Strong-electric-field eigenvalue asymptotics for the Iwatsuka model

Journal Article · Sun May 01 04:00:00 EDT 2005 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.1897844· OSTI ID:20699169

Shirai, Shin-ichi ^[1]

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1. Research Institute for Mathematical Sciences, Kyoto University, Sakyo, Kyoto 606-8502 (Japan)

We consider the two-dimensional Schroedinger operator, H{sub g}(b)=-{partial_derivative}{sup 2}/{partial_derivative}x{sup 2}+[(1/{radical}(-1))({partial_derivative}/{partial_derivative}y)-b(x)]{sup 2}-gV(x,y), where V is a non-negative scalar potential decaying at infinity like (1+ vertical bar x vertical bar + vertical bar y vertical bar ){sup -m}, and (0,b(x)) is a magnetic vector potential. Here, b is of the form b(x)={integral}{sub 0}{sup x}B(t)dt and the magnetic field B is assumed to be positive, bounded, and monotonically increasing on R (the Iwatsuka model). Following the argument as in Refs. 15, 16, and 17 [Raikov, G. D., Lett. Math. Phys., 21, 41-49 (1991); Raikov, G. D, Commun. Math. Phys., 155, 415-428 (1993); Raikov, G. D. Asymptotic Anal., 16, 87-89 (1998)], we obtain the asymptotics of the number of discrete spectra of H{sub g}(b) crossing a real number {lambda} in the gap of the essential spectrum as the coupling constant g tends to {+-}{infinity}, respectively.

• OSTI ID: 20699169
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 5 Vol. 46; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COUPLING CONSTANTS
EIGENVALUES
ELECTRIC FIELDS
ELECTROMAGNETIC FIELDS
MAGNETIC FIELDS
MATHEMATICAL OPERATORS
POTENTIALS
SCALARS
SCHROEDINGER EQUATION
TWO-DIMENSIONAL CALCULATIONS
VECTORS