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An Isaac Newton Institute Workshop

Graph Models of Mesoscopic Systems, Wave-Guides and Nano-Structures

Excitonic influence on transport coefficients in low dimensional quantum systems

Author: H. Cornean (Aalborg University)

Abstract

This is joint work with P. Duclos and B. Ricaud. Consider a many-body fermionic Hamiltonian defined with periodic boundary conditions on a two dimensional torus (which models a very long and thin nano-ring). We will study the low lying spectrum of this operator, and show that in the Hartree-Fock approximation one can obtain effective one-particle models describing these particular states. Even though it sounds more physically oriented, the main purpose of this talk is to formulate clear mathematical problems related to PDEs, unbounded linear self-adjoint operators, and integral equations.