Thermodynamic formalism for quantum-mechanical systems (Q810981)

In recent years many authors have used methods originating from thermodynamics and statistical mechanics for the study of chaotic dynamics. A useful bibliography of the important papers is given in this work which takes further the application of thermodynamics to the study of Euclidean quantum mechanics on a lattice. The author introduces a class of deterministic chaotic maps that stimulate nonrelativistic quantum mechanical systems with arbitrary scalar and vector potentials. The author applies thermodynamic methods to the maps and shows that the partition function converges to the propagator of the Schrödinger equation with imaginary time and the free energy to the ground state energy in the appropriate scaling limit. The method is illustrated by determining the ground state energies for the harmonic and the anharmonic oscillators and the propagator of the hydrogen atom.