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Representation of propagator for open quantum systems in the form of a double functional integral with respect to conditional Wiener measure is proposed. It allows one to apply the approximate formulas exact for functional polynomials of a certain power to calculation of such integrals. Within this deterministic approach the problem is reduced to evaluation of usual (Riemann) integrals of low multiplicity. The formulas are in fact the basis of a numerical method of studying time evolution of the systems. The features of the method are discussed and some examples of calculations are given.

-The application of the numerical functional integration method to the solution of differential equations in quantum physics is discussed. We have developed a method of numerical evaluation of functional integrals in abstract complete separable metric spaces, which proves to have important advantages over the conventional Monte Carlo method of path integration. One of the considered applications is the investigation of open quantum systems (OQS), i.e., systems interacting with their environment. The density operator of OQS satisfies the known Lindblad differential equation. We have obtained the expression for matrix elements of this operator in the form of the double conditional Wiener integral and considered its application to some problems of nuclear physics. Another application is the solution of the Scrödinger equation with imaginary time and anticommuting variables for studying many-fermion systems. We have developed a numerical method based on functional integration over ordered subspaces. The binding energies of some nuclei are computed using this method. Comparison of the results with those obtained by other authors and with experimental values is presented.

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