Semiquantal analysis of a double-well coupled to dissipative bath: effective potential and coupled generalized Langevin equations

A semiquantal theory is applied to a double-well potential coupled to dissipative bath. The analysis demonstrates in a comprehensive way how the quantum effect, e.g., the spreading of the wave packet width, is suppressed along the bath coupling strength. A quasi-classical approximation is introduced to derive a compact analytical formula, by which the kinetic isotope effects are briefly discussed. The coupled generalized Langevin equations indicate that the auxiliary semiquantal coordinates modulate the effective barrier frequency along the system coordinate, basically to reduce the frequency and thus to enhance the dynamical friction effect.