Schr�dinger quantization and variational principles in dissipative quantum theory

Nonstationary Superconductivity: Quantum Dissipation and Time-Dependent Ginzburg-Landau Equation

“…As is shown by Wagner [7], in the dynamic regime with taking into account both the scalar potential ϕ = V/e and the vector potential A, when (in the SI system)…”

“…Afterwards, Wagner [7] carried out a comparative study of the Caldirola-Kanai and Schrödinger-Langevin equations on the basis of the hydrodynamic treatment, which was first suggested by Madelung [8]. In accordance with Madelung's picture, the wave function is represented as 2 Advances in Condensed Matter Physics ψ = √ ρ exp(iS/D).…”

Mesoscopic circuits with charge discreteness: Quantum transmission lines

“…From this, the classical Hamiltonian could be written in the standard way. So, quantization becomes attainable from the usual correspondence between position-momentum and its associated operators [8,9,10]. In our case, a similar procedure could be implemented and we obtain the time depending Hamiltonian:…”

“…The study of the spectral properties of the Hamiltonian (8), or (10), is difficult because of the nonlinear term associated with the magnetic energy. Without charge discreteness (q e → 0), this operator is quadratic and the usual normal modes technique could be used [13].…”

“…Dissipation can be considered in many forms, the usual one is to connect the system to a bath with many degree of freedom, and with some assumptions respect to the decaying rate [7]. Phenomenological RLC circuits can be also considered using Caldirola-Kanai theory [8,9,10] in a direct way [11].…”