Low-temperature quasi-classical approximation for quantum macroscopic phenomena

Quantum systems with two distinct time scales for "fast" (quantum) and "slo w" (quasi-classical) degrees of freedom with the respective frequencies Ome ga and omega much less than Omega are considered. A general path-integral r epresentation for a partition function involves ordinary coherent states fo r Bose and Fermi degrees of freedom as well as generalized coherent states for a nontrivial algebra of variables. Path-integral averaging over "fast" variables results in a nonlocal (in imaginary time) effective action for a "slow" (quasi-classical) variable, which becomes local in the low-temperatu re approximation. This low-temperature adiabatic path-integral approach, ex pressed by the inequality beta Omega much greater than 1 much greater than omega/Omega, yields an appropriate basis for a subsequent quasiclassical de scription. Theories of three complex condensed matter systems are developed with the "slow" and "fast" subsystems represented by localized and band el ectrons in the lattice Anderson model, by condensate and noncondensate boso ns in the Bogoliubov model (with broken translational symmetry), and by sof t-mode phonons and electrons induced in large molecules by an electron-phon on optical transition. The corresponding quantum macroscopic phenomena are the Kondo-type reorganization of the spectrum of correlated electrons, Bose condensation in nonuniform media, and chaotization of the phonon spectrum in molecules.