Thermal enhancement of the quantum decay rate in a dissipative system

Ganying Tu, Lituo Shen, 杨贞标

Hermann Grabert, Ulrich Weiß

Consider a macroscopic system rendered unstable by both thermal fluctuation and quantum tunneling. Kramer's classical theory of the rate of decay by thermal activation is extended to lower temperatures where quantum tunneling prevails. By means of a functional-integral approach, a general formula for the decay rate is derived which describes the transition between the high- and low-temperature regimes. The influence of dissipation on the decay rate is emphasized.

Sudarson Sekhar Sinha, Arnab Ghosh, Deb Shankar Ray

The spin-bath induced decay of a quantum system out of a metastable state, which can tunnel and undergo thermal activation, is considered. The treatment is based on the c-number description of bath degrees of freedom and a canonical thermal distribution of the associated c-number variables. We show that, apart from the usual frequency prefactor and its dynamical modification in the spatial diffusion-limited regime, i.e., the Grote-Hynes factor, the rate coefficient contains two other factors. One is a quantum correction to the dynamical factor resulting from quantum transmission and reflection of the particle at the finite barrier. This term exhibits exponential rate enhancement at low temperature. The other one is a quantum corrected Arrhenius factor, which incorporates the effect of thermal saturation. At 0 K, dissipation due to tunneling multiplies the tunneling probability by a factor that gets exponentially damped by friction, implying that, at this temperature, the behavior of spin bath is almost identical to that of a harmonic bath.

Peter Hänggi A, Waldemar Hontscha

The role of memory friction on dissipative quantum reaction rates is emphasized. The domain of low temperatures, bearing a variety of important tunnelling phenomena, is difficult to handle analytically. In order to fill this gap, we present new scaling relations for the bounce length τ B as a function of the dissipation renormalized barrier frequency μ. In addition, we propose a simple estimate for τ B , which in turn yields directly the thermal low temperature enhancement of the quantum decay rate for Ohmic friction, as well as for memory friction. Finally the range of validity of the theory is discussed and pictorally represented in a rate phase diagram.

Mio Murao, Fumiaki Shibata