Quantum Brownian motion and generalization of Arrhenius rate law

Department of Chemistry, Visva-Bharati, Shantiniketan-731 235, India

indian Association for the Cultivation of Science, Jadavpur, Kolkata-700 032, India

E-mail : pcdsr@mahendra.iacs.res.in Fax: 91-33-24722805

Max-Pianck-Institut fur Physik Komplexer Systeme, Nothnitzer Strabe 38, 01187 Dresden, Germany

Manuscript received 12 November 2002

Arrhenius rate law is now more than hundred years old. The dynamical basis of this phenomenological law was provided by Kramers in early nineteenforties. Since late seventies, the extensive experimental investigation in chemical dynamics and allied areas centered around Kramers' dynamical rate theory. The present paper is an outline of further development of rate theory in quantum mechanical context which takes into account of thermal activation and tunneling within an unified description. The theory is based on a new scheme for quantum Brownian motion recently proposed by us to establish quantum analogues of Kramers', Smoluchowski and Fokker-Pianck equations with true probability distribution functions in c-number phase space.