Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
نویسندگان
چکیده
Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complexvalued potential. Work partially supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT). Work partially supported by U.S. National Science Foundation grant PHY 01 39984. Work partially supported by U.S. National Science Foundation grant PHY 03 53181, and by an A.P. Sloan Fellowship. c © 2006 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.
منابع مشابه
Spectral Inequalities for Schrödinger Operators with Surface Potentials
We prove sharp Lieb-Thirring inequalities for Schrödinger operators with potentials supported on a hyperplane and we show how these estimates are related to LiebThirring inequalities for relativistic Schrödinger operators.
متن کاملConnection between the Lieb–Thirring conjecture for Schrödinger operators and an isoperimetric problem for ovals on the plane
To determine the sharp constants for the one dimensional Lieb– Thirring inequalities with exponent γ ∈ (1/2, 3/2) is still an open problem. According to a conjecture by Lieb and Thirring the sharp constant for these exponents should be attained by potentials having only one bound state. Here we exhibit a connection between the Lieb–Thirring conjecture for γ = 1 and an isporimetric inequality fo...
متن کاملLieb-Thirring type inequalities for non-selfadjoint perturbations of magnetic Schrödinger operators
Let H := H0 + V and H⊥ := H0,⊥ + V be respectively perturbations of the free Schrödinger operators H0 on L2 ( R2d+1 ) and H0,⊥ on L2 ( R2d ) , d ≥ 1 with constant magnetic field of strength b > 0, and V is a complex relatively compact perturbation. We prove Lieb-Thirring type inequalities for the discrete spectrum ofH andH⊥. In particular, these estimates give a priori information on the distri...
متن کاملHardy-lieb-thirring Inequalities for Fractional Schrödinger Operators
We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schrödinger-like operators remain true, with possibly different constants, when the critical Hardy-weight C|x|−2 is subtracted from the Laplace operator. We do so by first establishing a Sobolev inequality for such operators. Similar results are true for fractional powers of the Laplacian and the Hardy-weight and,...
متن کاملLieb-Thirring inequalities with improved constants
where V+ = (|V |+ V )/2 is the positive part of V . Eden and Foias have obtained in [3] a version of a one-dimensional generalised Sobolev inequality which gives best known estimates for the constants in the inequality (2) for 1 ≤ γ < 3/2. The aim of this short article is to extend the method from [3] to a class of matrix-valued potentials. By using ideas from [6] this automatically improves on...
متن کامل