arXiv subjects

Kabir Ramola

Publications and source records attributed to Kabir Ramola.

At least 19 recordsLinked to original sources

arXiv2026

Critical behavior and crossover scaling in the Light-Heavy model

The Light-Heavy (LH) model involves two species of particles (light and heavy) coupled with a fluctuating surface (described by tilts). The dynamics include the inherent diffusion of the particles (or tilts) as well as the drive provided by the tilts (or particles). When the two are of similar magnitude, the system lies in the unscaled (uLH) regime, while a significantly weaker drive leads to the scaled (sLH) regime. In the unscaled limit, the model exhibits an order-disorder transition characterized by the fluctuation-dominated phase ordering (FDPO). In this state, interestingly the dynamics is driven by multiple modes, giving rise to dynamic clusters. Away from the critical regime the disordered phase retains vestiges of FDPO behavior on length scales smaller than the correlation length. We examine this local FDPO-like behavior by using a scaling function that links the off-critical and critical regimes. We next turn to the scaled model and show that the multi-mode dynamics present in the unscaled regime is replaced by dynamics that is effectively controlled by a single dominant mode in the scaled regime. Concurrently, the two-point correlations change from the $\mathcal{O}(1)$ FDPO form to an anomalous long-range form that decays as $1/\sqrt{L}$. Drawing on the analogy with the sABC model, where similar anomalous correlations appear at criticality, we derive an analytical expression for the two-point correlation function using the same approach used for that model.

cond-mat.stat-mech↗

arXiv2026

Fermions on a 1D lattice: localized sources and sinks with dephasing

We study a general one-dimensional spinless fermionic system subject to a localized source, sink, and bulk dephasing. Within the Lindblad framework, we compute the time evolution of the density profile and spatial correlation functions. We find that the presence of bulk dephasing suppresses certain coherent quantum features, such as the Friedel oscillations, and it alters the transport dynamics to exhibit two distinct dynamical regimes instead of three as observed in the absence of dephasing. This effect can be understood as the destruction of ballistic motion caused by the dephasing noise. Under strong dephasing, the density profile becomes similar to the one expected for a classical diffusive regime. We also investigate the system in the presence of both a localized source and sink, placed at a distance of $Δ$. Interestingly, quantum coherence generates secondary density peaks at integer multiples of the source-sink separation $Δ$, which are systematically washed out as bulk dephasing drives the system toward the classical diffusive limit.

cond-mat.stat-mech↗

arXiv2026

Energy-Weighted Site Percolation in Two Dimensions

We study a generalization of two-dimensional site percolation by assigning an energy cost $\varepsilon$ to bonds between nearest-neighbor occupied sites. This leads to a competition between entropy-driven cluster growth and energetic suppression (or enhancement) of connectivity. Varying $\varepsilon$ continuously interpolates between dense ferromagnetic-like clusters, ordinary classical percolation, and a dilute regime of minimally connected isolated clusters. Using Monte Carlo simulations and real-space renormalization-group (RG) methods, we show that bond energy shifts the percolation threshold smoothly. We define an energy-weighted correlation length that remains finite at the classical site occupation threshold ($p_c(\varepsilon=0)$) and shrinks with increasing $\varepsilon$, capturing the energetic suppression of large-scale connectivity. The cluster size distribution exhibits an energy-dependent cutoff that drives the transition from percolation-like clusters to isolated clusters. A real-space RG with Kadanoff block recursions reveals a systematic evolution of the correlation-length exponent $ν$ from $ν=1/2$ (dense clusters) to $ν=4/3$ (classical percolation), approaching $ν=1$ (minimally connected isolated clusters), in agreement with Coulomb-gas predictions for loop models where bond energy renormalizes loop fugacity. For large values of $\varepsilon$ (isotropic case), the suppression of nearest-neighbor bonds results in the emergence of antiferromagnetic sub-lattice ordering at high densities. Additionally, anisotropic bond energies lead to directionally selective cluster growth. Finally, we also discuss a lattice gas RG approach and scenarios where bond energy is renormalized across different scales.

