Bounds on the discrete spectrum of lattice Schrodinger operators

Autor(es)

Bach, V. ^[1] ; de Siqueira Pedra, W. ^[2] ; Lakaev, S. N. ^[3]

Afiliação do(s) autor(es)

^[1] TU Braunschweig, Inst Anal & Algebra, D-38106 Braunschweig - Germany

^[2] Univ Sao Paulo, IF Inst Fis, Sao Paulo - Brazil

^[3] Samarkand State Univ, Samarkand - Uzbekistan

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 59, n. 2 FEB 2018.
• Citações Web of Science: 2

Resumo

We discuss the validity of the Weyl asymptotics-in the sense of two-sided bounds-for the size of the discrete spectrum of (discrete) Schrodinger operators on the d-dimensional, d >= 1, cubic lattice Z(d) at large couplings. We show that the Weyl asymptotics can be violated in any spatial dimension d >= 1-even if the semi-classical number of bound states is finite. Furthermore, we prove for all dimensions d >= 1 that, for potentials well behaved at infinity and fulfilling suitable decay conditions, the Weyl asymptotics always hold. These decay conditions are mild in the case d >= 3 while stronger for d = 1, 2. It is well known that the semi-classical number of bound states is-up to a constant-always an upper bound on the size of the discrete spectrum of Schrodinger operators if d >= 3. We show here how to construct general upper bounds on the number of bound states of Schrodinger operators on Z(d) from semi-classical quantities in all space dimensions d >= 1 and independently of the positivity-improving property of the free Hamiltonian. Published by AIP Publishing. (AU)

• Processo FAPESP: 16/02503-8 - Comportamento macroscópico de sistemas de férmions não relativísticos interagentes
• Beneficiário: Walter Alberto de Siqueira Pedra
• Modalidade de apoio: Bolsas no Exterior - Pesquisa