Effects of environmental electrons on the tunneling processes of a heavy particle

Abstract

A new formalism to treat the tunneling processes of a heavy particle coupled to degenerate electron systems has been presented. This simple and transparent method follows that of Caldeira and Leggett in a general framework, but the term representing the dissipation is given in terms of the retarded density correlation function as far as the coupling is weak. Hence our method can incorporate the microscopic details of the electronic systems such as mutual interactions and randomness. It is found that in the Luttinger liquid, the dissipation can be either sub- or super-Ohmic depending on the type of interaction, while near the Anderson transition there exists a crossover from Ohmic to sub-Ohmic dissipation. It is also found that, in the case of sub-Ohmic dissipation, the tunneling rate vanishes discontinuously above some critical value as a function of the strength of dissipation.