2017/02/14 by Petr Plecháč, Plecháč, Petr, Mattias Sandberg +3
Physics and Astronomy · #35L65 #82C10 #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum, superfluid, helium dynamics #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.1702.04368
openalex publication_date 2017/02/14 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
In the classical work by Irving and Zwanzig [Irving J.H. and Zwanzig R.W., J.\nChem. Phys. 19 (1951), 1173-1180 ] it has been shown that quantum observables\nfor macroscopic density, momentum and energy satisfy the conservation laws of\nfluid dynamics. This work derives the corresponding classical molecular\ndynamics limit by extending Irving and Zwanzig's result to matrix-valued\npotentials for a general quantum particle system. The matrix formulation\nprovides the semi-classical limit of the quantum observables in the\nconservation laws, also in the case where the temperature is large compared to\nthe electron eigenvalue gaps. The classical limit of the quantum observables in\nthe conservation laws is useful in order to determine the constitutive\nrelations for the stress tensor and the heat flux by molecular dynamics\nsimulations. The main new steps to obtain the molecular dynamics limit is to:\n(i) approximate the dynamics of quantum observables accurately by classical\ndynamics, by diagonalizing the Hamiltonian using a non linear eigenvalue\nproblem, (ii) define the local energy density by partitioning a general\npotential, applying perturbation analysis of the electron eigenvalue problem,\n(iii) determine the molecular dynamics stress tensor and heat flux in the case\nof several excited electron states, and (iv) construct the initial particle\nphase-space density as a local grand canonical quantum ensemble determined by\nthe initial conservation variables.\n