arXiv subjects

Abhik Basu

Publications and source records attributed to Abhik Basu.

At least 19 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↗

arXiv2026

Nonmonotonic control of pattern formation by chemotaxis

We investigate pattern formation in generic two-species reaction--diffusion systems with chemotaxis. We show that chemotaxis can give rise to a striking nonmonotonic dependence of pattern formation on its strength, opening the possibility of re-entrant transitions between patterned and homogeneous states controlled by chemotaxis. In certain regimes, chemotaxis also induces additional heretofore unexplored instabilities. Furthermore, varying the strength of chemotaxis can drive morphological transitions between spot and stripe patterns.

cond-mat.stat-mech↗

arXiv2026

Chemotaxis-induced linear instabilities and pattern formation in a reaction-diffusion model

We study linear instabilities and pattern formation in a spatially extended Selkov model for glycolysis with diffusion and chemotactic interactions between two species. Linear stability analysis reveals two distinct bifurcations: a zero-wavevector, finite-frequency Hopf bifurcation leading to spatially homogeneous oscillations, and a finite-wavevector Turing instability with a saddle-node bifurcation leading to stationary inhomogeneous patterns. The selected wavevector, $k_c$, depends sensitively on the nature and strength of chemotaxis and varies nonmonotonically with the chemotaxis parameters, allowing re-entrant transitions between homogeneous and patterned states. For sufficiently strong chemotaxis, when the two species mutually attract or mutually repel each other, an unusual instability emerges in which the preferred wavevector diverges as a finite threshold in chemotactic strength is approached. We complement the linear analysis with extensive direct numerical simulations (DNS) of the nonlinear partial differential equations in two dimensions. The DNS confirm the predicted instabilities and their nonmonotonic and re-entrant character, and also reveal spatially uniform oscillatory states for suitable parameters. The stationary patterns include spots and, unexpectedly, stable stripes. We further uncover transitions between spot and stripe morphologies controlled by chemotactic strength and diffusivity ratios. The stability of the striped states is consistent with linear amplitude equations, whereas the spot-stripe transition is attributed to nonlinear effects beyond linear stability. Our results demonstrate that chemotaxis can act as a nonmonotonic control parameter for instability selection, wavelength selection, re-entrant pattern formation, and nonlinear pattern morphology in reaction-diffusion systems.

nlin.PS↗

arXiv2026

Correlated disorder versus correlated noise: Ordering in active systems

Can quenched disorder generate ordering in driven systems? Using a recently proposed hydrodynamic model, we show that sufficiently long-ranged quenched disorder can induce long-range order in two-dimensional (2D) nonreciprocal XY systems, even when the clean system exhibits only short-range order at finite noise. Active surfaces tangentially advected by quenched velocities, governed by the same hydrodynamic equation, become statistically flat with super- or subdiffusive relaxation. In three dimensions (3D), quenched disorder combined with nonreciprocity produces a novel transition between strong-coupling and asymptotically noninteracting regimes, supporting either long- or short-range order. In both 2D and 3D, the exponents are nonuniversal, which vary continuously with the degree of transversality of the quenched disorder. The degree of transversality of the quenched disorder can be tuned to induce transitions in the model for fixed disorder and noise variances.

cond-mat.stat-mech↗

arXiv2026

Quenched activity induces nonuniversal scaling in nonreciprocal XY Models and surfaces

Active XY models and active surfaces are two paradigmatic nonequilibrium systems with distinct microscopic origins. We show that the hydrodynamic theories for a quenched-disordered nonreciprocal random bond two-dimensional XY model and an inversion-symmetric active surface tangentially advected by quenched velocities are identical. This theory predicts sub-logarithmic phase order in the XY model and sub- or super-logarithmic positional order in the surface for short-range disorder with nonuniversal exponents, which vary continuously with the degree of transversality of the disorder variance. We argue that the nonreciprocal random bond XY model can disorder through vortex proliferation.

cond-mat.stat-mech↗

arXiv2026

Stationary densities in a weakly nonconserving asymmetric exclusion processes with finite resources

