Heat kernel estimates for two-dimensional relativistic Hamiltonians with magnetic field

TL;DR

This paper investigates heat kernel estimates for two-dimensional relativistic Hamiltonians with magnetic fields, analyzing how the heat kernel's long-term behavior depends on magnetic flux, including Aharonov-Bohm fields.

Contribution

It provides new insights into the heat kernel behavior for relativistic Hamiltonians with specific magnetic fields, highlighting flux dependence.

Findings

Heat kernel behavior depends on magnetic flux for compactly supported radial fields.

Long-term heat kernel estimates are derived for Aharonov-Bohm magnetic fields.

Results connect magnetic flux with heat kernel decay properties.

Abstract

We study semigroups generated by two-dimensional relativistic Hamiltonians with magnetic field. In particular, for compactly supported radial magnetic field we show how the long time behaviour of the associated heat kernel depends on the flux of the field. Similar questions are addressed for Aharonov-Bohm type magnetic field.