arXiv subjects

Abhishek Dhar

Publications and source records attributed to Abhishek Dhar.

At least 19 recordsLinked to original sources

arXiv2026

Anomalous topological phases in a Chern insulator connected to leads in a cylindrical geometry

The observed robustly quantized Hall conductance in quantum Hall systems and Chern insulators (CI) is normally understood in terms of the bulk topology of isolated systems, not coupled to leads. It is assumed that the leads act as inert reservoirs. Within a model of a CI coupled to leads with a cylindrical geometry, we show that this is not always true. We identify the Hall conductance with a boundary invariant, the winding number of the phase of the reflection coefficient. We find anomalous topological phases where the boundary invariant is not the same as the bulk Chern number, even in the limit of weak lead coupling.

cond-mat.mes-hall↗

arXiv2026

Entanglement Scaling and Full Counting Statistics in Excited States of Two-Dimensional Rotating Fermions

We investigate the entanglement entropy of a class of $N$-particle excited state of fermions confined in a two-dimensional harmonic trap rotating at an angular frequency $Ω$. The excited state is constructed by filling a particular set of $N$ single-particle energy levels. We analytically compute the Rényi entropies of order $q$ in a disc of radius $r$ around the centre of the trap, and the cumulants corresponding to number fluctuations of fermions within the disc. We found that the area law scaling of entanglement entropy holds even for a class of excited states. We also verified the well-known series expansion of entanglement entropy in terms of the particle number cumulants for non-interacting fermions. We further derive the centered cumulant generating function, demonstrating that the associated probability distribution function in the disc has identical scaling properties, up to a variable shift, to the known ground-state result. Finally, we extend our result to an annular region, showing that both the Rényi entropy and particle number cumulants of the annulus decompose into sums of the corresponding quantities of the two bounding discs. These additive relations hold as long as the width of the annulus is sufficiently large.

cond-mat.stat-mech↗

arXiv2026

Quasiparticle Diffusion for the Toda Fluid in Equilibrium

Many-body integrable systems can be understood as a gas of quasiparticles. They propagate ballistically and drive large-scale transport. However, with the exception of the hard rods system, no tools have been available to numerically track such quasiparticles. Focusing on the Toda fluid, whose integrability relies on the availability of a Lax pair, we present a numerical scheme to track quasiparticle trajectories as determined by the time-dependent eigenvectors of the Lax matrix. Simulating the Toda fluid in thermal equilibrium, this tracking scheme is used to numerical confirm Brownian motion of a quasiparticle. Simulated is also the motion of a tagged particle. Our numerical results for the diffusion constant matches with a novel TBA prediction. We believe our numerical scheme can be extended to other classical many-particle models possessing a Lax matrix.

cond-mat.stat-mech↗

arXiv2026

Quantum Chaos and Diffusive Transport from Geometric Randomness

The physics of quantum chaos and diffusive transport is typically studied in settings with microscopic disorder or many-body interactions. In this Letter, we demonstrate that these phenomena can arise purely from geometric randomness. By studying non-interacting quantum particles on random locally tree-like layered graphs with uniform couplings, we show that the geometric randomness and effective graph dimensionality dictates the presence of chaotic dynamics or lack thereof. These graphs can be considered as structurally disordered generalisations of regular square lattices or ladders, or equivalently as multi-component one-dimensional chains with random links between the components. We find that an extensive layer size yields robust quantum chaos, level repulsion, and diffusive transport. Conversely, in the quasi-one-dimensional limit, we find the coexistence of extensive number of localised and delocalised states -- this leads to suppressed level repulsion accompanied by the latter driving ballistic transport. These results establish geometric randomness as a fundamental and independent mechanism for generating and tuning quantum chaos.

cond-mat.stat-mech↗

arXiv2026

Absence of hidden analytic conserved quantities in harmonically confined rods

Systems of hard rods of equal length in a one-dimensional harmonic trap have been observed to exhibit peculiar non-ergodic behavior that might suggest the existence of a novel hidden conserved quantity beyond the two well known ones, i.e., the total energy and the center-of-mass energy. In this work, we investigate this possibility by systematically constraining the forms of the conserved quantities, and we rigorously rule out the existence of any extra hidden conserved quantity that is analytic in the positions and momenta of the rods involved. We do so by showing two key results: conservation during free motion demands the $U(1)$ invariance of these quantities under rotations of the position and momenta of each rod, and conservation during collisions demand an $S_N$ invariance under the permutation of the momenta of the rods as long as one of the rods have non-zero length. We then show that these conditions imply that any conserved quantity is functionally dependent on the two known conserved quantities. In addition, we show that in the special case where all rods have zero length (i.e., when they are point particles), conservation under collisions only requires invariance under a smaller $S_N$ group of permutations of the labels of the rods, which leads to a much larger set of analytic conserved quantities that we explicitly write down. In all, this rigorously clarifies the structure of conserved quantities in the hard rod problem, and motivates the application of such systematic methods to other classical systems.

