arXiv subjects

Astik Haldar

Publications and source records attributed to Astik Haldar.

12 recordsLinked to original sources

arXiv2026

Death by mutants: unusual multicritical dynamics in a two-species model for absorbing state transitions

We explore the phases and active-to-absorbing state phase transitions (AAPT) in a two-species model, where the species A and its mutant B are {\em asymmetrically} or {\em nonreciprocally} coupled. We identify a multicritical point that connects the global absorbing state of both the species and its mutant, with a uniform active state. The critical dynamics at this multicritical point is studied within the lowest order perturbation theory. This asymmetric coupling between species A and mutant B leads to unequal and distinct upper critical dimensions $d_c^A$ and $d_c^B$ respectively for A and B dynamics. We show that the multicritical point in this model is characterised by an unusual breakdown of scale-invariance by fluctuation-induced logarithmic modulations with power law behaviour of the order parameter and correlation lengths of the species A at all dimensions $d<d_c^A$. Above $d_c^A$, conventional scale-invariance is restored. The dynamics of the mutant species B belongs to the DP universality class with an upper critical dimension of $d_c^B=4$

cond-mat.stat-mech↗

arXiv2025

Anisotropy can make a moving active fluid membrane rough or crumpled

We present a hydrodynamic theory of anisotropic and inversion-asymmetric moving active permeable fluid membranes. These are described by an anisotropic Kardar-Parisi-Zhang equation. Depending upon the anisotropy parameters, the membrane is either effectively isotropic and algebraically rough with translational short, but orientational long range order, or unstable, suggestive of membrane crumpling.

cond-mat.stat-mech↗

arXiv2024

Availability versus carrying capacity: Phases of asymmetric exclusion processes competing for finite pools of resources

We address how the interplay between the finite availability and carrying capacity of particles at different parts of a spatially extended system can control the steady state currents and density profiles in the one-dimensional current-carrying lanes connecting the different parts of the system. To study this, we set up a minimal model consisting of two particle reservoirs of the same finite carrying capacity connected by two equally sized anti-parallel asymmetric exclusion processes (TASEP). We focus on the steady-state currents and particle density profiles in the two TASEP lanes. The ensuing phases and the phase diagrams, which can be remarkably complex, are parametrized by the model parameters defining particle exchange between the TASEP lanes and the reservoirs and the filling fraction of the particles that determine the total resources available. These parameters may be tuned to make the densities of the two TASEP lanes globally uniform or piece-wise continuous in the form of a combination of a single localized domain wall and a spatially constant density or a pair of delocalized domain walls. Our model reveals that the two reservoirs can be preferentially populated or depopulated in the steady states.

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arXiv2023

Anomalous Collective Dynamics of Auto-Chemotactic Populations

While the role of local interactions in nonequilibrium phase transitions is well studied, a fundamental understanding of the effects of long-range interactions is lacking. We study the critical dynamics of reproducing agents subject to autochemotactic interactions and limited resources. A renormalization group analysis reveals distinct scaling regimes for fast (attractive or repulsive) interactions; for slow signal transduction, the dynamics is dominated by a diffusive fixed point. Furthermore, we present a correction to the Keller-Segel nonlinearity emerging close to the extinction threshold and a novel nonlinear mechanism that stabilizes the continuous transition against the emergence of a characteristic length scale due to a chemotactic collapse.

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arXiv2023

Logarithmic or algebraic: roughening of an active Kardar-Parisi-Zhang surface

The Kardar-Parisi-Zhang (KPZ) equation sets the universality class for growing and roughening of nonequilibrium surfaces without any conservation law and nonlocal effects. We argue here that the KPZ equation can be generalized by including a symmetry-permitted nonlocal nonlinear term of active origin that is of the same order as the one included in the KPZ equation. Including this term, the 2D active KPZ equation is stable in some parameter regimes, in which the interface conformation fluctuations exhibit sublogarithmic or superlogarithmic roughness, with nonuniversal exponents, giving positional generalised quasi-long-ranged order. For other parameter choices, the model is unstable, suggesting a perturbatively inaccessible algebraically rough interface or positional short-ranged order. Our model should serve as a paradigmatic nonlocal growth equation.

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arXiv2023

Active XY model on a substrate: Density fluctuations and phase ordering

We explore the generic long wavelength properties of an active XY model on a substrate, consisting of collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active spinners with a conservation law. The spins rotate actively in response to the local density fluctuations and local phase differences, on a solid substrate. We investigate this system by Monte-Carlo simulations of an agent-based model, which we set up, complemented by the hydrodynamic theory for the system. We demonstrate that this system can phase-synchronize without any hydrodynamic interactions. Our combined numerical and analytical studies show that this model, when stable, displays hitherto unstudied scaling behavior: As a consequence of the interplay between the mobility, active rotation and number conservation, such a system can be stable over a wide range of the model parameters characterized by a novel correspondence between the phase and density fluctuations. In different regions of the phase space where the phase-ordered system is stable, it shows phase ordering which is generically either logarithmically stronger than the conventional quasi long range order (QLRO) found in its equilibrium limit, together with "miniscule number fluctuations", or logarithmically weaker than QLRO along with "giant number fluctuations", showing a novel one-to-one correspondence between phase ordering and density fluctuations in the ordered states. Intriguingly, these scaling exponents are found to depend explicitly on the model parameters. We further show that in other parameter regimes there are no stable, ordered phases. Instead, two distinct types of disordered states with short range phase-order are found, characterized by the presence or absence of stable clusters of finite sizes.

