Tunneling Processes of a Heavy Particle Coupled to Electron Systems

Kaoru Awaka, Gen Tatara, Hidetoshi Fukuyama

Kaoru Awaka, Gen Tatara, Hidetoshi Fukuyama

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 imaginary part 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 for 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. In the case of sub-Ohmic dissipation, the tunneling rate is found to vanish discontinuously above some critical value as a function of the strength of dissipation.

Yu. E. Lozovik, Alexey V. Filinov, A. S. Arkhipov

Don DeVault

‘Tunnelling’ is the metaphorical name given to the process, possible in quantum mechanics, but not in classical mechanics, whereby a particle can disappear from one side of a potential-energy barrier and appear on the other side without having enough kinetic energy to mount the barrier. One can think of this as a manifestation of the wave-nature of particles. The wavelength is larger if a particle is lighter. In particular electrons, being very light compared to atoms, have wavelengths as large or larger than atoms at energies found in the valence shells of molecules. Thus, they easily ooze through and around atoms and molecules. We are also concerned with the tunnelling of heavy particles: nuclei, atoms, molecules.

M. Kira, Ilkka Juhani Tittonen, Stig Stenholm

Samuel Powell