Abstract
Path integral formulation of the coupled channel problem in the case of multidimensional quantum tunneling is presented and two-time influence functionals are introduced. The two-time influence functionals are calculated explicitly for the three simplest cases: Harmonic oscillators linearly or quadratically coupled to the translational motion and a system with finite number of equidistant energy levels linearly coupled to the translational motion. The effects of these couplings on the transmission probability are studied for two limiting cases, adiabatic case and when the internal system has a degenerate energy spectrum. The condition for the transmission probability to show a resonant structure is discussed and exemplified. Finally, the properties of the dissipation factor in the adiabatic limit and its correlation with the friction coefficient in the classically accessible region are studied.
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