Anderson localization in the nondiscrete Maryland model

Journal Article · Sat Aug 01 04:00:00 EDT 1987 · Theor. Math. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01039202· OSTI ID:5828643

Geiler, V A; Margulis, V A

A study is made of a Schroedinger operator H = H/sub 0/ + V, where V is an almost periodic point potential and the Hamiltonian H/sub 0/ is subject to certain conditions that are satisfied, in particular, by two- and three-dimensional operators of the form H/sub 0/ = -..delta.. and H/sub 0/ = (idel-A)/sup 2/, where A is the vector potential of a homogeneous magnetic field. It is shown that under certain conditions of incommensurability for V the forbidden gaps of H/sub 0/ are densely filled by nondegenerate localized states of the operator H; the form of the corresponding eigenfunctions is found.

• Research Organization: Mordovian State Univ., USSR
• OSTI ID: 5828643
• Journal Information: Theor. Math. Phys.; (United States), Journal Name: Theor. Math. Phys.; (United States) Vol. 70:2; ISSN TMPHA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
BAND THEORY
CANONICAL TRANSFORMATIONS
COUPLING CONSTANTS
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
ELECTRONS
ELEMENTARY PARTICLES
ENERGY GAP
ENERGY-LEVEL TRANSITIONS
EQUATIONS
FERMIONS
FIELD THEORIES
FORBIDDEN TRANSITIONS
FUNCTIONS
HALL EFFECT
HAMILTONIANS
HILBERT SPACE
LEPTONS
LOCALITY
MAGNETIC FIELDS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATRICES
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
SPACE
TENSORS
TRANSFORMATIONS
VECTORS
WAVE EQUATIONS