Second-Order Langevin Equation in Quantized Hamilton Dynamics

Abstract

We derive a semi-classical Langevin equation that, in conjuction with a quantum fluctuation–dissipation theorem, can be used to run canonical dynamics and to determine thermal averages in the second-order quantized Hamilton dynamics (QHD-2). In contrast to our earlier work [J. Chem. Phys. 122 (2005) 234109], the bath is no longer treated classically, and the friction is represented at the second-order. As a result, the quantum fluctuation variables are kept close to their optimal values, similarly to the recently developed phase-space canonical averaging for QHD-2 [J. Chem. Phys. 126 (2007) 204108]. The theory is exact for the quantum harmonic oscillator and the free particle, and gives good agreement with the quantum answer for a variety of quartic potentials.