ACCURATE QUANTUM AND STATISTICAL-MECHANICS FROM SYSTEM-SPECIFIC OPERATOR EXPANSIONS

An effective and flexible numerical scheme is proposed to calculate th e quantum and statistical mechanics of multidimensional systems in a s imple economic way. The basic idea is to split the Hamiltonian operato r into a reference separable part, whose solution can be obtained by a combination of analytic and numerical techniques, and a term containi ng nonseparable interactions and then to employ a symmetric decomposit ion of the time evolution operator, which is exact up to a high order in the time step. The method is applicable to a wide range of coupling potentials and requires numerical effort that scales only linearly wi th the number of degrees of freedom involved. To verify the utility of the present approach, two model systems with strongly anharmonic mode coupling are considered. The applications show that the method accura tely describes the dynamics for fairly long times with moderate coupli ng strengths and is still much less arduous than a general numerically exact calculation.