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Kavita Jain

Publications and source records attributed to Kavita Jain.

At least 19 recordsLinked to original sources
arXiv2026

Jamming transition in an active exclusion process

Multiple studies on active matter have shown that activity can induce or suppress a phase transition, or modify the critical behavior of a passive system. Here we investigate how activity affects the jamming transition which is a paradigmatic example of nonequilibrium phase transitions in passive systems. We consider a one-dimensional system of active particles with hardcore interactions and a direction of self-propulsion which can be reversed at a given switching rate. For a class of particle hop rates and infinite switching rate, our model reduces to a passive system which is known to exhibit a transition between a high-density fluid phase and a low-density jammed phase in the stationary state. Using Monte Carlo simulations and a mean field theory, we study how the mean mobility of the particle and the hole cluster distribution vary with density and finite switching rate. Our main result is that activity hinders the formation of jam and can even inhibit it; more precisely, we find that the jamming transition occurs at a critical density that decreases with decreasing switching rate, and at sufficiently small switching rate, the system exists only in the fluid phase.

cond-mat.stat-mech↗
arXiv2026

Kink-kink correlations in nonlinear quenches across a quantum critical point

When a quantum system exhibiting a second order phase transition is quenched across the critical point in large but finite time, the dynamics are not adiabatic in the critical region and the Kibble-Zurek (KZ) mechanism provides a framework to determine local observables such as the mean defect density. However, to find higher-point functions, one has to go beyond the KZ paradigm asshown in recent works on one-dimensional transverse field Ising model (TFIM) following a linear quench. It has been found that (i) besides the KZ scale, the quench dynamics depend on another length scale that arises due to the finite phase difference between the low energy modes, and (ii) contrary to the expectations based on the KZ mechanism, in general, the correlation functions do not decay exponentially with distance. Motivated by these results for the linear quench, we are interested in understanding if these properties are universal, and consider the 1D TFIM when the transverse field varies algebraically in the vicinity of the critical field. We focus on the equal-time,longitudinal kink-kink correlation function at the end of the quench from the paramagnetic to the ferromagnetic phase, and find that (i) the correlator depends only on the KZ length for superlinear quenches, otherwise an additional dephasing length is required to describe it, and (ii) the dephased correlator decays as a compressed exponential with an exponent that changes continuously with the quench exponent. Our results are obtained using an adiabatic perturbation theory, analytical arguments and exact numerical integration of the relevant equations.

cond-mat.stat-mech↗
arXiv2026

When can fitness epistasis be ignored in a polygenic trait at equilibrium?

Although many phenotypic traits are determined by a large number of genetic variants, the behavior of allele frequencies in a polygenic trait is not completely understood. The problem is especially challenging when the quantitative trait of interest is under epistatic selection as the allele frequency at a locus is affected by those at other loci. Here, we consider a panmictic, diploid finite population evolving under stabilizing selection and symmetric mutations when the population is in linkage equilibrium. In the stationary state, using a diffusion theory, we calculate the marginal distribution of allele frequency, and find parameter regimes where fitness epistasis can not be ignored for an accurate description of the frequency distribution. For such parameters, the mean deviation in the phenotypic optimum and genic variance are, however, found to be well captured even when epistatic interactions are neglected. Thus, while the presence of epistasis may not be evident in phenotypic quantities, it can strongly affect the allele frequency distribution.We also find that the allele frequency distribution at a locus is unimodal if its effect size is below a threshold effect and bimodal otherwise; these results are the stochastic analog of the deterministic ones where the stable allele frequency becomes bistable when the effect size exceeds a threshold. Our analytical results are verified against Monte Carlo simulations and numerical integration of a Langevin equation.

q-bio.PE↗
arXiv2025

Dynamics of fixation probability in a population with fluctuating size

In many biological processes, the size of a population changes stochastically with time, and recent work in the context of cancer and bacterial growth have focused on the situation when the mean population size grows exponentially. Here, motivated by the evolutionary process of genetic hitchhiking in a selectively neutral population, we consider a model in which the mean size of the population increases linearly. We are interested in understanding how the fluctuations in the population size impact the first passage statistics, and study the fixation probability that a mutant reaches frequency one by a given time in a population whose size follows a conditional Wright-Fisher process. We find that at sufficiently short and long times, the fixation probability can be approximated by a model that ignores temporal correlations between the inverse of the population size, but at intermediate times, it is significantly smaller than that obtained by neglecting the correlations. Our analytical and numerical study of the correlation functions show that the conditional Wright-Fisher process of interest is neither a stationary nor a Gaussian process; we also find that the variance of the inverse population size initially increases linearly with time $t$ and then decreases as $t^{-2}$ at intermediate times followed by an exponential decay at longer times. Our work emphasizes the importance of temporal correlations in populations with fluctuating size that are often ignored in population-genetic studies of biological evolution.

