A Feynman path centroid dynamics approach for the computation of time correlation functions involving nonlinear operators

The centroid dynamics formalism is extended to the calculation of time corr elation functions of nonlinear operators. It is shown that centroid correla tion functions can be related to quantum mechanical ones via higher order K ubo-type transforms. A key step is the construction of the correlation func tions from a mixed classical/semiclassical centroid representation of the o perators. A general methodology is developed to relate these Kubo-type tran sforms to the desired quantum correlation functions. The approach is tested using a one-dimensional anharmonic potential for which the [x(2)x(2)(t)] a nd the [x(3)x(3)(t)] correlation functions are computed. Applications of th is new approach are also outlined. (C) 2000 American Institute of Physics. [S0021-9606(00)50827-7].