arXiv subjects

Saurav Pandey

Publications and source records attributed to Saurav Pandey.

4 recordsLinked to original sources

arXiv2024

Generalized hydrodynamics and approach to Generalized Gibbs equilibrium for a classical harmonic chain

We study the evolution of a classical harmonic chain with nearest-neighbor interactions starting from domain wall initial conditions. The initial state is taken to be either a product of two Gibbs Ensembles (GEs) with unequal temperatures on the two halves of the chain or a product of two Generalized Gibbs Ensembles (GGEs) with different parameters in the two halves. For this system, we construct the Wigner function and demonstrate that its evolution defines the Generalized Hydrodynamics (GHD) describing the evolution of the conserved quantities. We solve the GHD for both finite and infinite chains and compute the evolution of conserved densities and currents. For a finite chain with fixed boundaries, we show that these quantities relax as $\sim 1/\sqrt{t}$ to their respective steady-state values given by the final expected GE or GGE state, depending on the initial conditions. Exact expressions for the Lagrange multipliers of the final expected GGE state are obtained in terms of the steady state densities. In the case of an infinite chain, we find that the conserved densities and currents at any finite time exhibit ballistic scaling while, at infinite time, any finite segment of the system can be described by a current-carrying non-equilibrium steady state (NESS). We compute the scaling functions analytically and show that the relaxation to the NESS occurs as $\sim 1/t$ for the densities and as $\sim 1/t^2$ for the currents. We compare the analytic results from hydrodynamics with those from exact microscopic numerics and find excellent agreement.

cond-mat.stat-mech↗

arXiv2023

Boltzmann entropy of a freely expanding quantum ideal gas

We study the time evolution of the Boltzmann entropy of a microstate during the non-equilibrium free expansion of a one-dimensional quantum ideal gas. This quantum Boltzmann entropy, $S_B$, essentially counts the "number" of independent wavefunctions (microstates) giving rise to a specified macrostate. It generally depends on the choice of macrovariables, such as the type and amount of coarse-graining, specifying a non-equilibrium macrostate of the system, but its extensive part agrees with the thermodynamic entropy in thermal equilibrium macrostates. We examine two choices of macrovariables: the $U$-macrovariables are local observables in position space, while the $f$-macrovariables also include structure in momentum space. For the quantum gas, we use a non-classical choice of the $f$-macrovariables. For both choices, the corresponding entropies $s_B^f$ and $s_B^U$ grow and eventually saturate. As in the classical case, the growth rate of $s_B^f$ depends on the momentum coarse-graining scale. If the gas is initially at equilibrium and is then released to expand to occupy twice the initial volume, the per-particle increase in the entropy for the $f$-macrostate, $\Delta s_B^f$, satisfies $\log{2}\leq\Delta s_B^f\leq 2\log{2}$ for fermions, and $0\leq\Delta s_B^f\leq\log{2}$ for bosons. For the same initial conditions, the change in the entropy $\Delta s_B^U$ for the $U$-macrostate is greater than $\Delta s_B^f$ when the gas is in the quantum regime where the final stationary state is not at thermal equilibrium.

cond-mat.stat-mech↗

arXiv2021

A Generalization of Cyclic Code Equivalence Algorithm to Constacyclic Codes

Recently, a new algorithm to test equivalence of two cyclic codes has been introduced which is efficient and produced useful results. In this work, we generalize this algorithm to constacyclic codes. As an application of the algorithm we found many constacyclic codes with good parameters and properties. In particular, we found 23 new codes that improve the minimum distances of BKLCs.

cs.IT↗

arXiv2021

COVID-19: Analytic results for a modified SEIR model and comparison of different intervention strategies

The Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is one of the standard models of disease spreading. Here we analyse an extended SEIR model that accounts for asymptomatic carriers, believed to play an important role in COVID-19 transmission. For this model we derive a number of analytic results for important quantities such as the peak number of infections, the time taken to reach the peak and the size of the final affected population. We also propose an accurate way of specifying initial conditions for the numerics (from insufficient data) using the fact that the early time exponential growth is well-described by the dominant eigenvector of the linearized equations. Secondly we explore the effect of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number, $R_0$, to a target value $R^{\rm target}_0 < 1$, but in distinct ways, which we implement in our model equations. We find that for the same $R^{\rm target}_0 < 1$, TQ is more efficient in controlling the pandemic than SD. However, for TQ to be effective, it has to be based on contact tracing and our study quantifies the required ratio of tests-per-day to the number of new cases-per-day. Our analysis shows that the largest eigenvalue of the linearised dynamics provides a simple understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. We apply our results to the COVID data for India to obtain heuristic projections for the course of the pandemic, and note that the predictions strongly depend on the assumed fraction of asymptomatic carriers.

q-bio.PE↗