Infinitely many singular interactions on noncompact manifolds

Journal Article · Fri May 15 00:00:00 EDT 2015 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2015.03.016· OSTI ID:22451174

Kaynak, Burak Tevfik, E-mail: [e-mail]; Turgut, O. Teoman, E-mail: [e-mail]

We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional non-compact manifold. To facilitate the reading of the paper, we first present the arguments in the setting of Cartan–Hadamard manifolds and then subsequently discuss the general case. For this purpose, we employ the heat kernel techniques as well as some comparison theorems of Riemannian geometry, thus generalizing the arguments in the flat case following the approach presented in Albeverio et al. (2004). - Highlights: • Schrödinger-operator for infinitely many singular interactions on noncompact manifolds. • Proof of the finiteness of the ground-state energy.

• OSTI ID: 22451174
• Journal Information: Annals of Physics, Vol. 356; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
DELTA FUNCTION
GEOMETRY
GROUND STATES
KERNELS
MATHEMATICAL MANIFOLDS
RIEMANN SPACE
TWO-DIMENSIONAL CALCULATIONS