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We study the perturbation of bound states embedded in the continuous spectrum which are unstable by the Fermi Golden Rule. The approach to resonance theory based on spectral deformation is extended to a more general class of quantum systems characterized by Mourreâ€™s inequality and smoothness of the resolvent. Within the framework of perturbation theory itâ€¦ (More)

- Gian Michele Graf, Jan Philip Solovej
- 1993

We consider some two-body operators acting on a Fock space with either fermionic or no statistics. We prove that they are bounded below by one-body operators which mimic exchange eeects. This allows us to compare two-body correlations of fermionic and bosonic systems with those in Hartree-Fock, respectively Hartree theory. Applications of the fermionicâ€¦ (More)

- W H Aschbacher, J Frr, Gian Michele Graf, Kai Schnee, Matthias 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 of external potentials v and two-body potentials V. We prove that a minimizer does not have the symmetry properties of the potential v for jgj strictly larger thanâ€¦ (More)

- C. Buchendorfer, Gian Michele 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 quantum mechanical edge states. The scattering phase attains a limit for large magnetic fields which we interpret in terms of classical trajectories.

- Charles Fe erman, Gian Michele Graf
- 1996

QUANTUM ELECTRODYNAMICS WITH NON-RELATIVISTIC MATTER Charles Fe erman Department of Mathematics, Fine Hall Princeton University Princeton, New Jersey 08544 J urg Frohlich and Gian Michele Graf Theoretical Physics ETH-H onggerberg CH{8093 Z urich Abstract We prove that the quantum-mechanical ground state energy of a system consisting of an arbitraryâ€¦ (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 the system, in the adiabatic limit, the current through the pump is given by a formula of BÃ¼ttiker, PrÃªtre, and Thomas, relating it to the frozen S-matrix and itsâ€¦ (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, when appropriately defined. An appropriate definition of the edge conductance may be obtained through a suitable time averaging procedure or by including aâ€¦ (More)

- Joseph E. Avron, Alex Elgart, Gian Michele Graf, Lorenzo 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 dual to Wigner's time delay. The energy shift determines the charge transport, the dissipation, the noise, and the entropy production. We prove a general lowerâ€¦ (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 certain operator in the one-particle Hilbert space. The formula is equivalent to a formula of Levitov and Lesovik in the finite dimensional case and may be viewed as itsâ€¦ (More)

- Charles Fefferman, Juerg Froehlich, Gian Michele 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 for arbitrary atomic numbers and fine structure constant. We also announce bounds for the energy of many electrons and nuclei in a classical vector potential andâ€¦ (More)