A splitting integrator for the BCS equations of superconductivity

TL;DR

This paper introduces a fast, efficient splitting integrator for the BCS equations of superconductivity, enabling accurate and cost-effective simulations that preserve physical energy over time.

Contribution

A novel splitting-based numerical scheme for BCS equations that is computationally efficient and preserves physical properties, demonstrated through extensive numerical experiments.

Findings

Computational cost increases linearly with discretization dimension.

The scheme accurately preserves the physical energy.

Numerical experiments confirm the scheme's effectiveness.

Abstract

The BCS equations are the centerpiece of the microscopic description of superconductivity. Their space discretization yields a system of coupled ordinary differential equations. In this work, we come up with fast time evolution schemes based on a splitting approach. One of the schemes only requires basic operations. For the physically important case of the BCS equations for a contact interaction potential, the computational cost of the schemes increases only linearly with the dimension of the space discretization. Their accuracy is demonstrated in extensive numerical experiments. These experiments also show that the physical energy of the system is preserve up to very small errors.