Equilibrium spacetime correlations of the Toda lattice on the hydrodynamic scale. (English) Zbl 1538.82099
Summary: We report on molecular dynamics simulations of spacetime correlations of the Toda lattice in thermal equilibrium. The correlations of stretch, momentum, and energy are computed numerically over a wide range of pressure and temperature. Our numerical results are compared with the predictions from linearized generalized hydrodynamics on the Euler scale. The system size is \(N=3000,\, 4000\) and time \(t =600\), at which ballistic scaling is well confirmed. With no adjustable parameters, the numerically obtained scaling functions agree with the theory within a precision of less than 3.5%.
MSC:
| 82M37 | Computational molecular dynamics in statistical mechanics |
| 82B23 | Exactly solvable models; Bethe ansatz |
| 82B30 | Statistical thermodynamics |
| 81V55 | Molecular physics |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K60 | Lattice dynamics; integrable lattice equations |
| 82C20 | Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics |
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