Classical Langevin Dynamics Derived from Quantum Mechanics

Classical Langevin Dynamics Derived from Quantum Mechanics

​Hoel, Håkon, and Anders Szepessy, "Classical Langevin Dynamics Derived from Quantum Mechanics", arXiv preprint 1906.09858
Håkon Hoel, Anders Szepessy
Stochastic methods, Quantum dynamics and nonequilibrium statistical mechanics, Stochastic differential and integral equations, Stochastic ordinary differential equations
2019
The classical work by Zwanzig [J. Stat. Phys. 9 (1973) 215-220] derived Langevin dynamics from a Hamiltonian system of a heavy particle coupled to a heat bath. This work extends Zwanzig's model to a quantum system and formulates a more general coupling between a particle system and a heat bath. The main result proves that ab initio Langevin molecular dynamics, with a certain rank one friction matrix determined by the coupling, approximates for any temperature canonical quantum observables, based on the system coordinates, more accurately than any Hamiltonian system in these coordinates, for large mass ratio between the system and the heat bath nuclei.