On Moments of Negative Eigenvalues for the Pauli Operator

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This paper concerns the three-dimensional Pauli operator ℙ=(ยท(p-A(x)))2+< B>V(x) with a nonhomogeneous magnetic field B=curl A. The following Lieb–Thirring type inequality for the moment of negative eigenvalues is established as ∑j<0 |j|C13 |V(x)|5/2- dx+C23 [bp(x)]3/2 |V(x)|- dx,where p>3/2 and bp(x) is the Lp average of |B| over certain cube centered at x with a side length scaling like |B|-1/2. We also show that, if B has a constant direction, ∑j<0 |j|C1, 3 |V(x)|+3/2- dx+C2, 3 bp(x) |V(x)|+1/2- dx,where >1/2 and p>1. Copyright 1998 Academic Press.

Document Type: Research Article

Affiliations: Department of Mathematics, University of Kentucky, Lexington, Kentucky, 40506

Publication date: November 1, 1998

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