arXiv subjects

Santhosh Ganapa

Publications and source records attributed to Santhosh Ganapa.

5 recordsLinked to original sources

arXiv2023

Thermalization, Chaos and Hydrodynamics in Classical Hamiltonian Systems

We will discuss various aspects of thermalization, chaos and hydrodynamics in one dimensional classical Hamiltonian systems. We study two problems. First, we will revisit the Fermi-Pasta-Ulam-Tsingou (FPUT) problem in order to understand what thermalization is and discuss what leads the system starting from a typical initial condition to a thermal state. Here we discuss the various possibilities like the role of averaging, the choice of observables, the choice of initial conditions and the role of chaos in thermalization. Then, we study the evolution of a blast wave in an alternate mass hard particle (AHP) gas and study the evolution of conserved fields in the system at short times. We find a good agreement with the Taylor-von Neumann-Sedov (TvNS) solution, which was studied during the Second World War in the context of atomic explosions, everywhere except near the core of the blast. We then model this behaviour by using the Navier-Stokes-Fourier (NSF) equations.

nlin.CD↗

arXiv2023

Quasiperiodicity in the $α-$Fermi-Pasta-Ulam-Tsingou problem revisited: an approach using ideas from wave turbulence

The Fermi-Pasta-Ulam-Tsingou (FPUT) problem addresses fundamental questions in statistical physics, and attempts to understand the origin of recurrences in the system have led to many great advances in nonlinear dynamics and mathematical physics. In this work we revisit the problem and study quasiperiodic recurrences in the weakly nonlinear $α-$FPUT system in more detail. We aim to reconstruct the quasiperiodic behaviour observed in the original paper from the canonical transformation used to remove the three wave interactions, which is necessary before applying the wave turbulence formalism. We expect the construction to match the observed quasiperiodicity if we are in the weakly nonlinear regime. Surprisingly, in our work we show that this is not always the case and in particular, the recurrences observed in the original paper cannot be constructed by our method. We attribute this disagreement to the presence of small denominators in the canonical transformation used to remove the three wave interactions before arriving at the starting point of wave turbulence. We also show that these small denominators are present even in the weakly nonlinear regime, and they become more significant as the system size is increased. We also discuss our results in the context of the problem of equilibration in the $α-$FPUT system, and point out some mathematical challenges when the wave turbulence formalism is applied to explain thermalization in the $α-$FPUT problem. We argue that certain aspects of the $α-$FPUT system such as presence of the stochasticity threshold, thermalization in the thermodynamic limit and the cause of quasiperiodicity are not clear, and that they require further mathematical and numerical studies.

cond-mat.stat-mech↗

arXiv2021

Blast in a One-Dimensional Cold Gas: From Newtonian Dynamics to Hydrodynamics

A gas composed of a large number of atoms evolving according to Newtonian dynamics is often described by continuum hydrodynamics. Proving this rigorously is an outstanding open problem, and precise numerical demonstrations of the equivalence of the hydrodynamic and microscopic descriptions are rare. We test this equivalence in the context of the evolution of a blast wave, a problem that is expected to be at the limit where hydrodynamics could work. We study a one-dimensional gas at rest with instantaneous localized release of energy for which the hydrodynamic Euler equations admit a self-similar scaling solution. Our microscopic model consists of hard point particles with alternating masses, which is a nonintegrable system with strong mixing dynamics. Our extensive microscopic simulations find a remarkable agreement with Euler hydrodynamics, with deviations in a small core region that are understood as arising due to heat conduction.

cond-mat.stat-mech↗

arXiv2021

The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas

We study the response of an infinite system of point particles on the line initially at rest on the instantaneous release of energy in a localized region. We make a detailed comparison of the hydrodynamic variables predicted by Euler equations for non-dissipative ideal compressible gas and the results of direct microscopic simulations. At long times the profiles of the three conserved variables evolve to self-similar scaling forms, with a scaling exponent as predicted by the Taylor-von Neumann-Sedov (TvNS) blast-wave solution. The scaling functions obtained from the microscopic dynamics show a remarkable agreement with the TvNS predictions, except at the blast core, where the TvNS solution predicts a diverging temperature which is not observed in simulations. We show that the effect of heat conduction becomes important and present results from a numerical solution of the full Navier-Stokes-Fourier equations. A different scaling form is observed in the blast core and this is carefully analyzed. Our microscopic model is the one-dimensional alternate mass hard-particle gas which has the ideal gas equation of state but is non-integrable and known to display fast equilibration.

cond-mat.stat-mech↗

arXiv2020

Thermalization of local observables in the $α$-FPUT chain

Most studies on the problem of equilibration of the Fermi-Pasta-Ulam-Tsingou (FPUT) system have focused on equipartition of energy being attained amongst the normal modes of the corresponding harmonic system. In the present work, we instead discuss the equilibration problem in terms of local variables, and consider initial conditions corresponding to spatially localized energy. We estimate the time-scales for equipartition of space localized degrees of freedom and find significant differences with the times scales observed for normal modes. Measuring thermalization in classical systems necessarily requires some averaging, and this could involve one over initial conditions or over time or spatial averaging. Here we consider averaging over initial conditions chosen from a narrow distribution in phase space. We examine in detail the effect of the width of the initial phase space distribution, and of integrability and chaos, on the time scales for thermalization. We show how thermalization properties of the system, quantified by its equilibration time, defined in this work, can be related to chaos, given by the maximal Lyapunov exponent. Somewhat surprisingly we also find that the ensemble averaging can lead to thermalization of the integrable Toda chain, though on much longer time scales.

cond-mat.stat-mech↗