Towards construction of analog solver of Schroedinger and Ginzburg-Landau equation based on Long Line

TL;DR

This paper explores the development of an analog electronic circuit-based solver for the Schrödinger and Ginzburg-Landau equations, extending Kron's passive element models with nonlinear resistive components for potential quantum and superconductivity applications.

Contribution

It introduces a generalized passive element circuit model that incorporates nonlinear resistive components to solve Schrödinger and Ginzburg-Landau equations.

Findings

Numerical validation of Kron's model for various potential shapes.

Extension of Kron's model with nonlinear resistive elements.

Deformation of Schrödinger equation into Ginzburg-Landau form.

Abstract

The analog electronic computers are a type of circuitry used to calculate specific problems using the physical relationships between the voltages and currents following classical laws of physics. One specific class of these circuits are computers based on the interactions between passive circuit elements. Models presented by G.Kron in 1945 are the example of using such passive elements to construct a solver for the problem of free quantum particles confined by rectangular potential. Numerical validation of Kron second model is conducted for different shapes of particle confining potential. Model introduced by Kron is generalized by introduction of non-linear resistive elements what implies deformation of Schr\"odinger equation solution into Ginzburg-Landau form.