cond-mat.stat-mech↗

arXiv2026

Slow heat-driven flow in a gas of hard disks

We study a slow heat-driven flow in a gas of elastically colliding hard disks confined to a long channel. The initial state consists of two regions with large temperature and density contrasts but nearly equal pressures, leading to a low-Mach-number, nearly isobaric evolution. In the dilute limit, the corresponding isobaric hydrodynamic theory reduces to a previously known ideal-gas description. We extend this theory to finite densities by incorporating a non-ideal equation of state of a hard-disk fluid, and solve the resulting one-dimensional equations numerically. Finite-density effects produce appreciable deviations from the ideal-gas prediction. We then test the theory directly against event-driven molecular dynamics simulations of hard disks and find very good agreement in both the dilute and finite-density regimes. The results provide, to our knowledge, the first particle-level test of isobaric gas dynamics of a strongly inhomogeneous cooling flow.

cond-mat.stat-mech↗

arXiv2026

Stochastic dynamics of quasiparticles in the hard rod gas

We consider a one-dimensional gas of hard rods, one of the simplest examples of an interacting integrable model. It is well known that the hydrodynamics of such integrable models can be understood by viewing the system as a gas of quasiparticles. Here, we explore the dynamics of individual quasiparticles for a variety of initial conditions of the background gas. The mean, variance, and two-time correlations are computed exactly and lead to a picture of quasiparticles as drifting Brownian particles. For the case of a homogeneous background, we show that the motion of two tagged quasiparticles is strongly correlated, and they move like a rigid rod at late times. Apart from a microscopic derivation based on the mapping to point particles, we provide an alternate derivation which emphasizes that quasiparticle fluctuations are related to initial phase-space fluctuations, which are carried over in time by Euler scale dynamics. For the homogeneous state, we use the Brownian motion picture to develop a Dean-Kawasaki-type fluctuating hydrodynamic theory, formally having the same structure as that derived recently by Ferrari and Olla. We discuss differences with existing proposals on the hydrodynamics of hard rods and some puzzles.

cond-mat.stat-mech↗

arXiv2026

Hydrodynamics of the Fermi-Pasta-Ulam-Tsingou chain

We provide a pedagogical review of the hydrodynamics of the FPUT chain. There are three hydrodynamic fields corresponding to the conservation of mass, momentum and energy. We provide physically motivated derivations of the hydrodynamic equations at the levels of Euler and then Navier-Stokes-Fourier. Next we consider examples to test as to how successful the hydrodynamic description is in predicting the observed time evolution of nonequilibrium initial conditions such as domain walls and blasts. We find that in some cases there is good agreement of microscopic simulations with predictions from the Euler equations while, in several other cases, there is significant departure from the Euler predictions suggesting that the role of dissipation and noise is important in general.

cond-mat.stat-mech↗

arXiv2026

Quantized Transport in Floquet Topological Insulators

We study quantum transport in a periodically driven (Floquet) topological system coupled to static fermionic reservoirs. Using the Floquet nonequilibrium Green's-function (NEGF) formalism we show, from exact numerics for a strip geometry, that the two-terminal (longitudinal) conductance is quantized as $|W_{\varepsilon}|\,e^2/h$, while the Hall (transverse) conductance is quantized as $W_{\varepsilon}\,e^2/h$, where $W_{\varepsilon}$ is the Floquet winding invariant associated with the quasienergy gap at $\varepsilon = 0$ or $\varepsilon = Ω/2$. Quantization is achieved only after summing over the contribution of all Floquet sidebands. We provide an analytic understanding of this Floquet conductance sum rule, by considering the Hall conductance in the weak coupling limit. In that limit, we show that the Floquet Hall conductance gets contributions from the Floquet sidebands, which includes the signs of the velocities of the edge modes. Their sum yields exact quantization, as predicted by the Floquet sum rule. We find that in a wide range of parameter regime, the convergence is fast, making observation of the sum rule and Floquet winding numbers accessible to experiments.

cond-mat.mes-hall↗

arXiv2026

Adaptive MPC for Constrained Trajectory Tracking of Uncertain LTI System with Input-Rate Limits

