- Department of Physics
Technion - +972547592348
Joseph Avron
Technion Israel Institute of Technology, Physics, Faculty Member
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It is shown that the bands ( epsilon m(k) mod m=1,..., infinity ,k in (- pi , pi )) of one-dimensional Bloch Hamiltonians H=pn+V(x), n>or=2, V periodic, are uniquely determined by n-1 fibres ( epsilon m(ki) mod m=1,..., infinity ,... more
It is shown that the bands ( epsilon m(k) mod m=1,..., infinity ,k in (- pi , pi )) of one-dimensional Bloch Hamiltonians H=pn+V(x), n>or=2, V periodic, are uniquely determined by n-1 fibres ( epsilon m(ki) mod m=1,..., infinity , i=1,...,n-1). This extends known results on Hill's equation.
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The amazingly precise quantization of Hall conductance in a two-dimensional electron gas can be understood in terms of a topological invariant known as the Chern number.
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We define the relative index, Index(P,Q), for a pair of infinite-dimensional projections on a Hilbert space to be the integer that is the natural generalization of dim(P)-dim(Q) in finite-dimensional vector spaces. We show that the Hall... more
We define the relative index, Index(P,Q), for a pair of infinite-dimensional projections on a Hilbert space to be the integer that is the natural generalization of dim(P)-dim(Q) in finite-dimensional vector spaces. We show that the Hall conductance for independent electrons in the plane is the relative index where P and Q project on the states below the Fermi energy for
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It is shown that the integers found by Thouless et al. in the quantized Hall effect are the only quantized quantities associated with the energy bands. It is also proved that if two bands touch and then come apart as a parameter is... more
It is shown that the integers found by Thouless et al. in the quantized Hall effect are the only quantized quantities associated with the energy bands. It is also proved that if two bands touch and then come apart as a parameter is varied, then their individual integers (conductances) may ...
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ABSTRACT We describe a precise mathematical theory of the Laughlin argument for the quantization of the Hall conductance for general multiparticle Schrödinger operators with general background potentials. The quantization is a consequence... more
ABSTRACT We describe a precise mathematical theory of the Laughlin argument for the quantization of the Hall conductance for general multiparticle Schrödinger operators with general background potentials. The quantization is a consequence of the geometric content of the conductance, namely, that it can be identified with an integral over the first Chern class. This generalizes ideas of Thouless et al. for noninteracting Bloch Hamiltonians to general (interacting and nonperiodic) ones.