Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field

Details Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field

2006-04-10

arxiv.org/abs/quant-ph/0604068v2

Physics

Quantum Physics

some technical improvements, new references, to appear in Journ.Phys.A

Scientific paper

10.1088/0305-4470/39/31/019

We obtain lower and upper bounds on the heat kernel and Green functions of the Schroedinger operator in a random Gaussian magnetic field and a fixed scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic upper bounds and the Jensen inequality for the lower bound. We show that if the covariance of the electromagnetic (vector) potential is increasing at large distances then the lower bound is decreasing exponentially fast for large distances and a large time.

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