Localization and diffusion in quantum dissipative systems

A quantum dissipative system is studied based on a model constructed from q uantum dots coupled to a one-dimensional (1D) quantum wire via a Coulomb in teraction between them. In this model, the quantum dots are approximated by a symmetric double-well potential. We assume that the quantum wire is in s pinless Tomonaga-Luttinger (TL) liquid states. It is shown that. ill this s ystem, there is a transition from diffusion to localization for a tunneling electron in the double well. We obtain the Localization condition that rel ates tile TL parameter with those parameters characterizing the quantum dot s and the 1D quantum wire. The implication of our results for experimental identification of a TL liquid is discussed.