Comment on "quantum theory for mesosocopic electric circuits". Cond-mat/9907171 and cond-mat/9606206

TL;DR

This paper extends previous quantum models of mesoscopic LC circuits by incorporating dissipative effects through a resistance term, using an analogy with quantum damping theories.

Contribution

It introduces a generalized mesoscopic Hamiltonian that includes resistance, accounting for dissipation in quantum circuit models.

Findings

Inclusion of resistance modifies the quantum behavior of mesoscopic circuits.

The approach uses Caldirola-Kanai damping analogy for quantum dissipation.

Provides a framework for more realistic quantum circuit analysis.

Abstract

In references cond-mat/9907171 and cond-mat/9606206 (Phys.Rev.B.53, 4927 (1996)) by You-Quan Li and Bin Chen, was considered a mesoscopic LC circuit with charge discreteness. So, it was proposed a finite difference Schroedinger equation for the charge time behavior. In this comment, we generalize the corresponding mesoscopic Hamiltonian in order to taken into account the dissipative effects (resistance R). Namely, a quantum term RI, proportional to the current, is added to the mesoscopic LC circuit equation. This is carried-out in analogy with the theory of Caldirola-Kanai for quantum one particle damping.