cond-mat.stat-mech↗

arXiv2026

A constitutive model for discontinuous shear thickening in epithelial tissues

The rheological properties of biological tissues, though fundamental to many physiological and pathological processes such as embryonic development, wound healing, and tumor progression, remain poorly understood. A recent study showed that the active vertex model of biological tissues exhibits discontinuous shear thickening (DST), where stress and viscosity suddenly increase at a critical shear rate. What is the mechanism of DST here? Is it another nontrivial feature of activity or an inherent property of the system? To address this, we show that the thermal vertex model also exhibits DST at a small but non-zero temperature $T$. Solid-like and liquid-like cells coexist at the stress jump, and the stress-controlled flow curves exhibit the characteristic S-shape. We then introduce a constitutive model for DST in epithelial tissues. As $p_0$ increases, the theory predicts DST, followed by continuous shear thickening (CST), and finally Newtonian behavior, consistent with simulations. DST begins at the jamming point, $p_0^m$, and the Newtonian behavior starts at $p_0^*$, where the yield stress vanishes. Both $p_0^*$ and the liquid-to-solid transition stress, $σ^*$, govern the DST-CST boundary. Furthermore, $p_0^*$ and $σ^*$ also depend on $T$. Increasing $T$ reduces $p_0^*$, narrows the shear-thickening regime, and eventually destroys DST when $p_0^* \leq p_0^m$. Thus, the primary ingredients of DST in tissue models are a finite yield stress in the unjammed regime and non-zero fluctuations, whose specific form is not important. The theory agrees well with our simulation data and also provides further testable predictions.

cond-mat.soft↗

arXiv2025

Stress Response of Jammed Solids: Prestress and Screening

Unlike classical elasticity, where stresses arise from deformations relative to a stress-free reference configuration, rigidity in amorphous systems is maintained by disordered force networks that generate internal prestress. Previously, we introduced a ''stress-only'' formulation, where mechanical equilibrium resembles Gauss's law in a rank-2 tensor electrostatics with vector charges, and demonstrated that the mechanical response of jammed solids is described by the dielectric response of this gauge-theoretic formulation. Here, we extend this framework by incorporating scale-dependent screening that captures both dielectric and Debye-type behaviour. This introduces a characteristic length scale in stress correlations as well as in the response to external forces. Through numerical simulations of soft-sphere packings, we show that this length scale is set by the particle size, thus providing a natural ultraviolet cutoff while preserving long-wavelength emergent elasticity. We show that this lengthscale remains finite for all pressures, with no evidence for an emergent Debye-like screening near the frictionless unjamming transition. We demonstrate that although individual realisations show strong fluctuations, disorder averaging at fixed macroscopic conditions yields a robust dielectric-like response that persists up to unjamming. Finally, we also provide a physical interpretation of the gauge field within the electrostatic mapping: relative grain displacements in response to localised external perturbations correspond to difference in the gauge field, linking the field-theoretic description to particle-level mechanics.

cond-mat.soft↗

arXiv2025

Diffusive noise controls early stages of genetic demixing

Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive an exact fluctuating hydrodynamic description of this model from microscopic rules, which we then use to demonstrate that diffusive noise significantly alters early-time genetic demixing, which we characterize through heterozygosity, a key measure of diversity. Combining macroscopic fluctuation theory and microscopic simulations, we demonstrate that the scaling of density fluctuations in a spatial domain displays an early-time behaviour dominated by diffusive noise. Our exact results underscore the need for additional terms in existing continuum theories and highlight the necessity of including diffusive noise in models of spatially structured populations.

cond-mat.stat-mech↗

arXiv2025

Exact Fluctuating Hydrodynamics of the Scaled Light-Heavy Model

We study the exact fluctuating hydrodynamics of the scaled Light-Heavy model (sLH), in which two species of particles (light and heavy) interact with a fluctuating surface. This model is similar in definition to the unscaled Light-Heavy model (uLH), except it uses rates scaled with the system size. The consequence, it turns out, is a phase diagram that differs from that of the unscaled model. We derive the fluctuating hydrodynamics for this model using an action formalism involving the construction of path integrals for the probability of different states that give the complete macroscopic picture starting from the microscopic one. This is then used to obtain the two-point steady-state (static) correlation functions between fluctuations in the two density fields in the homogeneous phase. We show that these theoretical results match well with microscopic simulations away from the critical line. We derive an exponentially decaying form for the two-point steady-state correlation function with a correlation length that diverges as the critical line is approached. Finally, we also compute the dynamic correlations in the homogeneous phase and use them to determine the relaxation dynamics as well as the dynamic exponents of the system.

cond-mat.stat-mech↗

arXiv2024

Instabilities govern the low-frequency vibrational spectrum of amorphous solids

Amorphous solids exhibit an excess of low-frequency vibrational modes beyond the Debye prediction, contributing to their anomalous mechanical and thermal properties. Although a $ω^4$ power-law scaling is often proposed for the distribution of these modes, the precise exponent remains a subject of debate. In this study, we demonstrate that boundary-condition-induced instabilities play a key role in this variability. We identify two distinct types of elastic branches that differ in the nature of their energy landscape: Fictitious branches, where shear minima cannot be reached through elastic deformation alone and require plastic instabilities, and True branches, where elastic deformation can access these minima. Configurations on Fictitious branches show a vibrational density of states (VDoS) scaling as $D(ω) \sim ω^3$, while those on True elastic branches under simple and pure shear deformations exhibit a scaling of $D(ω) \sim ω^{5.5}$. Ensemble averaging over both types of branches results in a VDoS scaling of $D(ω) \sim ω^4$. Additionally, solids relaxed to their shear minima, with no residual shear stress, display a steeper scaling of $D(ω) \sim ω^{6.5}$ in both two and three dimensions. We propose two limiting behaviors for amorphous solids: if the system size is increased without addressing instabilities, the low-frequency VDoS scales with an exponent close to $3$. Conversely, by removing residual shear stress before considering large system sizes, the VDoS scales as $D(ω) \sim ω^{6.5}$.

