The quantum analog of Kramers rate theory is derived from a unique many-body rate approach (Miller formula), being valid at all temperatures. In contrast to the imaginary free energy method (‘‘bounce’’ method) for a dissipative system we do not have to invoke a different prescription of the rate formula for temperatures below the crossover temperature T0 to tunneling dominated escape. Miller’s many-body quantum transition state theory is shown to produce the results of the imaginary free energy technique; in particular it also describes correctly the subtle regime near crossover T∼T0.

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The quantum analog of Kramers reaction rate for a dissipative environment is derived on the basis of a periodic orbit approach for multidimensional tunneling. The resulting reaction rate expression holds at all temperatures, thus covering [in contrast to the imaginary free energy method ("bounce-"method)] the classical and the quantum regime on the same basis.

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The effect of a low-frequency dissipative medium on the tunneling rate of a particle trapped in a metastable potential is investigated with the aid of a frozen-bath sudden approximation. The sudden theory is formulated for arbitrary time-dependent friction and for all temperatures at which the escape process is dominated by tunneling. The validity criterion of the theory is only that the bath frequency spectrum be substantially lower than the system frequency. It is applicable both in the weak-and strong-damping limits. The sudden theory is applied to tunneling in a cubic potential and a piecewise harmonic potential where the barrier frequency differs from the well frequency. In contrast to the ImF method, the sudden theory, when valid, can provide estimates of tunneling rates from well-defined excited resonance states and is not limited to estimates of only thermal rates. We find that, if the barrier is thin relative -to the well, dissipation can serve to enhance tunneling rates from excited states. I. INTRGDUCTIQNThe theory of tunneling in dissipative systems has been developed extensively in the past decade. Caldeira and Leggett have formulated and solved the problem for tunneling at 0 K. Their main qualitative result is that dissipation will exponentially decrease the tunneling rate. Grabert, Hanggi, and coworkers have extended these results to nonzero temperatures. They found that an increase in temperature will increase the tunneling rate according to an exponential power law. It was also found that at higher temperatures, dissipation tends to "smear" the boundary between the tunneling and the thermal activation regime.The analytical methods used to solve the problem were mostly based on functional integration of the analytically continued free energy of the system around the steepestdescent solution.This method leads to the use of the instanton as the basic object that determines the rate of tunneling. Recently it has been demonstrated that these methods have a close connection to the semiclassical transition state theory of Miller. ' However, the physics underlying the relatively simple qualitative results has remained somewhat obscure. For example, it is clear that the exponential increase in the rate at low temperatures must be related to Auctuations caused by the bath but the exact connection has not been made. Moreover, the methods based on functional integration necessarily deal with a thermal system. They cannot be used to predict the efFect of dissipation on the rate from single isolated levels.Recently, we have shown that a normal-mode transformation of the Caldeira-Leggett Hamiltonian around the barrier of the system can lead to a very simple view of the dynamics. ' For example, it is easy to show that the new normal-mode barrier frequency will usually be smaller than the original system barrier frequency. Since the tunneling rate depends exponentially on the barrier frequency, it becomes obvious that a thicker barrier will exponentially decrease the rate. Similarly it was demonstrated that the e...