THE TRANSITION TO QUANTUM MECHANICS

Martin C. Gutzwiller

Bernard Rosen

Walter Greiner

Nicolaas P. Landsman

A formalism is developed for describing approximate classical behavior in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition probability. Both the limit where ħ→0 in a fixed finite system and the limit where the size of the system goes to infinity are incorporated. In either case, classical behavior is seen only for certain observables and in a restricted class of states.

KEN-ICHI AOKI, TAMAO KOBAYASHI

We investigate the critical dissipation of the double-well quantum mechanics. We adopt two-state approximation to define effective Ising models and apply the block decimation renormalization group and the finite range scaling method recently proposed for the long range Ising model. We briefly report the numerical results of the critical dissipation for various model parameters.