cond-mat.soft↗

arXiv2024

Long-Range Correlations in Elastic Moduli and Local Stresses at the Unjamming Transition

We explore the behavior of spatially heterogeneous elastic moduli as well as the correlations between local moduli in model solids with short-range repulsive potentials. We show through numerical simulations that local elastic moduli exhibit long-range correlations, similar to correlations in the local stresses. Specifically, the correlations in local shear moduli exhibit anisotropic behavior at large lengthscales characterized by pinch-point singularities in Fourier space, displaying a structural pattern akin to shear stress correlations. Focussing on two-dimensional jammed solids approaching the unjamming transition, we show that stress correlations exhibit universal properties, characterized by a quadratic $p^2$ dependence of the correlations as the pressure $p$ approaches zero, independent of the details of the model. In contrast, the modulus correlations exhibit a power-law dependence with different exponents depending on the specific interaction potential. Furthermore, we illustrate that while affine responses lack long-range correlations, the total modulus, which encompasses non-affine behavior, exhibits long-range correlations.

cond-mat.soft↗

arXiv2024

Effect of initial conditions on current fluctuations in non-interacting active particles

We investigate the effect of initial conditions on the fluctuations of the integrated density current across the origin ($x=0$) up to a given time $t$ in a one-dimensional system of non-interacting run-and-tumble particles. Each particle has initial probabilities $f^+$ and $f^-$ to move with an initial velocity $+v$ and $-v$ respectively, where $v>0$. We derive exact results for the variance (second cumulant) of the current for quenched and annealed averages over the initial conditions for the magnetization and the density fields associated with the particles. We show that at large times, the variance displays a $\sqrt{t}$ behavior, with a prefactor contingent on the specific density initial conditions used. However, at short times, the variance displays either linear $t$ or quadratic $t^2$ behavior, which depends on the combination of magnetization and density initial conditions, along with the fraction $f^+$ of particles in the positive velocity state at $t=0$. Intriguingly, if $f^+=0$, the variance displays a short time $t^2$ behavior with the same prefactor irrespective of the initial conditions for both fields.

cond-mat.stat-mech↗

arXiv2024

Universal stress correlations in crystalline and amorphous packings

We present a universal characterization of stress correlations in athermal systems, across crystalline to amorphous packings. Via numerical analysis of static configurations of particles interacting through harmonic as well as Lennard-Jones potentials, for a variety of preparation protocols and ranges of microscopic disorder, we show that the properties of the stress correlations at large lengthscales are surprisingly universal across all situations, independent of structural correlations, or the correlations in orientational order. In the near-crystalline limit, we present exact results for the stress correlations for both models, which work surprisingly well at large lengthscales, even in the amorphous phase. Finally, we study the differences in stress fluctuations across the amorphization transition, where stress correlations reveal the loss of periodicity in the structure at short lengthscales with increasing disorder.

cond-mat.soft↗

arXiv2024

Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems

We investigate the problem of effusion of particles initially confined in a finite one-dimensional box of size $L$. We study both passive as well active scenarios, involving non-interacting diffusive particles and run-and-tumble particles, respectively. We derive analytic results for the fluctuations in the number of particles exiting the boundaries of the finite confining box. The statistical properties of this quantity crucially depend on how the system is prepared initially. Two common types of averages employed to understand the impact of initial conditions in stochastic systems are annealed and quenched averages. It is well known that for an infinitely extended system, these different initial conditions produce quantitatively different fluctuations, even in the infinite time limit. We demonstrate explicitly that in finite systems, annealed and quenched fluctuations become equal beyond a system-size dependent timescale, $t \sim L^2$. For diffusing particles, the fluctuations exhibit a $\sqrt{t}$ growth at short times and decay as $1/\sqrt{t}$ for time scales, $t \gg L^2/D$, where $D$ is the diffusion constant. Meanwhile, for run-and-tumble particles, the fluctuations grow linearly at short times and then decay as $1/\sqrt{t}$ for time scales, $t \gg L^2/D_{\text{eff}}$, where $D_{\text{eff}}$ represents the effective diffusive constant for run-and-tumble particles. To study the effect of confinement in detail, we also analyze two different setups (i) with one reflecting boundary and (ii) with both boundaries open.