q-bio.PE↗
arXiv2025

Scaling regimes in slow quenches within a gapped phase

We consider the finite-time quench dynamics in the quantum transverse field Ising model which exhibits a second order phase transition from a paramagnetic to a ferromagnetic phase, as the transverse magnetic field is decreased. These dynamics have been thoroughly investigated in previous studies when the critical point is crossed during the quench; here, we quench the system from deep in the paramagnetic phase to just above the critical field so that the system remains in the gapped phase throughout the quench duration. On linearly quenching the infinitely large system, we find that the behavior of mean longitudinal defect density and mean transverse magnetization at the end of the quench falls into three distinct scaling regimes as the quench time is increased. For sufficiently small quench times, these observables remain roughly constant, but for larger quench times, a crossover occurs from the Kibble-Zurek scaling law to the quadratic quench rate law when the Kibble-Zurek time is of the order of relaxation time at the final quench field. These results are shown analytically using power series and uniform asymptotic expansions of the exact solution of the model, and also compared with an adiabatic perturbation theory in the third regime. We find that the above mentioned scaling regimes hold for quenches within the ferromagnetic phase also, and provide a general scaling argument for crossover from the Kibble-Zurek regime to an adiabatic regime for slow quenches within a gapped phase.

cond-mat.stat-mech↗
arXiv2024

Run-and-tumble particle with saturating rates

We consider a run-and-tumble particle whose speed and tumbling rate are space-dependent on an infinite line. Unlike most of the previous work on such models, here we make the physical assumption that at large distances, these rates saturate to a constant. For our choice of rate functions, we show that a stationary state exists, and the exact steady state distribution decays exponentially or faster and can be unimodal or bimodal. The effect of boundedness of rates is seen in the mean-squared displacement of the particle that displays qualitative features different from those observed in the previous studies where it approaches the stationary state value monotonically in time; in contrast, here we find that if the initial position of the particle is sufficiently far from the origin, the variance in its position either varies nonmonotonically or plateaus before reaching the stationary state. These results are captured quantitatively by the exact solution of the Green's function when the particle has uniform speed but the tumbling rates change as a step-function in space; the insights provided by this limiting case are found to be consistent with the numerical results for the general model.

cond-mat.stat-mech↗
arXiv2024

Current fluctuations in the symmetric zero-range process below and at critical density

Characterizing current fluctuations in a steady state is of fundamental interest and has attracted considerable attention in the recent past. However, the bulk of the studies are limited to systems that either do not exhibit a phase transition or are far from criticality. Here we consider a symmetric zero-range process on a ring that is known to show a phase transition in the steady state. We analytically calculate two density-dependent transport coefficients, namely, the bulk-diffusion coefficient and the particle mobility, that characterize the first two cumulants of the time-integrated current. We show that on the hydrodynamic scale, away from the critical point, the variance of the time-integrated current in the steady state grows with time $t$ as $\sqrt{t}$ and $t$ at short and long times, respectively. Moreover, we find an expression of the full scaling function for the variance of the time-integrated current and thereby the amplitude of the temporal growth of the current fluctuations. At the critical point, using a scaling theory, we find that, while the above-mentioned long-time scaling of the variance of the cumulative current continues to hold, the short-time behavior is anomalous in that the growth exponent is larger than one-half and varies continuously with the model parameters.

cond-mat.stat-mech↗
arXiv2024

Kibble-Zurek scalings and coarsening laws in slowly quenched classical Ising chains

We consider a one-dimensional classical ferromagnetic Ising model when it is quenched from a low temperature to zero temperature in finite time using Glauber or Kawasaki dynamics. Most of the previous work on finite-time quenches assume that the system is initially in equilibrium and focus on the excess defect density at the end of the quench which decays algebraically in quench time with Kibble-Zurek exponent. Here we are interested in understanding the conditions under which the Kibble-Zurek scalings do not hold and in elucidating the full dynamics of the defect density. We find that depending on the initial conditions and quench time, the dynamics of the defect density can be characterized by coarsening and/or the standard finite-time quench dynamics involving adiabatic evolution and Kibble-Zurek dynamics; the time scales for crossover between these dynamical phases are determined by coarsening time and stationary state relaxation time. As a consequence, the defect density at the end of the quench is either a constant or decays following coarsening laws or Kibble-Zurek scaling. For the Glauber chain, we formulate a low temperature scaling theory and find exact expressions for the final defect density for various initial conditions. For the Kawasaki chain where the dynamic exponents for coarsening and stationary state dynamics are different, we verify the above findings numerically and also examine the effect of unequal dynamic exponents.