This paper addresses the trajectory-tracking problem for discrete-time linear time-invariant systems with bounded parametric uncertainty, subject to hard constraints on system states, control inputs, and input rates. Unlike existing methods, which often consider only partial uncertainty, omit input-rate or state constraints, or focus on regulation problems, this work provides a systematic adaptive model predictive control (MPC) solution for constrained trajectory tracking under full parametric uncertainty. Determining the control input required to achieve zero tracking error under unknown parameters is challenging. Simultaneously, trajectory tracking under uncertainty with input-rate constraints induces temporal coupling in the control sequence, resulting in a time-varying admissible control set and rendering standard recursive feasibility arguments inapplicable. These challenges are overcome by systematically utilizing the estimated system parameters, coupled with a suitably designed adaptive learning process within a reformulated MPC framework. The recursive feasibility of the proposed MPC optimization routine is then rigorously established despite the time-varying admissible control set induced by input-rate constraints. Closed-loop stability is guaranteed via Lyapunov-based analysis, ensuring convergence of the tracking error and boundedness of system states. Simulation results validate the effectiveness of the pr

eess.SY↗

arXiv2026

Impurity dynamics in a zero-temperature gas

If energy is suddenly released in a localized region of space uniformly filled with identical stationary hard spheres, the outcome is a blast with an asymptotically spherical shock wave separating moving and stationary hard spheres. The radius $R(t)$ of the region filled with the moving spheres grows as $t^{2/(d+2)}$, where $d$ is the spatial dimension. The simplest way to inject energy is to kick a few `impurity' particles. Using hydrodynamics and kinetic theory, we argue that the typical displacement of an impurity scales as $R_{\rm imp} \sim λ(R/λ)^{(4+3d^2)/(8+3d^2)}$, where $λ$ is the mean-free path in the initial state. The number of collisions experienced by each impurity grows as $(R/λ)^{(8+2d^2)/(8+3d^2)}$, while its average speed decreases as $t^{-d(8-2d+3d^2)/[(2+d)(8+3d^2)]}$. In $2D$, the predictions for impurity displacement, collision numbers, and speed are $t^{2/5},~t^{2/5}$ and $t^{-2/5}$, respectively. These predictions are in reasonable agreement with the results of molecular dynamics simulations.

cond-mat.stat-mech↗

arXiv2025

Hydrodynamics of a hard-core active lattice gas

We present a fluctuating hydrodynamic description of an active lattice gas model with excluded volume interactions that exhibits motility-induced phase separation under appropriate conditions. For quasi-one dimension and higher, stability analysis of the noiseless hydrodynamics gives quantitative bounds on the phase boundary of the motility-induced phase separation in terms of spinodal and binodal. Inclusion of the multiplicative noise in the fluctuating hydrodynamics describes the exponentially decaying two-point correlations in the stationary-state homogeneous phase. Our hydrodynamic description and theoretical predictions based on it are in excellent agreement with our Monte Carlo simulations and pseudospectral iteration of the hydrodynamics equations. Our construction of hydrodynamics for this model is not suitable in strictly one-dimension with single-file constraints, and we argue that this breakdown is associated with micro-phase separation.

cond-mat.stat-mech↗

arXiv2025

Extreme dynamics and relaxation of quantum gases: A hydrodynamic approach

The evolution of quantum gases, released from traps, are studied through hydrodynamics, both analytically and numerically, in one and two dimensions. In particular, we demonstrate the existence of long time self-similar solutions of the Euler equations, for the density and velocity fields, and derive the scaling exponents as well as the scaling functions. We find that the expanding gas develops a shock front and the size of the cloud grows in time as a powerlaw. We relate the associated exponent to that appearing in the corresponding equation of state of the quantum gas. Furthermore, we study the relaxation dynamics of a trapped quantum gas and show that the resulting steady state is in excellent agreement with that derived analytically. Our hydrodynamic approach is versatile and can be used to unravel several other far-from-equilibrium collective phenomenon of extreme nature, relevant to the growing experimental interests in quantum gases.

cond-mat.quant-gas↗

arXiv2025

Adaptive Lattice-based Motion Planning

This paper proposes an adaptive lattice-based motion planning solution to address the problem of generating feasible trajectories for systems, represented by a linearly parameterizable non-linear model operating within a cluttered environment. The system model is considered to have uncertain model parameters. The key idea here is to utilize input/output data online to update the model set containing the uncertain system parameter, as well as a dynamic estimated parameter of the model, so that the associated model estimation error reduces over time. This in turn improves the quality of the motion primitives generated by the lattice-based motion planner using a nominal estimated model selected on the basis of suitable criteria. The motion primitives are also equipped with tubes to account for the model mismatch between the nominal estimated model and the true system model, to guarantee collision-free overall motion. The tubes are of uniform size, which is directly proportional to the size of the model set containing the uncertain system parameter. The adaptive learning module guarantees a reduction in the diameter of the model set as well as in the parameter estimation error between the dynamic estimated parameter and the true system parameter. This directly implies a reduction in the size of the implemented tubes and guarantees that the utilized motion primitives go arbitrarily close to the resolution-optimal motion primitives associated with the true model of the system, thus significantly improving the overall motion planning performance over time. The efficiency of the motion planner is demonstrated by a suitable simulation example that considers a drone model represented by Euler-Lagrange dynamics containing uncertain parameters and operating within a cluttered environment.

