Numerical integration with respect to Wiener measure in studying the open quantum systems

The method for numerical study of the open quantum systems is proposed. It is based on our recent results in the field of numerical integration with respect to probability measures in complete separable metric spaces. Our approximations satisfy the condition of being exact on a class of polynomial functionals of a given degree. The method does not require preliminary discretisation of space and time, it allows using the more preferable deterministic algorithms in computations instead of traditional probabilistic ones and proves to be more effective than the other existing nonperturbative numerical methods especially in the case of high dimensions. An iteration formula improving the results of numerical calculations for enlarged time intervals is obtained. Application to the problems of nuclear physics is considered. Key-Words: Functional integral, metric space, Gaussian measure, approximations, quantum mechanics, propagator, Markovian open system, density operator, numerical integration