The quantum thermal average plays a central role in describing the thermodynamic properties of a quantum system.Path integral molecular dynamics(PIMD)is a prevailing approach for computing quantum thermal averages by ...The quantum thermal average plays a central role in describing the thermodynamic properties of a quantum system.Path integral molecular dynamics(PIMD)is a prevailing approach for computing quantum thermal averages by approximating the quantum partition function as a classical isomorphism on an augmented space,enabling efficient classical sampling,but the theoretical knowledge of the ergodicity of the sampling is lacking.Parallel to the standard PIMD with N ring polymer beads,we also study the Matsubara mode PIMD,where the ring polymer is replaced by a continuous loop composed of N Matsubara modes.Utilizing the generalizedΓcalculus,we prove that both the Matsubara mode PIMD and the standard PIMD have uniformin-N ergodicity,i.e.,the convergence rate towards the invariant distribution does not depend on the number of modes or beads N.展开更多
基金supported by the National Key R&D Program of China(Project Nos.2020YFA0712000,2021YFA1001200)the National Natural Science Foundation of China(Grant Nos.12031013,12171013).
文摘The quantum thermal average plays a central role in describing the thermodynamic properties of a quantum system.Path integral molecular dynamics(PIMD)is a prevailing approach for computing quantum thermal averages by approximating the quantum partition function as a classical isomorphism on an augmented space,enabling efficient classical sampling,but the theoretical knowledge of the ergodicity of the sampling is lacking.Parallel to the standard PIMD with N ring polymer beads,we also study the Matsubara mode PIMD,where the ring polymer is replaced by a continuous loop composed of N Matsubara modes.Utilizing the generalizedΓcalculus,we prove that both the Matsubara mode PIMD and the standard PIMD have uniformin-N ergodicity,i.e.,the convergence rate towards the invariant distribution does not depend on the number of modes or beads N.
