arXiv subjects

Rahul Dandekar

Publications and source records attributed to Rahul Dandekar.

17 recordsLinked to original sources

arXiv2024

Current fluctuations in the Dyson Gas

We study large fluctuations of the current in a Dyson gas, a 1D system of particles interacting through a logarithmic potential and subjected to random noise. We adapt the macroscopic fluctuation theory to the Dyson gas and derive two coupled partial differential equations describing the evolution of the density and momentum. These equations are nonlinear and non-local, and the `boundary' conditions are mixed: some at the initial time and others at the final time. If the initial condition can fluctuate (annealed setting), this boundary-value problem is tractable. We compute the cumulant generating function encoding all the cumulants of the current.

cond-mat.stat-mech↗

arXiv2023

Dynamic Space Packing

Dynamic space packing (DSP) is a random process with sequential addition and removal of identical objects into space. In the lattice version, objects are particles occupying single lattice sites, and adding a particle to a lattice site leads to the removal of particles on neighboring sites. We show that the model is solvable and determine the steady-state occupancy, correlation functions, desorption probabilities, and other statistical features for the DSP of hyper-cubic lattices. We also solve a continuous DSP of balls into $\mathbb{R}^d$.

cond-mat.stat-mech↗

arXiv2023

Current fluctuations in an interacting active lattice gas

We study the fluctuations of the integrated density current across the origin up to time $T$ in a lattice model of active particles with hard-core interactions. This model is amenable to an exact description within a fluctuating hydrodynamics framework. We focus on quenched initial conditions for both the density and magnetization fields and derive expressions for the cumulants of the density current, which can be matched with direct numerical simulations of the microscopic lattice model. For the case of uniform initial profiles, we show that the second cumulant of the integrated current displays three regimes: an initial $\sqrt{T}$ rise with a coefficient given by the symmetric simple exclusion process, a cross-over regime where the effects of activity increase the fluctuations, and a large time $\sqrt{T}$ behavior with a prefactor which depends on the initial conditions, the Péclet number and the mean density of particles. Additionally, we study the limit of zero diffusion where the fluctuations intriguingly exhibit a $T^2$ behavior at short times. However, at large times, the fluctuations still grow as $\sqrt{T}$, with a coefficient that can be calculated explicitly. For low densities, we show that this coefficient can be expressed in terms of the effective diffusion constant $D_{\text{eff}}$ for non-interacting active particles.

cond-mat.stat-mech↗

arXiv2023

A Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation

We develop a biased Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels. Given a trajectory with a fixed number of collisions, the algorithm modifies both the waiting times between collisions, as well as the sequence of collisions, using local moves. We show that the algorithm is ergodic by giving a protocol that transforms an arbitrary trajectory to a standard trajectory using valid Monte Carlo moves. The algorithm can sample rare events with probabilities of the order of $10^{-40}$ and lower. The algorithm's effectiveness in sampling low-probability events is established by showing that the numerical results for the large deviation function of constant-kernel aggregation reproduce the exact results. It is shown that the algorithm can obtain the large deviation functions for other kernels, including gelling ones, as well as the instanton trajectories for atypical times. The dependence of the autocorrelation times, both temporal and configurational, on the different parameters of the algorithm is also characterized.

cond-mat.stat-mech↗

arXiv2022

Dynamical fluctuations in the Riesz gas

We consider an infinite system of particles on a line performing identical Brownian motions and interacting through the $|x-y|^{-s}$ Riesz potential, causing the over-damped motion of particles. We investigate fluctuations of the integrated current and the position of a tagged particle. We show that for $0 < s < 1$, the standard deviations of both quantities grow as $t^{\frac{s}{2(1+s)}}$. When $s>1$, the interactions are effectively short-ranged, and the universal sub-diffusive $t^\frac{1}{4}$ growth emerges with only amplitude depending on the exponent. We also show that the two-time correlations of the tagged-particle position have the same form as for fractional Brownian motion.

cond-mat.stat-mech↗

arXiv2022

Mass fluctuations in Random Average Transfer Process in open set-up

We define a new mass transport model on a one-dimensional lattice of size $N$ with continuous masses at each site. The lattice is connected to mass reservoirs of different `chemical potentials' at the two ends. The mass transfer dynamics in the bulk is equivalent to the dynamics of the gaps between particles in the Random Average Process. In the non-equilibrium steady state, we find that the multi-site arbitrary order cumulants of the masses can be expressed as an expansion in powers of $1/N$ where at each order the cumulants have a scaling form. We introduce a novel operator approach which allows us to compute these scaling functions at different orders of $1/N$. Moreover, this approach reveals that, to express the scaling functions for higher order cumulants completely one requires all lower order multi-site cumulants. This is in contrast to the Wick's theorem in which all higher order cumulants are expressed solely in terms of two-site cumulants. We support our results with evidence from Monte-Carlo simulations.

