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On Mott’s formula for the acconductivity in the Anderson model
"... Olivier Lenoble, and Peter Müller* We study the acconductivity in linear response theory in the general framework of ergodic magnetic Schrödinger operators. For the Anderson model, if the Fermi energy lies in the localization regime, we prove that the acconductivity is bounded from above by Cν 2 ( ..."
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Olivier Lenoble, and Peter Müller* We study the acconductivity in linear response theory in the general framework of ergodic magnetic Schrödinger operators. For the Anderson model, if the Fermi energy lies in the localization regime, we prove that the acconductivity is bounded from above by Cν 2 (log 1 ν)d+2 at small frequencies ν. This is to be compared to Mott’s formula, which predicts the leading term to be Cν 2 (log 1 ν)d+1.
Contribution à la théorie mathématique du transport quantique dans les systèmes de Hall
, 2011
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Quantum transport in disordered systems under magnetic fields: a study based on operator algebra
, 2013
"... Abstract: The linear conductivity tensor for generic homogeneous, microscopic quantum models was formulated as a noncommutative Kubo formula in Refs. [6, 53, 54]. This formula was derived directly in the thermodynamic limit, within the framework of C∗algebras and noncommutative calculi defined over ..."
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Abstract: The linear conductivity tensor for generic homogeneous, microscopic quantum models was formulated as a noncommutative Kubo formula in Refs. [6, 53, 54]. This formula was derived directly in the thermodynamic limit, within the framework of C∗algebras and noncommutative calculi defined over infinite spaces. As such, the numerical implementation of the formalism encountered fundamental obstacles. The present work defines a C∗algebra and an approximate noncommutative calculus over a finite realspace torus, which naturally leads to an approximate finitevolume noncommutative Kubo formula, amenable on a computer. For finite temperatures and dissipation, it is shown that this approximate formula converges exponentially fast to its thermodynamic limit, which is the exact noncommutative Kubo formula. The approximate noncommutative Kubo formula is then deconstructed to a form that is implementable on a computer and simulations of the quantum transport in a 2dimensional disordered lattice gas in a magnetic field are presented.
The Landauer resistivity on quantum wires
, 2002
"... We study the Landauer resistivity of the KronigPenney model which has various behavior depending on the potential and the Fermi energy. In the case of the Sturmian quasiperiodic potential, we discuss examples in which lim inf of it is zero. ..."
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We study the Landauer resistivity of the KronigPenney model which has various behavior depending on the potential and the Fermi energy. In the case of the Sturmian quasiperiodic potential, we discuss examples in which lim inf of it is zero.