arXiv subjects

Animesh Hazra

Publications and source records attributed to Animesh Hazra.

6 recordsLinked to original sources

arXiv2026

Odd diffusion and power-law correlations in chiral mass-transport processes

We study mass-conserving Markov jump processes on a square lattice, where masses hop with a preferred rotational sense, thus breaking both time-reversal and mirror symmetries. We consider closed systems with both periodic and open (reflecting) boundaries, the latter supporting a steady-state edge current. We show that odd diffusion, arising from the chiral transport, generically provides a mechanism for the emergence of scale-invariant two-point density correlations in nonequilibrium steady states even in the presence of lattice rotation symmetry -- a mechanism that is qualitatively distinct from the well-known mechanism of anisotropic hopping. We exactly calculate the steady-state equal-time density-density correlations, which exhibit an algebraic decay, $C(\mathbf{r}) \sim |\mathbf{r}|^{-4}$ for $|\mathbf{r}| \gg 1$. This algebraic behavior results from the interplay between the off-diagonal components of the diffusion and mobility tensors, demonstrating that chiral transport alone can generate power-law correlations in isotropic driven systems. Remarkably, the structure factor in the zero-wavenumber limit and the amplitude of the power laws depend nontrivially on chirality. While increasing chirality initially suppresses large-scale density fluctuations, the fluctuations beyond a threshold odd-diffusion strength vary nonmonotonically with chirality and develop a cusp singularity.

cond-mat.stat-mech↗

arXiv2026

Power laws, anisotropy and center-of-mass conservation in mass transport processes

We present exact results for steady-state density correlation functions in conserved-mass transport processes with {\it anisotropic}, reflection-symmetric hopping on a $d-$dimensional hypercubic lattice. In addition to mass conservation, we consider center-of-mass (CoM) conservation, imposed either along a specific axis or along all axes. CoM-conserving dynamics is implemented through coordinated {\it multidirectional} hopping of two equal chunks of masses in {\it opposite} directions. While anisotropy and mass conservation are known to generate power-law density correlations $C({\bf x}) \sim 1/|{\bf x}|^d$ at large distance $|{\bf x}| \gg 1$ {\it [Phys. Rev. A {\bf 42}, 1954 (1990)]}, an additional CoM conservation can qualitatively alter the nature of the power law. Indeed, when CoM is conserved in {\it all} directions, the correlations decay faster $-$ typically as $C({\bf x}) \sim 1/|{\bf x}|^{(d+2)}$, regardless of the presence (or absence) of anisotropy. Consequently, the systems exhibit an extreme {\it hyperuniformity} (``class I''), where the long-wavelength density fluctuations, despite the slow power-law decay, are anomalously suppressed. When CoM is conserved along particular ({\it not} all) directions, the slower $1/|{\bf x}|^{d}$ power-law decay is recovered. The above behavior can be understood from an analogy between the correlation function and an electrostatic potential: While a (rank-$2$) quadrupolar charge distribution gives rise to the $1/|{\bf x}|^{d}$ power law, the $1/|{\bf x}|^{(d+2)}$ power law originates from a higher-order (rank-$4$) multipolar charge distribution. These findings reveal a rich interplay between anisotropy and CoM conservation in nonequilibrium steady states.

cond-mat.stat-mech↗

arXiv2025

Generic power laws in higher-dimensional lattice models with multidirectional hopping

We show that, on a $d-$dimensional hypercubic lattice with $d>1$, conserved-mass transport processes, with {\it multidirectional} hopping that respect all symmetries of the lattice, exhibit power-law correlations for generic parameter values $-$ even {\it far} from phase transition point, if any. The key idea for generating the algebraic decay is the notion of {\it multidirectional} hopping, which means that several chunks of masses, or several particles, can hop out simultaneously from a lattice site in multiple directions, consequently breaking detailed balance. Notably, the systems we consider are described by a continuous-time Markov process, are diffusive, {\it lattice-rotation symmetric}, spatially homogeneous and thus have {\it no} net mass current. Using hydrodynamic and exact microscopic theory, we show that, for spatial dimensions $d > 1$, the steady-state static density-density and ``activity''-density correlation functions in the thermodynamic limit typically decay as $\sim 1/r^{(d+2)}$ at large distance $r=|{\bf r}|$; the strength of the power law is exactly calculated for several models and expressed in terms of the density-dependent bulk-diffusion coefficient and Onsager matrix (or, mobility tensor). In particular, our theory explains why center-of-mass-conserving dynamics, used to model novel disordered {\it hyperuniform} state of matter, result in generic long-ranged correlations. However, in a restricted parameter regime, the correlations can also be short ranged and are characterized through the Onsager matrix.

cond-mat.stat-mech↗

arXiv2025

Hyperuniformity in mass transport processes with center-of-mass conservation: Some exact results

