A quantum stochastic theory for nonadiabatic processes in condensed phases and on surfaces

摘要

A quantum stochastic theory for nonadiabatic processes in condensed phases and on surfaces is given. The present theory is primarily concerned with processes involving the fragmentation of twohyphen;particle systems and/or the rsquo;rsquo;collisionrsquo;rsquo; of two particles with internal structure, i.e., electronic, spin, and nuclear degrees of freedom. A fully quantum mechanical joint energy spacendash;quantum phase space master equation for twohyphen;particle systems is presented. A simpler form of this equation emerges in the limit where the length of thermal spatial fluctuations along the relative coordinates is much greater than half the wavelength for thermal momentum fluctuations associated with relative motion. (This limit is equivalent to fulfilling a rsquo;rsquo;thermal Heisenberg uncertaintyrsquo;rsquo; relation:Dgr;pmacr;Dgr;qmacr;planck;/2.)The simpler master equation is converted into a nonlinear quantum Fokkerndash;Planck equation for nonadiabatic systems. Introducing simplifying assumptions, we obtain a quantun analog of the stochastic Liouville equation augmented with irreversible kinetic terms, which describes nonadiabatic transitions and the interruption of coherence in energy space at different points in quantum phase space. The final results are appropriately modified to incorporate the influence of applied timehyphen;dependent electric and magnetic fields. The present work provides a formal theoretical framework for examining the role of quantum effects that are neglected in rsquo;rsquo;semiclassicalrsquo;rsquo; kinetic and rsquo;rsquo;diffusionalrsquo;rsquo; theories for nonadiabatic processes.