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arXiv2023

Mobility-induced order in active XY spins on a substrate

We elucidate that the nearly phase-ordered active XY spins in contact with a conserved, diffusing species on a substrate can be stable. For wide-ranging model parameters, it has stable uniform phases robust against noises. These are distinguished by generalized quasi-long range (QLRO) orientational order logarithmically stronger or weaker than the well-known QLRO in equilibrium, together with miniscule (i.e., hyperuniform) or giant number fluctuations, respectively. This illustrates a direct correspondence between the two. The scaling of both phase and density fluctuations in the stable phase-ordered states is nonuniversal: they depend on the nonlinear dynamical couplings. For other parameters, it has no stable uniformly ordered phase. Our model, a theory for active spinners, provides a minimal framework for wide-ranging systems, e.g., active superfluids on substrates, synchronization of oscillators, active carpets of cilia and bacterial flagella and active membranes.

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arXiv2022

Disorders can induce continuously varying universal scaling in driven systems

We elucidate the nature of universal scaling in disordered driven models. We in particularly explore the intriguing possibility of whether coupling with quenched disorders can lead to continuously varying universality classes. We examine this question in the context of the Kardar-Parisi-Zhang (KPZ) equation, with and without a conservation law, coupled with quenched disorders of appropriate structures. By using a renormalisation group (RG) framework, we show when the disorder is relevant in the RG sense, the scaling exponents can depend continuously on a dimensionless parameter that defines the disorder variance. This result is generic and holds for quenched disorders with or without spatially long ranged correlations, as long as the disorder remains "relevant perturbation" on the pure system in a renormalisation group sense and a dimensionless parameter naturally exists in its variance. We speculate on its implications for generic driven systems with quenched disorders, and compare and contrast with the scaling displayed in the presence of annealed disorders.

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arXiv2020

Universal properties of the Kardar-Parisi-Zhang equation with quenched columnar disorders

Inspired by the recent results on totally asymmetric simple exclusion processes on a periodic lattice with short-ranged quenched hopping rates [A. Haldar, A. Basu, Phys Rev Research 2, 043073 (2020)], we study the universal scaling properties of the Kardar-Parisi-Zhang (KPZ) equation with short-ranged quenched columnar disorder in general d-dimensions. We show that there are generic propagating modes in the system that have their origin in the quenched disorder and make the system anisotropic. We argue that the presence of the propagating modes actually make the effects of the quenched disorder irrelevant, making the universal long wavelength scaling property belong to the well-known KPZ universality class. On the other hand, when these waves vanish in a special limit of the model, new universality class emerges with dimension d = 4 as the lower critical dimension, above which the system is speculated to admit a disorder-induced roughening transition to a perturbatively inaccessible rough phase.

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arXiv2020

Marching on a rugged landscape: Universality in disordered asymmetric exclusion processes

We develop the hydrodynamic theory for number conserving asymmetric exclusion processes with short-range random quenched disordered hopping rates, which is one-dimensional Kardar-Parisi- Zhang (KPZ) equation with quenched columnar disorder. We show that when the system is away from half-filling, the universal spatio-temporal scaling of the density fluctuations is indistinguishable from its pure counterpart, with the model belonging to the one-dimensional Kardar-Parisi-Zhang universality class. In contrast, close to half-filling, the quenched disorder is relevant, leading to a new universality class. We physically argue that the irrelevance of the quenched disorder when away from half-filling is a consequence of the averaging of the disorder by the propagating density fluctuations in the system. In contrast, close to half-filling the density fluctuations are overdamped, and as a result, are strongly influenced by the quenched disorder.

cond-mat.stat-mech↗

arXiv2020

Asymmetric exclusion processes with fixed resources: Reservoir crowding and steady states

We study the nonequilibrium steady states of an asymmetric exclusion process (TASEP) coupled to a reservoir of unlimited capacity. We elucidate how the steady states are controlled by the interplay between the reservoir population that dynamically controls both the entry and exit rates of the TASEP, and the total particle number in the system. The TASEP can be in the low density, high density, maximal current and shock phases. We show that such a TASEP is different from an open TASEP for all values of available resources: here, the TASEP can support only localised domain walls for any (finite) amount of resources as opposed to delocalised domain walls in open TASEPs. Furthermore, in the limit of infinite resources, the TASEP can be found in its high density phase only for any finite values of the control parameters, in contrast to an open TASEP.

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arXiv2019

Flow can order: Phases of live XY spins in two dimensions

We present the hydrodynamic theory of active XY spins coupled with flow fields, for systems both having and or lacking number conservation in two dimensions (2D). For the latter, with strong activity or nonequilibrium drive, the system can synchronize, or be phase-ordered with various types of order, e.g., quasi long range order (QLRO) or new kind of order weaker or stronger than QLRO for sufficiently strong active flow-phase couplings. For the number conserving case, the system can show QLRO or order weaker than QLRO, again for sufficiently strong active flow-phase couplings. For other choices of the model parameters, the system necessarily disorders in a manner similar to immobile but active XY spins, or 2D Kardar-Parisi-Zhang surfaces.

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