characterized by a stochastically varying Hurst exponent calls for a generic multifractional model. In this talk I will present a simple, analytically tractable model which fills the gap between mathematical formulations of multifractional Brownian motion and empirical studies. In the model, called telegraphic multifractional Brownian motion (TeMBM), the Hurst exponent is modelled by a smoothed telegraph process which results in a stationary beta distribution of exponents as observed in biological experiments. I will also discuss a methodology to identify TeMBM in experimental data and present concrete examples from biology, climate and finance to demonstrate the efficacy of the presented approach.

We explore the phenomena of prethermalization in a many-body classical system of rotors under aperiodic drives characterised by waiting time distribution (WTD), where the waiting time is defined as the time between two consecutive kicks. We consider here two types of aperiodic drives: random and quasi-periodic. We observe a short-lived pseudo-thermal regime with algebraic suppression of heating for the random drive where WTD has an infinite tail, as observed for Poisson and binomial kick sequences. On the other hand, quasi-periodic drive characterised by a WTD with a sharp cut-off, as observed for Thue-Morse sequence of kick, leads to prethermal region where heating is exponentially suppressed. The kinetic energy growth is analyzed using an average surprise associated with WTD quantifying the randomness of drive. In all of the aperiodic drives we obtain the chaotic heating regime for late time, however, the diffusion constant gets renormalized by the average surprise of WTD in comparison to the periodic case.

Active-fluid turbulence has been found in bacterial suspensions, but not so far in their algal counterparts. We present the first experimental evidence for turbulence in dense algal suspensions of Chlamydomonas reinhardtii. We carry out a detailed analysis of the statistical properties of the flow present in these cell suspensions and show that they are quantitatively distinct from their counterparts in two-dimensional fluid and bacterial turbulence.

Refrigerators are inseparable from everyday life, industrial manufacturing, and research labs. In this talk, I will present our recent investigation on the refrigerator working between a finite-sized cold heat sink (which means that the heat capacity of the cold bath is finite) and an infinite-sized hot reservoir (environment). We assume that initially the finite-sized cold heat sink at temperature Ti ≤ Th, where Th is the hot reservoir temperature. By consuming the input work/power, the refrigerator transfers the heat from a finite-sized cold sink to the hot heat reservoir. Hence, the temperature of the finite-sized cold heat sink starts to decrease until it reaches the desired low-temperature Tf. By minimizing the input work in this heat transport process, we find the optimal path for temperature rate. We also calculate the coefficient of performance of the refrigerator.

Fundamental laws of physics are symmetric under time reversal (T) symmetry, hence we are tempted to deduce that the evolution of the world may be T-symmetric. On the other end, there is an important conjecture that a conservative system with many particles becomes randomized. The latter process, called thermalization, is related to the second law of thermodynamics that makes the macroscopic world asymmetric. In addition to these two divergent topics, I will cover additional T-breaking frameworks: multiscale energy transfer, open systems, and asymmetric objects. In driven dissipative nonequilibrium systems, including turbulence, the multiscale energy flux from large scales to small scales helps determine the arrow of time. In addition, open systems are often irreversible due to particle and energy exchanges between the system and the environment.

As natural environments are not static, the model parameters in biologically realistic problems are not constant in time, and such situations in population biology are often described in terms of effective parameters that subsume some of the details of the problem; however, it is not always possible to define an effective parameter. I will describe a simple solvable model to address when and why an effective parameter can not be defined, and the implications thereof.

We study some of the properties of non-equilibrium phase transitions of an interacting system that is in a state with large deviation from equilibrium. We consider a field theoretical model of scalar particles interacting with vector gauge fields with local U (1) gauge symmetry. We show that the evolution of this system towards an equilbrium state can be described using the principle of emergence of global gauge invariance. As a toy model we consider a scalar-vector model with local U (1) gauge invariance. Invoking the assumption of local U (1) gauge invariance breaking we evaluate time evolution of some of the observables of this system. To make our calculations explicit we calculate the time evolution of order parameter of this sytem and evaluate its scaling behaviour near transition region. In the mean-field approximation we show that, for the unperturbed case, that correspond to no external driving the order parameter has a universal algebriac decay m(t) ∼ t −1/2 . However for time-dependent diffusion coefficient, it is found that order parametr has a universal algabriac decay m(t) ∼ t −1/3 . The results are in total agreement with the recent findings using stochastic models of non-equilibrium system

Run-and-tumble (RT) motion is commonly observed in flagellated microswimmers, arising from synchronous and asynchronous flagellar beating. In addition to hydrodynamic interactions, mechanical coupling has recently been recognized to play a key role in flagellar synchronization. To explore this, we design a macroscopic model system that comprises dry, self-propelled robots linked by a rigid rod to model a biflagellated microorganism. To mimic a low Reynolds number environment, we program each robot to undergo overdamped active Brownian (AB) motion. We find that such a system exhibits RT-like behavior, characterized by sharp tumbles and exponentially distributed run times, consistent with real microswimmers. We quantify tumbling frequency and demonstrate its tunability across experimental parameters. Additionally, we provide a theoretical model that reproduces our results, elucidating physical mechanisms governing RT dynamics.

Proteins are biopolymers, composed of repeating sequence of amino acids (AA). In a typical sequence, the constituting AAs have different charges, hydrophobicity, and capacities to form directional and non-directional interactions. Such heterogeneity can results in sequences lacking a stable three dimensional structure. This class of proteins are intrinsically disordered protein (IDPs). A deeper understanding of IDPs require appropriate characterization of the conformations. To this end, scattering and single molecular spectroscopic measurements often assign a single Flory exponent (equivalently fractal dimension) to the IDPs. In this talk, I highlight limitation of this method by enhanced sampling of atomistic resolution conformations of disordered \beta-casein. I will show that the underlying energy landscape of the IDP contains a global minimum along with two shallow funnels. Employing static polymeric scaling laws separately for individual funnels, we find that they cannot be described by the same polymeric scaling exponent. Around the global minimum, the conformations are globular, whereas in the vicinity of local minima, we recover coil-like scaling. To elucidate the implications of structural diversity on equilibrium dynamics, we initiated standard MD simulations in the NVT ensemble with representative conformations from each funnel. Global and internal motions for different classes of trajectories show heterogeneous dynamics with globule to coil-like signatures. Thus, IDPs can behave as entirely different polymers in different regions of the conformational space.