Conserved densities of hard rods: microscopic to hydrodynamic solutions
arXiv:2407.17067 · doi:10.1088/1742-5468/ad96ab
Abstract
We consider a system of many hard rods moving in one dimension. As it is an integrable system, it possesses an extensive number of conserved quantities and its evolution on macroscopic scale can be described by generalised hydrodynamics. Using a microscopic approach, we compute the evolution of the conserved densities starting from non-equilibrium initial conditions of both quenched and annealed type. In addition to getting reduced to the Euler solutions of the hydrodynamics in the thermodynamic limit, the microscopic solutions can also capture effects of the Navier-Stokes terms and thus go beyond the Euler solutions. We demonstrate this feature from microscopic analysis and numerical solution of the Navier-Stokes equation in two problems -- first, tracer diffusion in a background of hard rods and second, the evolution from a domain wall initial condition in which the velocity distribution of the rods are different on the two sides of the interface. We supplement our analytical results using extensive numerical simulations.
44 pages, 9 figures
References in corpus (14)
- Quantum Quench in the Transverse Field Ising Chain
- Experimental Observation of a Generalized Gibbs Ensemble
- Generalized Thermalization in an Integrable Lattice System
- Generalized hydrodynamics in strongly interacting 1D Bose gases
- Ballistic macroscopic fluctuation theory
- Entangling power and quantum circuit complexity
- Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems
- Role of initial conditions in diffusive systems: compressibility, hyperuniformity and long-term memory
- Entropy growth during free expansion of an ideal gas
- Boltzmann entropy of a freely expanding quantum ideal gas
- Revised Enskog equation for hard rods
- Thermalization and hydrodynamics in an interacting integrable system: the case of hard rods
- Macroscopic diffusive fluctuations for generalized hard rods dynamics
- Tracer dynamics in the active random average process