arXiv subjects

Sahil Kumar Singh

Publications and source records attributed to Sahil Kumar Singh.

5 recordsLinked to original sources

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↗

arXiv2023

Thermalization and hydrodynamics in an interacting integrable system: the case of hard rods

We consider the relaxation of an initial non-equilibrium state in a one-dimensional fluid of hard rods. Since it is an interacting integrable system, we expect it to reach the Generalized Gibbs Ensemble (GGE) at long times for generic initial conditions. Here we show that there exist initial conditions for which the system does not reach GGE even at very long times and in the thermodynamic limit. In particular, we consider an initial condition of uniformly distributed hard-rods in a box with the left half having particles with a singular velocity distribution (all moving with unit velocity) and the right half particles in thermal equilibrium. We find that the density profile for the singular component does not spread to the full extent of the box and keeps moving with a fixed effective speed at long times. We show that such density profiles can be well described by the solution of the Euler equations almost everywhere except at the location of the shocks, where we observe slight discrepancies due to dissipation arising from the initial fluctuations of the thermal background. To demonstrate this effect of dissipation analytically, we consider a second initial condition with a single particle at the origin with unit velocity in a thermal background. We find that the probability distribution of the position of the unit velocity quasi-particle has diffusive spreading which can be understood from the solution of the Navier-Stokes equation of the hard rods. Finally, we consider an initial condition with a spread in velocity distribution for which we show convergence to GGE. Our conclusions are based on molecular dynamics simulations supported by analytical arguments.

cond-mat.stat-mech↗

arXiv2023

Blast waves in the zero temperature hard sphere gas: double scaling structure

We study the blast generated by sudden localized release of energy in a cold gas. Specifically, we consider one-dimensional hard-rod gas and two-dimensional hard disc gas. For this problem, the Taylor-von Neumann-Sedov (TvNS) solution of Euler equations has a self-similar form. The shock wave remains infinitely strong for the zero-temperature gas, so the solution applies indefinitely. The TvNS solution ignores dissipation, however. We show that this is erroneous in the core region which, in two dimensions, expands as $t^{2/5}$ while the shock wave propagates as $t^{1/2}$. A new self-similar solution depending on the scaling variable $r/t^{2/5}$ describes the core, while the TvNS solution describes the bulk. We demonstrate this from a numerical solution of the Navier-Stokes (NS) equations and from molecular dynamics simulations for a gas of hard discs in two dimensions and hard rods in one dimension. In both cases, the shock front position predicted by NS equations and by the TvNS solution agrees with that predicted by molecular dynamics simulations. However, the NS equations fail to describe the near-core form of the scaling functions.

cond-mat.stat-mech↗

arXiv2020

Chiral anomalies induced transport in Weyl semimetals in quantizing magnetic field

Weyl semimetals host relativistic chiral quasiparticles, which display quantum anomalies in the presence of external electromagnetic fields. Here, we study the manifestations of chiral anomalies in the longitudinal and planar magneto-transport coefficients of Weyl semimetals, in the presence of a quantizing magnetic field. We present a general framework for calculating all the transport coefficients in the regime where multiple Landau levels are occupied. We explicitly show that all the longitudinal and planar transport coefficients show Shubnikov-de Haas like quantum oscillations which are periodic in 1/B. Our calculations recover the quadratic-B dependence in the semiclassical regime, and predict a linear-B dependence in the ultra-quantum limit for all the transport coefficients.

cond-mat.mes-hall↗

arXiv2018

Entropy of hard square lattice gas with $k$ distinct species of particles: coloring problems and vertex models

Coloring the faces of 2-dimensional square lattice with $k$ distinct colors such that no two adjacent faces have the same color is considered by establishing connection between the $k$ coloring problem and a generalized vertex model. Associating the colors with $k$ distinct species of particles with infinite repulsive force between nearest neighbors of the same type and zero chemical potential $μ$ associated with each species, the number of ways $[W(k)]^N$ for large $N$ is related to the entropy of the {\it{hard square lattice gas}} at close packing of the lattice, where $N$ is the number of lattice sites. We discuss the evaluation of $W(k)$ using transfer matrix method with non-periodic boundary conditions imposed on at least one dimension and show the characteristic Toeplitz block structure of the transfer matrix. Using this result, we present some analytical calculations for non-periodic models that remain finite in one dimension. The case $k=3$ is found to approach the exact result obtained by Lieb for the residual entropy of ice with periodic boundary conditions. Finally, we show, by explicit calculation of the contribution of subgraphs and the series expansion of $W(k)$, that the genenralized Pauling type estimate(which is based on mean field approximation) dominates at large values of $k$. We thus also provide an alternative series expansion for the chromatic polynomial of a regular square graph.

math-ph↗