Numerical study of tunneling in a dissipative system

Quantum-mechanical resonance energies and their corresponding decay rates (inverse lifetimes) for the metastable system of a cubic potential coupled to a harmonic oscillator are computed numerically via the complex scaling method. This system, which mimics tunneling in dissipative media, is investigated for different barrier heights and a variety of coupling strengths. The large number of computed resonances allows one to calculate thermally averaged decay rates for temperatures up to the crossover temperature. The numerical results are compared to the sudden theory of dissipative tunneling, and rather good agreement is found. The suppression of the rate with increasing dissipation and the thermal enhancement of the rate, as predicted by the instanton method for dissipative tunneling, are also confirmed. When the time scale of the bath oscillator exceeds the time scale of the system, an interesting, counterintuitive observation is that the temperature for the crossover between tunneling and thermally activated escape increases with increasing coupling strength. This is in contrast to the usual behavior for ohmiclike dissipative systems. The numerical results in this work can be used as a benchmark to test other theories of dissipative tunneling.