Mesoscopic Circuit with Linear Dissipation

In the talk, I firstly demonstrate main ideas of quantum theory for mesoscopic electric circuits which we proposed several years ago. In the theory, the importance of the charge discreteness in a mesoscopic electric circuit is addressed. As a further development, we discuss the mesoscopic electric circuit in the presence of linear dissipation as well as magnetic flux. We propose a quantum Kirchoff equation for LCR circuit and discuss the oscillations for different criterion factors. We also solve the energy spectra and eigenvalues of physical current under a soluble symmetry hypothesis.