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We consider three one-dimensional quantum, charged and spinless particles interacting through delta potentials. We derive
sufficient conditions which guarantee the existence of at least one bound state. 相似文献
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Horia D. Cornean 《Annales Henri Poincare》2010,11(5):973-990
We show for a large class of discrete Harper-like and continuous magnetic Schrödinger operators that their band edges are Lipschitz continuous with respect to the intensity of the external constant magnetic field. We generalize a result obtained by Bellissard (Commun Math Phys 160:599–613, 1994), and give examples in favor of a recent conjecture of G. Nenciu. 相似文献
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François Bentosela Horia D. Cornean Bernard H. Fleury Nicola Marchetti 《Mathematical Methods in the Applied Sciences》2011,34(8):963-976
We develop a deterministic ab initio model for the input–output relationship of a multiple‐input multiple‐output (MIMO) wireless channel, starting from the Maxwell equations combined with Ohm's law. The main technical tools are scattering and geometric perturbation theories. The derived relationship can lead us to a deep understanding of how the propagation conditions and the coupling effects between the elements of multiple‐element arrays affect the properties of an MIMO channel, e.g. its capacity and its number of degrees of freedom. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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We give a constructive proof for the existence of a Bloch basis of rank \({N}\) which is both smooth (real analytic) and periodic with respect to its \({d}\)-dimensional quasi-momenta, when \({1\leq d\leq 2}\) and \({N\geq 1}\). The constructed Bloch basis is conjugation symmetric when the underlying projection has this symmetry, hence the corresponding exponentially localized composite Wannier functions are real. In the second part of the paper, we show that by adding a weak, globally bounded but not necessarily constant magnetic field, the existence of a localized basis is preserved. 相似文献
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We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch
electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the
Landau-Peierls formula in the low temperature and density limit as conjectured by Kjeldaas and Kohn (Phys Rev 105:806–813,
1957). 相似文献
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Horia D. Cornean 《Communications in Mathematical Physics》2000,212(1):1-27
Consider a charged Bose gas without self-interactions, confined in a three dimensional cubic box of side L S 1 and subjected to a constant magnetic field B p 0. If the bulk density of particles A and the temperature T are fixed, then define the canonical magnetization as the partial derivative with respect to B of the reduced free energy. Our main result is that it admits thermodynamic limit for all strictly positive A, T and B. It is also proven that the canonical and grand canonical magnetizations (the last one at fixed average density) are equal up to the surface order corrections. 相似文献
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This paper is the second in a series revisiting the (effect of) Faraday rotation. We formulate and prove the thermodynamic limit for the transverse electric conductivity of Bloch electrons, as well as for the Verdet constant. The main mathematical tool is a regularized magnetic and geometric perturbation theory combined with elliptic regularity and Agmon-Combes-Thomas uniform exponential decay estimates. 相似文献