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Colored Hofstadter butterflies
J. E. Avron
I explain the two colored butterflies shown in figures 1 and 4, their thermodynamic significance and their duality.
Topological quantum numbers in the Hall effect
J. E. Avron, D. Osadchy, R. Seiler
Topological quantum numbers account for the precise quantization that occurs in the integer Hall effect. In this theory, Kubo's formula for the conductance acquires a topological i…
Adiabatic charge pumping in open quantum systems
J. E. Avron, A. Elgart, G. M. Graf +2
We introduce a mathematical setup for charge transport in quantum pump connected to a number of external leads. It is proved that under rather general assumption on the Hamiltonian…
Butterflies and topological quantum numbers
J. E. Avron, D. Osadchy
The Hofstadter model illustrates the notion of topological quantum numbers and how they account for the quantization of the Hall conductance. It gives rise to colorful fractal diag…
Generic Jumps of Fredholm Indices and the Quantum Hall Effect
Joseph E. Avron, Lorenzo Sadun
We describe the generic behavior of Fredholm indices in the space of Toeplitz operators. We relate this behavior to certain conjectures and open problems that arise in the context…
An Adiabatic Theorem without a Gap Condition
J. E. Avron, A. Elgart
The basic adiabatic theorems of classical and quantum mechanics are over-viewed and an adiabatic theorem in quantum mechanics without a gap condition is described.