Path Integral studies of quantum systems at finite temperatures

This thesis presents and develops the path integral simulation techniques in application to small quantum systems at finite temperatures. The first goal is to obtain exact thermodynamic expressions for systems of noninteracting The rest and the major part of the thesis is dedicated to the development and testing of Bead-Fourier path integral molecular dynamics. Although, path integral molecular dynamics as well as path integral Monte Carlo are well First, molecular dynamics under Bead-Fourier scheme was developed and tested on the examples of quantum harmonic oscillator and Hydrogen atom. The main attention was paid to ergodicity problems. Then we addressed the question, Later, the formalism for identical particles was developed. Finally, the question of molecular dynamics efficacy was raised. It was shown, that formalisms for identical and distinguishable particles, both, can be reformulated into a more efficient ones, providing all dynamical variable