cs.RO↗

arXiv2025

Fixed Points and Universality Classes in Coupled Kardar-Parisi-Zhang Equations

We study coupled KPZ equations with three control parameters $X,Y,T$. These equations are used in the context of stretched polymers in a random medium, for the spacetime spin-spin correlator of the isotropic quantum Heisenberg chain, and for exciton-polariton condensates. In an earlier article we investigated merely the diagonal $X=Y$, $T=1$. Then the stationary measure is delta-correlated Gaussian and the dynamical exponent is obtained numerically to be close to $z = \tfrac{3}{2}$. We observed that the scaling functions of the dynamic correlator change smoothly when varying $X$. In this contribution, the analysis is extended to the whole $X$-$Y$-$T$ plane. Solutions are stable only if $XY \geq 0$. Based on numerical simulations, the static correlator still has rapid decay. We argue that the parameter space is foliated into distinct universality classes. They are labeled by $X$ and consist of half-planes parallel to the $Y$-$T$ plane containing the point $(X,X,1)$.

cond-mat.stat-mech↗

arXiv2025

Crystal to liquid cross-over for active particles with inverse-square power-law interaction

We consider a one-dimensional system comprising of $N$ run-and-tumble particles confined in a harmonic trap interacting via a repulsive inverse-square power-law interaction. We numerically compute the global density profile in the steady state which shows interesting crossovers between three different regimes: as the activity increases, we observe a change from a density with sharp peaks characteristic of a crystal region to a smooth bell-shaped density profile, passing through the intermediate stage of a smooth Wigner semi-circle characteristic of a liquid phase. We also investigate analytically the crossover between the crystal and the liquid regions by computing the covariance of the positions of these particles in the steady state in the weak noise limit. It is achieved by using the method introduced in Touzo {\it et al.} [Phys. Rev. E {\bf 109}, 014136 (2024)] to study the active Dyson Brownian motion. Our analytical results are corroborated by thorough numerical simulations.

cond-mat.stat-mech↗

arXiv2025

Page curve like dynamics in Interacting Quantum Systems

We study the dynamics of entanglement in a one-dimensional $XXZ$ spin-$1/2$ chain, with and without integrability-breaking interactions, that is connected to a bath. We start from a state where the system and bath are completely unentangled, and the bath is polarized spin-down. We consider two different initial states for the system - (i) a polarized spin-up state, and (ii) an infinite temperature state. In the particle representation of the spin chain, the polarized spin-up state corresponds to a filled state, while the polarized spin-down state corresponds to an empty state. Starting from these inhomogeneous quenches, in all the above-mentioned cases we obtain the Page curve like behavior in the entanglement. We report different power-law behavior in the growth of entanglement for different initial states and different kinds of baths (interacting and non-interacting). In an attempt to explore plausible deep connections between entanglement and Boltzmann entropy, we investigate the latter in both the filled and the infinite temperature case, for the system and the bath. For the filled case, the Boltzmann entropy of the system has the form of a Page curve but quantitatively deviates from the entanglement. On the other hand, the entropy of the bath keeps increasing. Remarkably, for the infinite temperature case, we find that the system and bath Boltzmann entropies agree with the entanglement entropy, after and before the Page time, respectively. Our findings are expected to hold for generic interacting quantum systems and could be of relevance to black hole physics.

quant-ph↗

arXiv2025

Spikes in Poissonian quantum trajectories

We consider the dynamics of a continuously monitored qubit in the limit of strong measurement rate where the quantum trajectory is described by a stochastic master equation with Poisson noise. Such limits are expected to give rise to quantum jumps between the pointer states associated with the non-demolition measurement. A surprising discovery in earlier work [Tilloy et al., Phys. Rev. A 92, 052111 (2015)] on quantum trajectories with Brownian noise was the phenomena of spikes observed in between the quantum jumps. Here, we show that spikes are observed also for Poisson noise. We consider three cases where the non-demolition is broken by adding, to the basic strong measurement dynamics, either unitary evolution or thermal noise or additional measurements. We present a complete analysis of the spike and jump statistics for all three cases using the fact that the dynamics effectively corresponds to that of stochastic resetting. We provide numerical results to support our analytic results.

quant-ph↗