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A comprehensive proof of localization for continuous Anderson models with singular random potentials

François Germinet, Abel Klein (2013)

Journal of the European Mathematical Society

We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution),...

A Lieb-Thirring bound for a magnetic Pauli Hamiltonian (II).

Luca Bugliaro, Charles L. Fefferman, Gian Michele Graf (1999)

Revista Matemática Iberoamericana

We establish a Lieb-Thirring type estimate for Pauli Hamiltonians with non-homogeneous magnetic fields. Besides of depending on the size of the field, the bound also takes into account the size of the field gradient. We then apply the inequality to prove stability of non-relativistic quantum mechanical matter coupled to the quantized ultraviolet-cutoff electromagnetic field for arbitrary values of the fine structure constant.

A numerically efficient approach to the modelling of double-Qdot channels

A. Shamloo, A.P. Sowa (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

We consider the electronic properties of a system consisting of two quantum dots in physical proximity, which we will refer to as the double-Qdot. Double-Qdots are attractive in light of their potential application to spin-based quantum computing and other electronic applications, e.g. as specialized sensors. Our main goal is to derive the essential properties of the double-Qdot from a model that is rigorous yet numerically tractable, and largely circumvents the complexities of an ab initio simulation....

A Two-Particle Quantum System with Zero-Range Interaction

Michele Correggi (2008/2009)

Séminaire Équations aux dérivées partielles

We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.

An Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups

Z. Gan (2010)

Mathematical Modelling of Natural Phenomena

We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some recent results on Schrödinger operators obtained in this...

Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields

Akira Iwatsuka, Hideo Tamura (1998)

Annales de l'institut Fourier

This article studies the asymptotic behavior of the number N ( λ ) of the negative eigenvalues < - λ as λ → + 0 of the two dimensional Pauli operators with electric potential V ( x ) decaying at ∞ and with nonconstant magnetic field b ( x ) , which is assumed to be bounded or to decay at ∞ . In particular, it is shown that N ( λ ) = ( 1 / 2 π ) ∫ V ( x ) > λ b ( x ) d x ( 1 + o ( 1 ) ) , when V ( x ) decays faster than b ( x ) under some additional conditions.

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