We characterize steady-state static and dynamic properties in a broad class of mass transport processes on a periodic hypercubic lattice of volume $L^d$, where both mass and {\it center-of-mass} (CoM) remain conserved and detailed balance is violated in the bulk; we specifically consider these models in $d=1$ and $2$ dimensions. Using a microscopic approach, we exactly determine the decay (or, growth) exponents for various dynamic and static correlation functions. We show that, despite constrained dynamics due to the CoM conservation (CoMC), the density relaxation is indeed diffusive. However, fluctuation properties are strikingly different from that in the diffusive systems with a single (mass) conservation law. In the thermodynamic limit, the steady-state variance $\langle {\cal Q}^2(T) \rangle_c$ of time-integrated bond current ${\cal Q}(T)$ across a bond in time interval $T$ exhibits the following long-time behavior: $\langle {\cal Q}^2(T) \rangle_c \simeq A_1 T + A_2 + A_3 T^{-d/2}$. Remarkably, depending on dimensions and microscopic details, the prefactor $A_1$ can vanish (e.g., for $d=1$), causing the variance to eventually {\it saturate}. The exponents governing the small-frequency behavior of the power spectrum $S_J(f) \sim f^{ψ_J}$ for bond current are exactly determined as $ψ_J=3/2$ and $2$ in $d=1$ and $2$ dimensions, respectively, implying a ``dynamic hyperuniformity''. We also compute the static structure factor $S(q)$, which, in the small-$q$ limit, varies as the square of wave number $q$, i.e., $S(q) \sim q^2$. Indeed, both dynamic and static fluctuations are anomalously suppressed, resulting in an extreme form of (``class I'') hyperuniformity in the systems.

cond-mat.stat-mech↗

arXiv2024

Dynamic fluctuations of current and mass in nonequilibrium mass transport processes

We study steady-state dynamic fluctuations of current and mass, as well as the corresponding power spectra, in conserved-mass transport processes on a ring of $L$ sites; these processes violate detailed balance, have nontrivial spatial structures, and their steady states are not described by the Boltzmann-Gibbs distribution. We exactly calculate, for all times $T$, the fluctuations $\langle \mathcal{Q}_i^2(T) \rangle$ and $\langle \mathcal{Q}_{sub}^2(l, T) \rangle$ of the cumulative currents upto time $T$ across $i$th bond and across a subsystem of size $l$ (summed over bonds in the subsystem), respectively; we also calculate the (two-point) dynamic correlation function for subsystem mass. In particular, we show that, for large $L \gg 1$, the bond-current fluctuation grows linearly for $T \sim {\cal O}(1)$, subdiffusively for $T \ll L^2$ and then again linearly for $T \gg L^2$. The scaled subsystem current fluctuation $\lim_{l \rightarrow \infty, T \rightarrow \infty} \langle \mathcal{Q}^2_{sub}(l, T) \rangle/2lT$ converges to the density-dependent particle mobility $χ$ when the large subsystem size limit is taken first, followed by the large time limit. Remarkably, the scaled current fluctuation $D \langle \mathcal{Q}_i^2(T)\rangle/2 χL \equiv {\cal W}(y)$ as a function of scaled time $y=DT/L^2$ is expressed in terms of a universal scaling function ${\cal W}(y)$, where $D$ is the bulk-diffusion coefficient. Similarly, the power spectra for current and mass time series are characterized by the respective universal scaling functions, which are calculated exactly. We provide a microscopic derivation of equilibrium-like Green-Kubo and Einstein relations, that connect the steady-state current fluctuations to the response to an external force and to mass fluctuation, respectively.

cond-mat.stat-mech↗

arXiv2024

Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry

We study a paradigmatic model of absorbing-phase transition - the Oslo model - on a one-dimensional ring of $L$ sites with a fixed global density $\barρ$; notably, microscopic dynamics conserve both mass and \textit{center of mass (CoM), but lacks time-reversal symmetry}. Despite having highly constrained dynamics due to CoM conservation, the system exhibits diffusive relaxation away from criticality and superdiffusive relaxation near criticality. Furthermore, the CoM conservation severely restricts particle movement, rendering the mobility to vanish exactly. Indeed the temporal growth of current fluctuation is qualitatively different from that observed in diffusive systems with a single conservation law. Away from criticality, steady-state fluctuation $\langle \mathcal{Q}_i^2(T,Δ) \rangle$ of current $\mathcal{Q}_i$ across $i$th bond up to time $T$ \textit{saturates} as $\langle \mathcal{Q}_i^2 \rangle \simeq Σ_Q^2(Δ) - {\rm const.} T^{-1/2}$; near criticality, it grows subdiffusively as $\langle \mathcal{Q}_i^2 \rangle \sim T^α$, with $0 < α< 1/2$, and eventually \textit{saturates} to $Σ_Q^2(Δ)$. The asymptotic current fluctuation $Σ_Q^2(Δ)$ is a \textit{nonmonotonic} function of $Δ$: It diverges as $Σ_Q^2(Δ) \sim Δ^2$ for $Δ\gg ρ_c$ and $Σ_Q^2(Δ) \sim Δ^{-δ}$, with $δ> 0$, for $Δ\to 0^+$. By using a mass-conservation principle, we exactly determine the exponents $δ= 2(1-1/ν_\perp)/ν_\perp$ and $α= δ/z ν_\perp$ via the correlation-length and dynamic exponents, $ν_\perp$ and $z$, respectively. Finally, we show that, in the steady state, the self-diffusion coefficient $\mathcal{D}_s(\barρ)$ of tagged particles is connected to activity by $\mathcal{D}_s(\barρ) = a(\barρ) / \barρ$.

cond-mat.stat-mech↗