Asymmetric exclusion process (TASEP) along a one-dimensional (1D) open channel sets the paradigm for 1D driven models and nonequilibrium phase transitions in open 1D models. Inspired by the phenomenologies of an open TASEP with Langmuir kinetics (Lk) and with finite resources, we study the stationary densities and phase transitions in a TASEP with Lk connected to a particle reservoir at its both ends. We calculate the stationary density profiles and the phase transitions. The resulting phase diagrams in the plane of the control parameters are significantly different from their counterparts in an open TASEP with Lk. In particular, some of the phases admissible in the open TASEP with Lk model are no longer possible. Intriguingly, our model that is closely related to a TASEP coupled with Lk on a ring with a point defect, admits more phases than the latter. Phenomenological implications of our results are discussed.

cond-mat.stat-mech↗

arXiv2025

Strong coupling phases of conserved growth models are crumpled

We show that stochastically driven nonequilibrium conserved growth models admit generic strong coupling phases for sufficiently strong nonlocal chemical potentials underlying the dynamics. The models exhibit generic roughening transitions between perturbatively accessible weak coupling phases satisfying an exact relation between the scaling exponents in all dimensions $d$, and strong coupling phases. In dimensions below the critical dimension $d_c$, the latter phases are unstable and argued to be crumpled, and thus distinct from the well-known strong coupling rough phase of the Kardar-Parisi-Zhang equation in dimensions $d\geq 2$. At $d_c$, conventional spatio-temporal scaling in the weak coupling phase is logarithmically modulated and are exactly obtained.

cond-mat.stat-mech↗

arXiv2025

Stationary densities and delocalized domain walls in asymmetric exclusion processes competing for finite pools of resources

We explore the stationary densities and domain walls in the steady states of a pair of asymmetric exclusion processes (TASEP) antiparallelly coupled to two particle reservoirs without any spatial extent by using the model in Haldar et al., Phys. Rev. E {\bf 111}, 014154 (2025). We show that the model admits a pair of {\em delocalized} domain walls, which exist for some choices of the model parameters that define the effective entry and exit rates into the TASEP lanes. Surprisingly, in the parameter space spanned by these model parameters, the region corresponding to delocalized domain walls covers an {\em extended} region, in contrast to the delocalized domain walls that appear only along a line in the relevant parameter space of the other known variants of TASEP. This implies large fluctuations in the TASEP particle numbers even in the thermodynamic limit that can be found over a range of the control parameters. The corresponding phase diagrams in the plane of the control parameters have different topology from those for an open TASEP or other models with multiple TASEPs connected to two reservoirs.

cond-mat.stat-mech↗

arXiv2025

Universality of shocks in conserved driven single-file motions with bottlenecks

Driven single-file motion, in which particles move unidirectionally along one-dimensional channels, sets the paradigm for wide variety of one-dimensional directed movements, ranging from intracellular transport and urban traffic to ant trails and controlled robot swarms. Motivated by the phenomenologies of these systems in closed geometries, regulated by number conservation and bottlenecks, we explore the domain walls (DWs) or shocks in a conceptual one-dimensional cellular automaton with a fixed particle number and a bottleneck. For high entry and exit rates of the cellular automaton, and with sufficiently large particle numbers, the DWs formed are independent of the associated rate parameters, revealing a {\em hitherto unknown universality} in their {\em shapes}, which are however enclosed by nonuniversal boundary layers. In contrast, the DWs do depend upon these parameters, if small, and hence have nonuniversal shapes, but without boundary layers. Nonuniversal delocalized DWs can be formed by additional tuning of the control parameters. Our predictions on the DWs are testable in model experiments.

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

Rough or crumpled: Strong coupling phases of a generalized Kardar-Parisi-Zhang surface

We study a generalized Kardar-Parisi-Zhang (KPZ) equation [Jana et al., Phys. Rev. E 109, L032104 (2024)] that sets the paradigm for universality in roughening of growing nonequilibrium surfaces without any conservation laws but with competing local and nonlocal nonlinear effects. This equation in two dimensions exhibits two distinct strong coupling regimes: a rough phase and a crumpled phase, in addition to a weak coupling phase. The conformation fluctuations of such a rough surface are given by nonuniversal scaling exponents, with orientational long-range order and positional short-range order, whereas the crumpled phase has positional and orientational short-range order.

