The effects of a magnetic field on asymptotics of the trace of the heat kernel. (English) Zbl 0657.46028
Author’s summary: This paper looks at the effect of a uniform magnetic field on the trace of the heat kernel for a Schrödinger operator with a well type poential. Using weighted Sobolev space techniques and noticing the gauge invariance of the perturbation, I show that the magnetic field first appears at a higher term in the small time asymptotic expansion of the trace of the heat kernel than might be naively expected.
Reviewer: J.Włoka
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 47Gxx | Integral, integro-differential, and pseudodifferential operators |
Keywords:
uniform magnetic field on the trace of the heat kernel for a Schrödinger operator with a well type poential; weighted Sobolev space; gauge invarianceReferences:
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