cond-mat.stat-mech↗

arXiv2022

Macroscopic fluctuations of a driven tracer in the symmetric exclusion process

The dynamics of an asymmetric tracer in the symmetric simple exclusion process (SEP) is mapped, in the continuous scaling limit, to the local current through the origin in the zero-range process (ZRP) with a biased bond. This allows us to study the hydrodynamics of the SEP with an asymmetric tracer with a step initial condition, leading to the average displacement as a function of the bias and the densities on both sides. We then derive the cumulant generating function of the process in the high-density limit, by using the Macroscopic Fluctuation Theory and obtain agreement with the microscopic results of Poncet et al (2021). For more general initial conditions, we show that the tracer variance in the high-density limit depends only on the generalized susceptibility in the initial condition.

cond-mat.stat-mech↗

arXiv2021

Transport and fluctuations in mass aggregation processes: mobility driven clustering

We calculate the bulk-diffusion coefficient and the conductivity in a broad class of conserved-mass aggregation processes on a ring of discrete sites. These processes involve chipping and fragmentation of masses, which diffuse around and aggregate upon contact with their neighboring masses. We find that, even in the absence of microscopic time reversibility, the systems satisfy an Einstein relation, which connects the ratio of the conductivity and the bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation dominates over chipping, the conductivity or, equivalently, the mobility, gets enhanced. The enhancement in conductivity, in accordance with the Einstein relation, results in large mass fluctuations, implying a {\it mobility driven clustering} in the system. Indeed, in a certain parameter regime, we demonstrate that the conductivity diverges beyond a critical density, signaling the onset of a condensation transition observed in the past. In a striking similarity to Bose-Einstein condensation, the condensate formation along with the diverging conductivity thus underlies a dynamic "superfluidlike" transition in these nonequilibrium systems. Notably, the bulk-diffusion coefficient remains finite in all cases. Our analytic results are in a quite good agreement with simulations.

cond-mat.stat-mech↗

arXiv2020

Hard core run and tumble particles on a one dimensional lattice

We study the large scale behavior of a collection of hard core run and tumble particles on a one dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin variable until the direction of spin is reversed. We map the run and tumble model to a mass transfer model with fluctuating directed bonds. We calculate the steady state single site mass distribution in the mass model within a mean field approximation for larger spin-flip rates and by analyzing an appropriate coalescence fragmentation model for small spin-flip rates. We also calculate the hydrodynamic coefficients of diffusivity and conductivity for both large and small spin-flip rates and show that the Einstein relation is violated in both regimes. We also show how the non-gradient nature of the process can be taken into account in a systematic manner to calculate the hydrodynamic coefficients.

cond-mat.stat-mech↗

arXiv2020

Non Gaussian information of heterogeneity in Soft Matter

Heterogeneity in dynamics in the form of non-Gaussian molecular displacement distributions appears ubiquitously in soft matter. We address the quantification of such heterogeneity using an information-theoretic measure of the distance between the actual displacement distribution and its nearest Gaussian estimation. We explore the usefulness of this measure in two generic scenarios of random walkers in heterogeneous media. We show that our proposed measure leads to a better quantification of non-Gaussianity than the conventional ones based on moment ratios.

cond-mat.soft↗

arXiv2019

Exact Hyperuniformity Exponents and Entropy Cusps in Models of Active-Absorbing Transition

Recent studies of nonequilibrium phase transitions have shown that in many systems which have transitions involving an arrested phase, the arrested states show suppressed density fluctuations and a cusp in the configurational entropy at the transition point. We study quasistatic driving in the 1D fixed-energy abelian sandpile model, and in conserved lattice gases with range $n$ in 1D, and exactly determine the measure over the absorbing states for both cases, along with the behaviour of density fluctuations and the configurational entropy of absorbing states. We show that both models exhibit hyperuniformity near the transition, and also that the configurational entropy shows a cusp at the transition point in the conserved lattice gases.

cond-mat.stat-mech↗

arXiv2018

A novel Recurrence-Transience transition and Tracy-Widom growth in a cellular automaton with quenched noise

We study the growing patterns formed by a deterministic cellular automaton, the rotor-router model, in the presence of quenched noise. By the detailed study of two cases, we show that: (a) the boundary of the pattern displays KPZ fluctuations with a Tracy-Widom distribution, (b) as one increases the amount of randomness, the rotor-router path undergoes a transition from a recurrent to a transient walk. This transition is analysed here for the first time, and it is shown that it falls in the 3D Anisotropic Directed Percolation universality class.