cond-mat.stat-mech↗
arXiv2021

Slow quench dynamics in classical systems: kinetic Ising model and zero-range process

While a large number of studies have focused on the nonequilibrium dynamics of a system when it is quenched instantaneously from a disordered phase to an ordered phase, such dynamics have been relatively less explored when the quench occurs at a finite rate. Here we study the slow quench dynamics in two paradigmatic models of classical statistical mechanics, {viz.}, one-dimensional kinetic Ising model and mean-field zero-range process, when the system is annealed slowly to the critical point. Starting from the time evolution equations for the spin-spin correlation function in the Ising model and the mass distribution in the zero-range process, we derive the Kibble-Zurek scaling laws. We then test a recent proposal that critical coarsening which is ignored in the Kibble-Zurek argument plays a role in the nonequilibrium dynamics close to the critical point. We find that the defect density in the Ising model and a scaled mass distribution in the zero-range process decay linearly to the respective value at the critical point with the time remaining until the end of the quench provided the final quench point is approached sufficiently fast, and sublinearly otherwise. As the linear scaling for the approach to the critical point also holds when a system following an instantaneous quench is allowed to coarsen for a finite time interval, we conclude that critical coarsening captures the scaling behavior in the vicinity of the critical point if the annealing is not too slow.

cond-mat.stat-mech↗
arXiv2020

Evolutionary dynamics and eigenspectrum of confluent Heun equation

We consider a biological population evolving under the joint action of selection, mutation and random genetic drift. The evolutionary dynamics are described by a one-dimensional Fokker-Planck equation whose eigenfunctions obey a confluent Heun equation. These eigenfunctions are expanded in an infinite series of orthogonal Jacobi polynomials and the expansion coefficients are found to obey a three-term recursion equation. Using scaling ideas, we obtain an expression for the expansion coefficients and an analytical estimate of the number of terms required in the series for an accurate determination of the eigenfunction. The eigenvalue spectrum is studied using a perturbation theory for weak selection and numerically for strong selection. In the latter case, we find that the eigenvalue for the first excited state exhibits a sharp transition: for mutation rate below one, the eigenvalue increases linearly with increasing mutation rate and then remains a constant; higher eigenvalues are found to display a more complex behavior.

q-bio.PE↗
arXiv2018

Modes of rapid polygenic adaptation

Many experimental and field studies have shown that adaptation can occur very rapidly. Two qualitatively different modes of fast adaptation have been proposed: selective sweeps wherein large shifts in the allele frequencies occur at a few loci and evolution via small changes in the allele frequencies at many loci. While the first process has been thoroughly investigated within the framework of population genetics, the latter is based on quantitative genetics and is much less understood. Here we summarize results from our recent theoretical studies of a quantitative genetic model of polygenic adaptation that makes explicit reference to population genetics to bridge the gap between the two frameworks. Our key results are that polygenic adaptation may be a rapid process and can proceed via subtle or dramatic changes in the allele frequency depending on the sizes of the phenotypic effects relative to a threshold value. We also discuss how the signals of polygenic selection may be detected in the genome. While powerful methods are available to identify signatures of selective sweeps at loci controling quantitative traits, the development of statistical tests for detecting small shifts of allele frequencies at quantitative trait loci is still in its infancy.

q-bio.PE↗
arXiv2018

Interference effects of deleterious and beneficial mutations in large asexual populations

Linked beneficial and deleterious mutations are known to decrease the fixation probability of a favorable mutation in large asexual populations. While the hindering effect of strongly deleterious mutations on adaptive evolution has been well studied, how weak deleterious mutations, either in isolation or with superior beneficial mutations, influence the fixation of a beneficial mutation has not been fully explored. Here, using a multitype branching process, we obtain an accurate analytical expression for the fixation probability when deleterious effects are weak, and exploit this result along with the clonal interference theory to investigate the joint effect of linked beneficial and deleterious mutations on the rate of adaptation. We find that when the mutation rate is increased beyond the beneficial fitness effect, the fixation probability of the beneficial mutant decreases from Haldane's classical result towards zero. This has the consequence that above a critical mutation rate that may depend on the population size, the adaptation rate decreases exponentially with the mutation rate and is independent of the population size. In addition, we find that for a range of mutation rates, both beneficial and deleterious mutations interfere and impede the adaptation process in large populations. We also study the evolution of mutation rates in adapting asexual populations, and conclude that linked beneficial mutations have a stronger influence on mutator fixation than the deleterious mutations.

