The Heat Kernel Coefficients to the Matrix Schr\"odinger Operator

TL;DR

This paper develops algorithms and explicit formulas for calculating heat kernel coefficients of matrix Schrödinger operators, with special focus on one-dimensional cases and improved computational methods.

Contribution

It introduces new algorithms and explicit expressions for heat kernel coefficients of matrix Schrödinger operators, including enhancements for one-dimensional cases.

Findings

Derived explicit formulas for heat kernel coefficients.

Developed algorithms for Taylor coefficients of $H_k$.

Provided improved computational methods for 1D cases.

Abstract

The heat kernel coefficients $H_k$ to the Schr\"odinger operator with a matrix potential are investigated. We present algorithms and explicit expressions for the Taylor coefficients of the $H_k$. Special terms are discussed, and for the one-dimensional case some improved algorithms are derived.