Quantum Tunneling in dissipative systems and it s Applications

A. O. Caldeira

N. G. Kelkar, D. Lozano Gómez, Edgar J. Patiño

H. Dekker

N. Emir Anuar

We present a formalism for which a dissipative system is given by a variational principle. The formalism applies to dynamical systems where its trajectory is monotonic. Subsequently, we derive its Lagrangian and Hamiltonian. From the Hamiltonian, we quantize canonically the classical particle in a viscous media. We study the free quantum particle in a viscous media and the dissipative quantum tunnelling. It is found that the dissipation influences tunnelling probability by a factor that closely resembles the result of Caldeira and Leggett.

This chapter is devoted to quantum tunneling, as a basic quantum process, essential for important applications. Tunneling between two wells, of the double well potential of a one particle system of interest, makes sense only when a second system, capable to distinguish between the presence of the particle in a well, or in the other well, is present. The potential of interaction between such two systems is called tunneling operator. We treat a few problems of interest as tunneling in a quasi-continuum of states, the energy shift in a well by the proximity of another well, dissipation effects, and tunneling spectrum.