Exactly solvable quantum macroscopic motions and decoherence mechanism based on many quantum-mechanical space theory

Summary

Exactly solvable macroscopic systems composed of harmonic oscillators are investigated on the basis of non-standard analysis. Wave functions for the motions of the centre-of-mass coordinate of the systems, which are described as ultra-eigenfunctions representing a classical ensemble of the macroscopic objects in a non-standard extension of quantum mechanics, are explicitly obtained. Many quantum-mechanical spaces are naturally introduced as the physical background of the ultra-eigenfunctions. The so-called wave function collapse described by the transition from pure states to mixed states, that is decoherence among different ultra-eigenfunctions, is derived from integrations with respect to the freedom of the many quantum-mechanical spaces contained in the ultra-eigenfunctions. It is also shown that this decoherence mechanism is quite different from that of coherent states reproducing classical trajectories. The relation to the coarse-grained operators by van Kampen will also be discussed.