An Improved Combes-Thomas Estimate of Magnetic Schr\"{o}dinger Operators

TL;DR

This paper improves the Combes-Thomas estimate for magnetic Schrödinger operators, allowing unbounded potentials and showing rapid decay of operator kernels in trace-class norms for Schwartz functions.

Contribution

It provides an enhanced trace-class Combes-Thomas estimate for magnetic Schrödinger operators, extending applicability to unbounded potentials and demonstrating faster decay of kernels.

Findings

Trace-class Combes-Thomas estimate is improved.

Operator kernels decay faster than any polynomial for Schwartz functions.

Results apply to magnetic Schrödinger operators with unbounded potentials.

Abstract

In the present paper, we prove an improved Combes-Thomas estimate, i.e., the Combes-Thomas estimate in trace-class norms, for magnetic Schr\"{o}dinger operators under general assumptions. In particular, we allow unbounded potentials. We also show that for any function in the Schwartz space on the reals the operator kernel decays, in trace-class norms, faster than any polynomial.