PATH-INTEGRAL CALCULATION OF QUANTUM TUNNELING FOR CUBIC POTENTIAL ATFINITE-TEMPERATURE

The periodic instanton method is used to study the decay rates of meta stable ground state and excited states of the cubic potential. The ima ginary part of the energy is calculated through the standard procedure in the path-integral scheme. A formula of the decay rate valid for th e entire region of energy is obtained. This formula provides a linkage between classical thermal activation at high temperatures and purely quantum tunneling at zero temperature. It is shown that in the low ene rgy limit this more general result reduces exactly to the vacuum resul t. The temperature dependence of the decay rate agrees with earlier wo rks in the literature.