Heat kernel asymptotics for magnetic Schr\"odinger operators

TL;DR

This paper develops explicit parametrices for magnetic Schrödinger operators on R^d, enabling a detailed small-time expansion of their heat kernels both on and off the diagonal, advancing understanding of their spectral properties.

Contribution

It introduces explicit constructions of parametrices for magnetic Schrödinger operators, providing comprehensive small-time heat kernel asymptotics.

Findings

Complete small-t heat kernel expansion on and off the diagonal.

Explicit parametrix constructions for magnetic Schrödinger operators.

Enhanced understanding of spectral and geometric properties.

Abstract

We explicitly construct parametrices for magnetic Schr\"odinger operators on R^d and prove that they provide a complete small-t expansion for the corresponding heat kernel, both on and off the diagonal.