A reformulation in a superspace is given for Van Hove and Janner’s perturbation theory based on the two-resolvent method for nonequilibrium quantum statistical mechanics. This is attained by introducing an ordered superoperator in the superspace. As an application of our formalism, the derivation of an asymptotic generalized master equation in a Markovian form is given. Further, it is investigated how a quantum subdynamics theory similar to the Brussels school’s one can be formally constructed. Our subdynamics theory is formulated on every eigenspace of a superoperator (the ss-Hamiltonian) of which the eigenvalue is related to the intrinsic parameter E of Van Hove and Janner’s generalized master equation.
High-order perturbative
ab initio calculations are challenging due to the rapidly growing configuration space and the difficulty of assessing convergence. In this letter, we introduce perturbation theory quantum Monte Carlo (PTQMC), a stochastic approach designed to compute high-order many-body perturbative corrections. By representing the perturbative wave function with random walkers in configuration space, PTQMC avoids the exponential scaling inherent to conventional constructions of high-rank excitation operators. Benchmark calculations for the Richardson pairing model demonstrate that PTQMC accurately reproduces exact many-body perturbation theory (MBPT) coefficients up to 16th order, even in strongly divergent regimes. We further show that combining PTQMC with series resummation techniques yields stable and precise energy estimates in cases where the straightforward perturbative series fails. Finally, we propose the effective number of configurations,
eS, as a global measure of perturbative wave-function complexity that can be directly extracted within PTQMC. We demonstrate that the saturation behavior of
eS provides a more reliable indicator of the validity of perturbative expansions than energy convergence alone.
The perturbation quantum system was discussed within the framework of quantum phase space representation formulated by Torres-Vega and Frederick(TF) and studied the nondegenerate perturbation theory.The energy and the wave functions of the system in quantum phase space representation has been obtained;the one dimensional anharmonic oscillator system was used for an example to analyses the behaviour of quantum system in quantum phase space representation.The actual physical system in quantum phase space representation by using the approximate methods has been discussed.