arXiv subjects

Mrinal Sarkar

Publications and source records attributed to Mrinal Sarkar.

12 recordsLinked to original sources

arXiv2026

Universality of superdiffusion in simple random graphs

Random walks with long-range jumps can drive superdiffusive transport, replacing ordinary diffusion with an effective long-range kinetic operator. Such superdiffusive kinetics is also central to critical phenomena, notably the self-avoiding walk with long-range jump statistics, or L\'evy-SAW. This work investigates how the critical behavior is affected when the long-range connectivity itself becomes random. We study self-avoiding walks (SAWs) on a one-dimensional long-range random ring graph, where bonds are independently generated with Bernoulli probability $\sim|i-j|^{-(1+\sigma)}$. We term this walk Sparse-SAW. The same random bonds are responsible for both long-range superdiffusive transport and quenched disorder, with both simultaneously controlled by the single parameter $\sigma$, placing the problem beyond the conventional Harris and Weinrib-Halperin frameworks. Through large-scale Monte Carlo simulations and a Gaussian-truncated field theory, we show that Sparse-SAW belongs to the same universality class as the clean superdiffusive L\'evy-SAW. The random bonds generate short-range uncorrelated and long-range correlated mass disorder while simultaneously producing the long-range kinetic operator. Under coarse-graining, the latter dominates, restoring the clean critical behavior. Our study suggests that the full non-Gaussian Bernoulli statistics may lead to disorder physics beyond the conventional theory of quenched disorder, while establishing random graphs as an efficient platform for extracting the critical exponents of the clean superdiffusive L\'evy-SAW universality class.

cond-mat.stat-mech↗

arXiv2026

Emergent quantum chaos from correlations on a random graph

This work demonstrates that sparse long-range random bonds on a one-dimensional lattice alone can generate quantum-chaotic spectral correlations and also drive a localization transition in a noninteracting single-particle Hamiltonian. The model is a one-dimensional ring in which each pair of sites is connected independently with a probability $p_{ij}= d_{ij}^{-(1+\sigma)}$. Each bond carries identical unit hopping and on-site disorder is absent. Despite the absence of on-site disorder and interaction, the model displays quantum chaotic spectra with Gaussian orthogonal ensemble (GOE) level statistics at small $\sigma$ and localized eigenstates with Poisson statistics at larger $\sigma$. The transition occurs in the range $ 0.80 \lesssim \sigma_c \lesssim 0.85$, far above the summability threshold of the mean hopping profile ($\sigma=0$). A Gaussian field theory retaining only the mean and variance of the Bernoulli bonds instead predicts a threshold at $\sigma=1$, suggesting that higher cumulants are infrared-relevant. Our findings hint towards a universality class that is distinct from both the power-law random banded matrix model and the standard Anderson transition.

cond-mat.dis-nn↗

arXiv2025

Long range to short range crossover in one dimension

This work investigates the critical behavior of one-dimensional systems with long-range (LR) interactions, focusing on the crossover to short-range (SR) universality. Through large-scale Monte Carlo simulations of self-avoiding L\'evy flights on a 1D lattice, we compute the anomalous dimension \eta, the correlation length exponent \nu, and the susceptibility exponent \gamma across a wide range of LR decay parameters \sigma. Our results provide strong numerical evidence that supports Sak's scenario. They identify the crossover at \sigma^* = 1 and demonstrate the continuity of critical exponents across this point, with strong corrections to scaling. The study also reveals deviations from Flory-type scaling predictions and discusses the limitations of effective dimension approaches in general. These findings clarify the nature of the LR-SR crossover in low-dimensional systems and open avenues for exploring criticality in disordered and complex networks.

cond-mat.stat-mech↗

arXiv2025

Stationary-state dynamics of interacting phase oscillators in presence of noise and stochastic resetting

We explore the impact of global resetting on Kuramoto-type models of coupled limit-cycle oscillators with distributed frequencies both in absence and presence of noise. The dynamics comprises repeated interruption of the bare dynamics at random times with simultaneous resetting of phases of all the oscillators to a predefined state. To characterize the stationary-state behavior, we develop an analytical framework that spans across different generalizations of the Kuramoto model involving either quenched or annealed disorder or both, and for any choice of the natural frequency distribution. The framework applies to the dynamics both in absence and presence of resetting, and is employed to obtain in particular the stationary-state synchronization order parameter of the system, which is a measure of spontaneous ordering among the oscillator phases. A key finding is the pivotal role of correlations in shaping the ordering dynamics under resettling.

