Isothermal quantum dynamics: Nose-Hoover dynamics for coherent states

Abstract

The method of Nose and Hoover(1,2) to create canonically distributed positions and momenta in classical molecular dynamics simulations is frequently used. Hamilton's equations of motion are supplemented by time-dependent pseudofriction terms that convert the microcanonical isoenergetic time evolution into a canonical isothermal time evolution, thus permitting the calculation of canonical ensemble averages by time averaging. We show that for one quantum particle in an external harmonic oscillator, the equations of motion in terms of coherent states can easily be modified in an analogous manner to mimic the coupling of the system to a thermal bath and create a quantum canonical ensemble.(3) The method is generalised. to a system of two identical quantum particles. In the resulting equations of motion, one obtains an additional attractive term for bosons and a repulsive term for fermions in the dynamics of the pseudofriction coefficients, leading to a correctly sampled thermal weight.