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Semiclassical asymptotics of the ground state energy for the Neumann problem associated with superconductivity. (English) Zbl 1085.35119
Summary: We consider the Neumann-Schrödinger operator in a bounded domain in $$\mathbb{R}^2$$. In the case, where the corresponding magnetic field is nonconstant, we get the semiclassical asymptotics with lower order term of the first eigenvalue. This paper is an improvement of results of [B. Helffer and A. Morame, J. Funct. Anal. 185, No. 2, 604–680 (2001; Zbl 1078.81023)] in which they got the asymptotics for the constant magnetic field case.
Reviewer: Reviewer (Berlin)
##### MSC:
 35Q40 PDEs in connection with quantum mechanics 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 35P15 Estimates of eigenvalues in context of PDEs 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 82D55 Statistical mechanical studies of superconductors