cond-mat.stat-mech↗

arXiv2025

Asymmetric simple exclusion process on a random comb: Transport properties in the stationary state

We address the dynamics of interacting particles on a disordered lattice formed by a random comb. The dynamics comprises that of the asymmetric simple exclusion process, whereby motion to nearest-neighour sites that are empty is more likely in the direction of a bias than in the opposite direction. The random comb comprises a backbone lattice from each site of which emanates a branch with a random number of sites. The backbone and the branches run in the direction of the bias. The number of branch sites or alternatively the branch lengths are sampled independently from a common distribution, specifically, an exponential distribution. The system relaxes at long times into a nonequilibrium stationary state. We analyse the stationary-state density of sites across the random comb, and also explore the transport properties, in particular, the stationary-state drift velocity of particles along the backbone. We show that in the stationary state, the density is uniform along the backbone and nonuniform along the branches, decreasing monotonically from the free-end of a branch to its intersection with the backbone. On the other hand, the drift velocity as a function of the bias strength has a non-monotonic dependence, first increasing and then decreasing with increase of bias. However, remarkably, as the particle density increases, the dependence becomes no more non-monotonic. We understand this effect as a consequence of an interplay between biased hopping and hard-core exclusion, whereby sites towards the free end of the branches remain occupied for long times and become effectively non-participatory in the dynamics of the system. This results in an effective reduction of the branch lengths and a motion of the particles that takes place primarily along the backbone.

cond-mat.stat-mech↗

arXiv2024

Synchronization through frequency shuffling

A wide variety of engineered and natural systems are modelled as networks of coupled nonlinear oscillators. In nature, the intrinsic frequencies of these oscillators are not constant in time. Here, we probe the effect of such a temporal heterogeneity on coupled oscillator networks, through the lens of the Kuramoto model. To do this, we shuffle repeatedly the intrinsic frequencies among the oscillators at either random or regular time intervals. What emerges is the remarkable effect that frequent shuffling induces earlier onset (i.e., at a lower coupling) of synchrony among the oscillator phases. Our study provides a novel strategy to induce and control synchrony under resource constraints. We demonstrate our results analytically and in experiments with a network of Wien Bridge oscillators with internal frequencies being shuffled in time.

cond-mat.stat-mech↗

arXiv2023

Universality of critical dynamics on a complex network

We investigate the role of the spectral dimension $d_s$ in determining the universality of phase transitions on a complex network. Due to its structural heterogeneity, a complex network generally acts as a disordered system. Specifically, we study the synchronization and entrainment transitions in the nonequilibrium dynamics of the Kuramoto model and the phase transition of the equilibrium dynamics of the classical $XY$ model, thereby covering a broad spectrum from nonlinear dynamics to statistical and condensed matter physics. Using linear theory, we obtain a general relationship between the dynamics occurring on the network and the underlying network properties. This yields the lower critical spectral dimension of the phase synchronization and entrainment transitions in the Kuramoto model as $d_s=4$ and $d_s=2$ respectively, whereas for the phase transition in the $XY$ model it is $d_s=2$. To test our theoretical hypotheses, we employ a network where any two nodes on the network are connected with a probability proportional to a power law of the distance between the nodes; this realizes any desired $d_s\in [1, \infty)$. Our detailed numerical study agrees well with the prediction of linear theory for the phase synchronization transition in the Kuramoto model. However, it shows a clear entrainment transition in the Kuramoto model and phase transition in the $XY$ model at $d_s \gtrsim 3$, not $d_s=2$ as predicted by linear theory. Our study indicates that network disorder in the region $2 \leq d_s \lesssim 3$ introduces strong finite-size fluctuations, which makes it extremely difficult to probe the existence of the ordered phase as predicted, affecting the dynamics profoundly.

cond-mat.stat-mech↗

arXiv2022

Synchronization in the Kuramoto model in presence of stochastic resetting

What happens when the paradigmatic Kuramoto model involving interacting oscillators of distributed natural frequencies and showing spontaneous collective synchronization in the stationary state is subject to random and repeated interruptions of its dynamics with a reset to the initial condition? While resetting to a synchronized state, it may happen between two successive resets that the system desynchronizes, which depends on the duration of the random time interval between the two resets. Here, we unveil how such a protocol of stochastic resetting dramatically modifies the phase diagram of the bare model, allowing in particular for the emergence of a synchronized phase even in parameter regimes for which the bare model does not support such a phase. Our results are based on an exact analysis invoking the celebrated Ott-Antonsen ansatz for the case of Lorentzian distribution of natural frequencies, and numerical results for Gaussian frequency distribution. Our work provides a simple protocol to induce global synchrony in the system through stochastic resetting.