q-bio.PE↗
arXiv2018

Polygenic adaptation in changing environments

Although many phenotypic traits are determined by a large number of genetic variants, how a polygenic trait adapts in response to the changes in the environment is still poorly understood. Here we study the adaptation dynamics of a polygenic trait that is determined by a finite number of genetic loci in an infinitely large population which is evolving under stabilising selection and recurrent mutations. We find that in a changing environment, modeled here by a linearly moving phenotypic optimum, the mean trait also moves linearly with time. But its speed is smaller than that of the phenotypic optimum when the effect sizes of the genetic variants are small and approaches that of the environmental change for larger effect sizes. Our study thus highlights the influence of the genetic architecture of a polygenic trait on its adaptability.

q-bio.PE↗
arXiv2017

Rapid adaptation of a polygenic trait after a sudden environmental shift

Although a number of studies have shown that natural and laboratory populations initially well-adapted to their environment can evolve rapidly when conditions suddenly change, the dynamics of rapid adaptation are not well understood. Here a population genetic model of polygenic selection is analyzed to describe the short-term response of a quantitative trait after a sudden shift of the phenotypic optimum. We provide explicit analytical expressions for the time scales over which the trait mean approaches the new optimum. We find that when the effect sizes are small relative to a scaled mutation rate, the genomic signatures of polygenic selection are small to moderate allele frequency changes that occur in the short-term phase in a synergistic fashion. In contrast, selective sweeps, i.e., dramatic changes in the allele frequency may occur provided the size of the effect is sufficiently large. Applications of our theoretical results to the relationship between QTL and selective sweep mapping and to tests of fast polygenic adaptation are discussed.

q-bio.PE↗
arXiv2017

Fixation probability of a nonmutator in a large population of asexual mutators

In an adapted population of mutators in which most mutations are deleterious, a nonmutator that lowers the mutation rate is under indirect selection and can sweep to fixation. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large population of asexual mutators. We show that when beneficial mutations are absent, the fixation probability is a nonmonotonic function of the mutation rate of the mutator: it first increases sublinearly and then decreases exponentially. We also find that beneficial mutations can enhance the fixation probability of a nonmutator. Our analysis is relevant to an understanding of recent experiments in which a reduction in the mutation rates has been observed.

q-bio.PE↗
arXiv2016

Critical dynamics of classical systems under slow quench

We study the slow quench dynamics of a one-dimensional nonequilibrium lattice gas model which exhibits a phase transition in the stationary state between a fluid phase with homogeneously distributed particles and a jammed phase with a macroscopic hole cluster. Our main result is that in the critical region ({\it i.e.}, at the critical point and in its vicinity) where the dynamics are assumed to be frozen in the standard Kibble-Zurek argument, the defect density exhibits an algebraic decay in the inverse annealing rate with an exponent that can be understood using critical coarsening dynamics. However, in a part of the critical region in the fluid phase, the standard Kibble-Zurek scaling holds. We also find that when the slow quench occurs deep into the jammed phase, the defect density behavior is explained by the rapid quench dynamics in this phase.

cond-mat.stat-mech↗
arXiv2016

Deterministic evolution of an asexual population under the action of beneficial and deleterious mutations on additive fitness landscapes

We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact solution for the frequency distribution is known to be a Poisson distribution. Here we include beneficial mutations and obtain exact expressions for the frequency distribution at all times using an eigenfunction expansion method. We find that the stationary distribution is non-Poissonian and related to the Bessel function of the first kind. We also provide suitable approximations for the stationary distribution and the time to relax to the steady state. Our exact results, especially at mutation-selection equilibrium, can be useful in developing semi-deterministic approaches to understand stochastic evolution.

q-bio.PE↗
arXiv2016

Critical dynamics of the jamming transition in one-dimensional nonequilibrium lattice-gas models

We consider several one-dimensional driven lattice gas models that show a phase transition in the stationary state between a high-density fluid phase in which the particles are homogeneously distributed and a low-density jammed phase where a hole cluster of macroscopic length forms in front of a particle. Using a hydrodynamic equation for an interface growth model obtained from the driven lattice gas models of interest here, we find that in the fluid phase, the roughness exponent and the dynamic exponent that, respectively, characterise the scaling of the saturation width and the relaxation time of the interface with the system size are given by the KPZ exponents. However, at the critical point, we show analytically that when the equal time density-density correlation function decays slower than inverse distance, the roughness exponent varies continuously with a parameter in the hop rates but it is one half otherwise. Using these results and numerical simulations for the density-density autocorrelation function, we further find that the dynamic exponent $z=3/2$ in all the cases.

cond-mat.stat-mech↗