Fano-Anderson

The diabatic two-state representation for homogeneous CT can be extended to heterogeneous CT processes between a reactant in a condensed-phase solvent and a metal electrode. The system Hamiltonian is then given by the Fano-Anderson model" " " ... 

S. Longhi, Bound states in the continuum in a single-level Fano-Anderson model, Eur. Phys. J. B 57 (2007) 45. 

J. MartoreU, D.W.L. Sprung, W. van Dijk, J.G. Muga, Memory effects induced by initial switching conditions in a Fano-Anderson model, Phys. Rev A 79 (2009) 062104. 

There is a particular class of problems that quantum computers have difficult for simulating. Those are ones which deal with interactions of Fermionic systems. Negrevergne et al. [25] describe a NMR quantum simulation of a many-body problem, the so-called Fano-Anderson model. It consists of an n-sites ring containing an impurity atom at the center. In this system, an electron can hop either between the nearest neighbor sites, at the ring... 

There are but few models of irreversibility which can be solved exactly. Such a model was originally introduced by Ref. [Friedrichs 1948] but it also goes under the name the Fano model, [Fano 1961 Cohen-Tannoudji 1992], It offers the theory of a single quantum state imbedded in a continuum or a quasi-continuum. It has been used in molecular physics as the Bixon-Jortner model [Bixon 1968] and in solid state physics as an Anderson model [Anderson 1961]. 

Other variants are due to Fano [76], Anderson [77], Lee [78], and Friedrichs [79] and have been successfully applied to study, for example, autoionization, photon emission, or cavities coupled to waveguides. The dynamics can be solved in several ways, using coupled differential equations for the time-dependent amplitudes and Laplace transforms or finding the eigenstates with Feshbach s (P,Q) projector formalism [80], which allows separation of the inner (discrete) and outer (continuum) spaces and provides explicit expressions ready for exact calculation or phenomenological approaches. For modern treatments with emphasis on decay, see Refs. [31, 81]. Writing the eigenvector as [31, 76]... 

The interactions between a localized vibrational state with the host elastic continuum can be described by the perturbation theory of Fano or in an equivalent way, with the second quantization field theoretical method of Anderson. The Anderson-Fano Hamiltonian appropriate for xenon hydrate is ... 

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