London superconductivity approach in a time-dependent background

TL;DR

This paper develops an exact quantum solution for charge dynamics in a superconductor with time-varying parameters, introducing a novel quantization scheme and analyzing information measures.

Contribution

It presents a new quantization method for superconductor charge using the Lewis-Riesenfeld invariant, providing exact solutions and analyzing their informational properties.

Findings

Time-independent complexity measure.

Quantities expressed via a nonlinear differential equation.

Exact wave-functions for charge in time-dependent superconductors.

Abstract

The main goal of this paper is to obtain the exact quantum solutions for charge space in a superconductor with time-dependent parameters using the London approach. We introduce a new quantization scheme for the charge inside a superconductor based on the Lewis and Riesenfeld invariant operator method. From the wave-functions obtained, we calculated the time-dependent uncertainties and the mean energy of the system. Information measures were also obtained, such as Shannon entropy and complexity. The later is always time-independent and also does not depend on conductivity. The others quantities are written in terms of a time-dependent function, \r{ho}(t), c-number quantity satisfying a nonlinear differential equation.