题 目：Quantum Generalised Langevin Equation
报告人：Prof. Lev Kantorovich（ Physics Department, King’s College London, United Kingdom）
A fully quantum Generalised Langevin Equation (GLE) for an open quantum phonon system surrounded by one (or more) quantum phonon heat bath(s) kept at constant temperature(s) is derived from general principles of quantum statistical mechanics. The Hamiltonian of the open system is assumed of the most general form, as well as the force acting on atoms in the bath region(s); however, the bath(s) is(are) considered as harmonic, and the coupling to the open system linear with respect to atomic displacements in the bath(s).
We find that non-operator (c-number) equations of motion for atomic average positions (where is a coordinate of atom A in the open part and is the time-dependent density operator for the whole system: open part + bath(s)) have a rather general GLE form with memory friction and a Gaussian distributed random (stochastic) force. We obtain a general expression for the friction kernel for this Hamiltonian and show that the origin of the stochastic forces comes from one-phonon fluctuations in the heat bath(s).
A class of solutions for the bath is found which ensures that quantum GLE goes correctly into the classical GLE  upon either high temperature or limit.
The derived equations form a basis for fully quantum mechanical non-equilibrium molecular dynamics (MD) simulations for an open system surrounded by quantum heat bath(s) at constant temperature (NVT ensemble), and can be used in simulations of various physical processes where quantum effects are important, such as e.g. quantum heat transport, quantum character of H atoms in molecules and solids, irradiation, etc.
1 L. Kantorovich – Phys. Rev. B 78 094304 (2008)