cond-mat.stat-mech↗

arXiv2018

Hierarchical Lattice Models of Hydrogen Bond Networks in Water

We develop a graph-based model of the hydrogen bond network in water, with a view towards quantitatively modeling the molecular-level correlational structure of the network. The networks are formed are studied by the constructing the model on two infinite-dimensional lattices. Our models are built \emph{bottom up}, based on microscopic information coming from atomistic simulations, and we show that the predictions of the model are consistent with known results from ab-initio simulations of liquid water. We show that simple entropic models can predict the correlations and clustering of local-coordination defects around tetrahedral waters observed in the atomistic simulations. We also find that orientational correlations between bonds are longer ranged than density correlations, and determine the directional correlations within closed loops and show that the patterns of water wires within these structures are also consistent with previous atomistic simulations. Our models show the existence of density and compressibility anomalies, as seen in the real liquid, and the phase diagram of these models is consistent with the singularity-free scenario previously proposed by Sastry and co-workers (Sastry et al, PRE 53, 6144 (1996)).

cond-mat.stat-mech↗

arXiv2018

Logarithmic speed-up of relaxation in A-B annihilation with exclusion

We show that the decay of the density of active particles in the reaction $A+B \rightarrow 0$ in one dimension, with exclusion interaction, results in logarithmic corrections to the expected power law decay, when the starting initial condition (i.c.) is periodic. It is well-known that the late-time density of surviving particles goes as $t^{-1/4}$ with random initial conditions, and as $t^{-1/2}$ with alternating initial conditions ($ABABAB$...). We show that the decay for periodic i.c.s made of longer blocks ($A^{n}B^{n}A^{n}B^{n}$...) do not show a pure power-law decay when $n$ is even. By means of first-passage Monte Carlo simulations, and a mapping to a q-state coarsening model which can be solved in the Independent Interval Approximation (IIA), we show that the late-time decay of the density of surviving particles goes as $t^{-1/2}(\log{(t)})^{-1}$ for $n$ even, but as $t^{-1/2}$ when $n$ is odd. We relate this kinetic symmetry breaking in the Glauber Ising model. We also see a very slow crossover from a $t^{-1/2}(\log{(t)})^{-1}$ regime to eventual $t^{-1/2}$ behaviour for i.c.s made of mixtures of odd- and even-length blocks.

cond-mat.stat-mech↗

arXiv2014

Comment on `Self-organized cooperative criticality in coupled complex systems'

In a recent Letter (EPL 105, 40006; arXiv:1309.7107), Liu and Hu presented a model of toppling-coupled sandpiles, where they found that the avalanche exponents for two toppling-coupled sandpiles are the same as those for a single uncoupled sandpile. In this Comment we provide a proof of this observation for the case when there is conservation of grains in the bulk.

cond-mat.stat-mech↗

arXiv2013

Proportionate growth in patterns formed in the rotor-router model

We study the growing patterns in the rotor-router model formed by adding $N$ walkers at the center of a $L \times L$ two-dimensional square lattice, starting with a periodic background of arrows, and relaxing to a stable configuration. The pattern is made of large number of triangular regions, where in each region all arrows point in the same direction. The square circumscribing the region, where all the arrows have been rotated atleast one full circle, may be considered as made up of smaller squares of different sizes, all of which grow linearly with $N$, for $ 1 \ll N < 2 L$. We use the Brooks-Smith-Stone-Tutte theorem relating tilings of squares by smaller squares to resistor networks, to determine the exact relative sizes of the different elements of the asymptotic pattern. We also determine the scaling limit of the function describing the variation of number of visits to a site with its position in the pattern. We also present evidence that deviations of the sizes of different small squares from the linear growth for finite $N$ are bounded and quasiperiodic functions of $N$.

cond-mat.stat-mech↗

arXiv2013

A class of exactly solved assisted hopping models of active-absorbing state transitions on a line

We construct a class of assisted hopping models in one dimension in which a particle can move only if it does not lie in an otherwise empty interval of length greater than $n+1$. We determine the exact steady state by a mapping to a gas of defects with only on-site interaction. We show that this system undergoes a phase transition as a function of the density $ρ$ of particles, from a low-density phase with all particles immobile for $ρ\le ρ_c = \frac{1}{n+1}$, to an active state for $ρ> ρ_c$. The mean fraction of movable particles in the active steady state varies as $(ρ- ρ_c)^β$, for $ρ$ near $ρ_c$. We show that for the model with range $n$, the exponent $β=n$, and thus can be made arbitrarily large.

cond-mat.stat-mech↗