nlin.AO↗

arXiv2022

Biased random walk on random networks in presence of stochastic resetting: Exact results

We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the direction of the bias. For the bare model as also when the model is subject to stochastic resetting, whereby the walkers on the branches reset with a constant rate to the respective backbone sites, we obtain exact stationary-state static and dynamic properties for a given disorder realization of branch lengths sampled following an arbitrary distribution. We derive a criterion to observe in the stationary state a non-zero drift velocity along the backbone. For the bare model, we discuss the occurrence of a drift velocity that is non-monotonic as a function of the bias, becoming zero beyond a threshold bias because of walkers trapped at very long branches. Further, we show that resetting allows the system to escape trapping, resulting in a drift velocity that is finite at any bias.

cond-mat.stat-mech↗

arXiv2021

Synchronization transition in the two-dimensional Kuramoto model with dichotomous noise

We numerically study the celebrated Kuramoto model of identical oscillators arranged on the sites of a two-dimensional periodic square lattice and subject to nearest neighbor interactions and dichotomous noise. In the nonequilibrium stationary state attained at long time, the model exhibits a Berezinskii-Kosterlitz-Thouless ($BKT$)-like transition between a phase at low noise amplitude characterized by quasi long-range order (critically ordered phase) and algebraic decay of correlations and a phase at high noise amplitude that is characterized by complete disorder and exponential decay of correlations. The interplay between the noise amplitude and the noise correlation time is investigated, and the complete, nonequilibrium stationary-state phase diagram of the model is obtained. We further study the dynamics of a single topological defect for various amplitude and correlation time of the noise. Our analysis reveals that a finite correlation time promotes vortex excitations, thereby lowering the critical noise amplitude of the transition with an increase in correlation time. In the suitable limit, the resulting phase diagram allows to estimate the critical temperature of the equilibrium $BKT$ transition, which is consistent with that obtained from the study of the dynamics in the Gaussian white noise limit.

nlin.AO↗

arXiv2020

Kuramoto model with additional nearest-neighbor interactions: Existence of a nonequilibrium tricritical point

A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled through the sine of their phase differences. We study here a variation of the model by including nearest-neighbor interactions on a one-dimensional lattice. While the mean-field interaction resulting from the global coupling favors global synchrony, the nearest-neighbor interaction may have cooperative or competitive effects depending on the sign and the magnitude of the nearest-neighbor coupling. For unimodal and symmetric frequency distributions, we demonstrate that as a result, the model in the stationary state exhibits in contrast to the usual Kuramoto model both continuous and first-order transitions between synchronized and incoherent phases, with the transition lines meeting at a tricritical point. Our results are based on numerical integration of the dynamics as well as an approximate theory involving appropriate averaging of fluctuations in the stationary state.

nlin.AO↗

arXiv2020

Noise-induced synchronization in the Kuramoto model on finite 2D lattice

We consider the celebrated Kuramoto model with nearest neighbour interactions, arranged on a two-dimensional square lattice in presence of two kinds of noise - annealed and quenched. We focus on both the steady state and relaxation dynamics of the model. The bare model with annealed noise on finite $2D$ lattice, in the stationary state, exhibits a crossover from synchronization to desynchronization as noise strength varies. Finite-size scaling (FSS) analysis reveals that, in the thermodynamic limit, this crossover becomes a true phase transition, which is Kosterlitz-Thouless ($KT$)-type analogous to that of $2D$ $XY$ model. On the other hand, when the noise is quenched, it does not show any kind of synchronization-desynchronization phase transition in the thermodynamic limit. But we do observe a crossover from low noise-strength synchronization to high noise-strength desynchronization in finite lattices. We analyze the crossover phenomena through the linear stability of the stationary state solutions and obtain the crossover noise-strength from the onset of local instability of the unsynchronized one. The relaxation dynamics also differs for these two types of noise. In case of annealed noise, the system, in the critically ordered phase, exhibits algebraic relaxation which is described by the phenomenological Edwards-Wilkinson (EW) model of growing surface, yielding the same dynamic exponent $z =2$. In disordered phase, the system shows an exponential decay. On the contrary, the system with quenched noise, as opposed to the annealed one, always relaxes to the stationary state exponentially. Both the system-size and noise-strength dependency of the average relaxation time in the synchronized regime are also investigated.

nlin.AO↗