| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Journal of Mathematical Physics; v. 59, n. 2 FEB 2018. |
| Web of Science Citations: | 2 |
| Abstract | |
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) | |
| FAPESP's process: | 16/02503-8 - Macroscopic behavior of non-relativistic interacting many fermion systems |
| Grantee: | Walter Alberto de Siqueira Pedra |
| Support type: | Scholarships abroad - Research |