Lieb-thirring Inequality for the Aharonov-bohm Hamiltonian and Eigenvalue Estimates
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منابع مشابه
Negative Discrete Spectrum of Perturbed Multivortex Aharonov-bohm Hamiltonians
The diamagnetic inequality is established for the Schrödinger operator H 0 in L (R), d = 2, 3, describing a particle moving in a magnetic field generated by finitely or infinitely many Aharonov-Bohm solenoids located at the points of a discrete set in R, e.g., a lattice. This fact is used to prove the Lieb-Thirring inequality as well as CLR-type eigenvalue estimates for the perturbed Schrödinge...
متن کاملSpectral Properties of Perturbed Multivortex Aharonov-bohm Hamiltonians
The diamagnetic inequality is established for the Schrödinger operator H 0 in L (R), d = 2, 3, describing a particle moving in a magnetic field generated by finitely or infinitely many Aharonov-Bohm solenoids located at the points of a discrete set in R, e.g., a lattice. This fact is used to prove the Lieb-Thirring inequality as well as CLR-type eigenvalue estimates for the perturbed Schrödinge...
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We present an overview over recent results concerning semi-classical spectral estimates for magnetic Schrödinger operators. We discuss how the constants in magnetic and non-magnetic eigenvalue bounds are related and we prove, in an abstract setting, that any non-magnetic Lieb-Thirring-type inequality implies a magnetic Lieb-Thirring-type inequality with possibly a larger constant.
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We show that the Aharonov-Bohm Hamiltonian considered on a disc has a four-parameter family of self-adjoint extensions. Among the infinitely many self-adjoint extensions, we determine to which parameters the Friedrichs extension HF corresponds and its lowest eigenvalue is found. Moreover, we note that the diamagnetic inequality holds for HF .
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تاریخ انتشار 2002