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.

cond-mat.stat-mech↗

arXiv2024

Flat or crumpled: states of active symmetric membranes

We set up and study the hydrodynamic theory for inversion-symmetric active fluid and tethered membranes. For some choices of the activity parameter, such membranes are stable and described by linear hydrodynamic equations, which are exact in the asymptotic long wavelength limit, giving stable flat phases with translational quasi long range orders. For other choices of the activity parameter, the system is linearly unstable in the long wavelength limit, implying crumpling, or has intermediate wavevector instabilities, suggesting patterns. We argue that in such an active membrane thermal noises dominate over any active noises, and use those to calculate the correlation functions of membrane conformation fluctuations in the stable case, and the associated correlation functions of the embedding bulk flow velocities

cond-mat.stat-mech↗

arXiv2024

Distributed fixed resources exchanging particles: Phases of an asymmetric exclusion process connected to two reservoirs

We propose and study a conceptual one-dimensional model to explore how the combined interplay between fixed resources and particle exchanges between different parts of an extended system can affect the stationary densities in a current carrying channel connecting different parts of the system. To this end, we consider a model composed of a totally asymmetric simple exclusion process (TASEP) connecting two particle reservoirs without any internal dynamics but which can directly exchange particles between each other, ensuring nonvanishing currents in the steady states. The total particle number in the system that defines the "resources" available, although is kept constant by the model dynamics, can take any value independent of the model parameters that define the dynamics of the model. We show how the resulting phase diagrams of the model are controlled by the parameters, which define the various dynamical update rules together with the total available resources. These control parameters can be tuned to make the density on the TASEP lane globally uniform or piecewise continuous with localized domain walls, and can also control populations of the two reservoirs. In general, the phase diagrams are quite different from a TASEP with open boundaries. In the limit of large amount of resources, the phase diagrams in the plane of the control parameters become topologically identical to that for an open TASEP together with delocalization of domain walls.

cond-mat.stat-mech↗

arXiv2023

Availability, storage capacity, and diffusion: Stationary states of an asymmetric exclusion process connected to two reservoirs

We explore how the interplay of finite availability, carrying capacity of particles at different parts of a spatially extended system and particle diffusion between them control the steady state currents and density profiles in a one-dimensional current-carrying channel connecting the different parts of the system. To study this, we construct a minimal model consisting of two particle reservoirs of finite carrying capacities connected by a totally asymmetric simple exclusion process (TASEP). In addition to particle transport via TASEP between the reservoirs, the latter can also directly exchange particles, modeling particle diffusion between them that can maintain a steady current in the system. We investigate the steady state density profiles and the associated particle currents in the TASEP lane. The resulting phases and the phase diagrams are quite different from an open TASEP, and are characterised by the model parameters defining particle exchanges between the TASEP and the reservoirs, direct particle exchanges between the reservoirs, and the filling fraction of the particles that determines the total resources available. These parameters can be tuned to make the density on the TASEP lane globally uniform or piecewise continuous, and can make the two reservoirs preferentially populated or depopulated.

cond-mat.stat-mech↗

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.

cond-mat.stat-mech↗

arXiv2022

Universal scaling regimes in rotating fluid turbulence

We analyse the scaling properties of the energy spectra in fully developed incompressible turbulence in forced, rotating fluids in three dimensions (3D), which are believed to be characterised by universal scaling exponents in the inertial range. To elucidate the scaling regimes, we set up a scaling analysis of the 3D Navier-Stokes equation for a rotating fluid that is driven by large-scale external forces. We use scaling arguments to extract the scaling exponents, which characterise the different scaling regimes of the energy spectra. We speculate on the intriguing possibility of two-dimensionalisation of 3D rotating turbulence within our scaling theory. Our results can be tested in large scale simulations and relevant laboratory-based experiments.

cond-mat.stat-mech↗

arXiv2022

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.

cond-mat.stat-mech↗