cond-mat.stat-mech↗

arXiv2023

Stress correlations in near-crystalline packings

We derive exact results for stress correlations in near-crystalline systems in two and three dimensions. We study energy minimized configurations of particles interacting through Harmonic as well as Lennard-Jones potentials, for varying degrees of microscopic disorder and quenched forces on grains. Our findings demonstrate that the macroscopic elastic properties of such near-crystalline packings remain unchanged within a certain disorder threshold, yet they can be influenced by various factors, including packing density, pressure, and the strength of inter-particle interactions. We show that the stress correlations in such systems display anisotropic behavior at large lengthscales and are significantly influenced by the pre-stress of the system. The anisotropic nature of these correlations remains unaffected as we increase the strength of the disorder. Additionally, we derive the large lengthscale behavior for the change in the local stress components that shows a $1/r^d$ radial decay for the case of particle size disorder and a $1/r^{d-1}$ behavior for quenched forces introduced into a crystalline network. Finally, we verify our theoretical results numerically using energy-minimised static particle configurations.

cond-mat.soft↗

arXiv2023

Enhanced Vibrational Stability in Glass Droplets

We show through simulations of amorphous solids prepared in open boundary conditions that they possess significantly fewer low-frequency vibrational modes compared to their periodic boundary counterparts. Specifically, using measurements of the vibrational density of states, we find that the $D(ω) \sim ω^4$ law changes to $D(ω) \sim ω^δ$ with $δ\approx 5$ in two dimensions and $δ\approx 4.5$ in three dimensions. Crucially, this enhanced stability is achieved when utilizing slow annealing protocols to generate solid configurations. We perform an anharmonic analysis of the minima corresponding to the lowest-frequency modes in such open-boundary systems and discuss their correlation with the density of states. A study of various system sizes further reveals that small systems display a higher degree of localization in vibrations. Lastly, we confine open-boundary solids in order to introduce macroscopic stresses in the system which are absent in the unconfined system, and find that the $D(ω) \sim ω^4$ behavior is recovered.

cond-mat.soft↗

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

Generalized disorder averages and current fluctuations in run and tumble particles

We present exact results for the fluctuations in the number of particles crossing the origin up to time $t$ in a collection of non-interacting run and tumble particles in one dimension. In contrast to passive systems, such active particles are endowed with two inherent degrees of freedom: positions and velocities, which can be used to construct density and magnetization fields. We introduce generalized disorder averages associated with both these fields and perform annealed and quenched averages over various initial conditions. We show that the variance $σ^2$ of the current in annealed versus quenched magnetization situations exhibits a surprising difference at short times: $σ^2 \sim t$ versus $σ^2 \sim t^2$ respectively, with a $\sqrt{t}$ behavior emerging at large times. Our analytical results demonstrate that in the strictly quenched scenario, where both the density and magnetization fields are initially frozen, the fluctuations in the current are strongly suppressed. Importantly, these anomalous fluctuations cannot be obtained solely by freezing the density field.

cond-mat.stat-mech↗

arXiv2023

Green's Functions For Random Resistor Networks

We analyze random resistor networks through a study of lattice Green's functions in arbitrary dimensions. We develop a systematic disorder perturbation expansion to describe the weak disorder regime of such a system. We use this formulation to compute ensemble averaged nodal voltages and bond currents in a hierarchical fashion. We verify the validity of this expansion with direct numerical simulations of a square lattice with resistances at each bond exponentially distributed. Additionally, we construct a formalism to recursively obtain the exact Green's functions for finitely many disordered bonds. We provide explicit expressions for lattices with up to four disordered bonds, which can be used to predict nodal voltage distributions for arbitrarily large disorder strengths. Finally, we introduce a novel order parameter that measures the overlap between the bond current and the optimal path (the path of least resistance), for a given resistance configuration, which helps to characterize the weak and strong disorder regimes of the system.

cond-mat.dis-nn↗

arXiv2022

First contact breaking distributions in strained disordered crystals

We derive exact probability distributions for the strain ($ε$) at which the first stress drop event occurs in uniformly strained disordered crystals, with quenched disorder introduced through polydispersity in particle sizes. We characterize these first stress drop events numerically as well as theoretically, and identify them with the first contact breaking event in the system. Our theoretical results are corroborated with numerical simulations of quasistatic volumetric strain applied to disordered near-crystalline configurations of athermal soft particles. We develop a general technique to determine the $distribution$ of strains at which the first stress drop events occur, through an exact mapping between the cumulative distribution of first contact breaking events and the volume of a convex polytope whose dimension is determined by the number of defects $N_d$ in the system. An exact numerical computation of this polytope volume for systems with small numbers of defects displays a remarkable match with the distribution of strains generated through direct numerical simulations. Finally, we derive the distribution of strains at which the first stress drop occurs, assuming that individual contact breaking events are uncorrelated, which accurately reproduces distributions obtained from direct numerical simulations.

cond-mat.soft↗