Boltzmann-conserving classical dynamics in quantum time-correlation functions: "Matsubara dynamics"

摘要: We show that a single change in the derivation of linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results classical dynamics which conserves quantum Boltzmann distribution. rederive (standard) LSC-IVR approach by writing (exact) time-correlation function terms normal modes free ring-polymer (i.e., discrete imaginary-time Feynman path), taking limit number polymer beads N → ∞, such lowest normal-mode frequencies take their "Matsubara" values. The we propose is to truncate Liouvillian, not explicitly powers ħ(2) at ħ(0) (which gives back standard approximation), but derivatives corresponding Matsubara frequencies. resulting inherently (since all O(ħ(2)) disappear from Liouvillian ∞) and distribution because Hamiltonian symmetric with respect translation. Numerical tests approximation converges better agreement than exact result. too computationally expensive be applied complex systems, its further may lead practical methods.