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- W H Aschbacher, J Frr, Gregory Graf, Kai Schnee, Melissa Troyer
- 2001

The present paper is concerned with minimizers of the Hartree energy functional H g ; ] = 1 2 krk 2 2 + (; v) 2 + g(; V jj 2) 2 with g < 0 on the connguration space R d , d 2, for a general class ofâ€¦ (More)

- C. Buchendorfer, Gregory Graf
- 2006

We consider a charged particle following the boundary of a two-dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantumâ€¦ (More)

We introduce a mathematical setup for charge transport in quantum pumps connected to a number of external leads. It is proved that under rather general assumption on the Hamiltonian describing theâ€¦ (More)

We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, whenâ€¦ (More)

- J. E. Avron, Anna Elgart, Gregory Graf, L. Sadun
- Physical review letters
- 2001

We study adiabatic quantum pumps on time scales that are short relative to the cycle of the pump. In this regime the pump is characterized by the matrix of energy shift which we introduce as the dualâ€¦ (More)

Using operator algebraic methods we show that the moment generating function of charge transport in a system with infinitely many non-interacting Fermions is given by a determinant of a certainâ€¦ (More)

- Charles Fefferman, J. FrÃ¶hlich, Gregory Graf
- Proceedings of the National Academy of Sciencesâ€¦
- 1996

We announce a proof of H-stability for the quantized radiation field, with ultraviolet cutoff, coupled to arbitrarily many non-relativistic quantized electrons and static nuclei. Our result holds forâ€¦ (More)

Coherent states in the time-energy plane provide a natural basis to study adiabatic scattering. We relate the (diagonal) matrix elements of the scattering matrix in this basis with the frozenâ€¦ (More)

- Gregory Graf, M. Porta
- 2012

Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particleâ€¦ (More)

Using operator algebraic methods we show that the moment generating function of charge transport in a system with infinitely many non-interacting Fermions is given by a determinant of a certainâ€¦ (More)