A quantum particle on a general discrete structure with a local external potential is described by a generalized tight-binding Hamiltonian on a graph. Here, we show that this model can be naturally mapped on a classical statistical model (the Gaussian model) on the same graph. This equivalence provides not only a powerful technical tool for model solving, but it also puts into evidence general fundamental properties of quantum inhomogeneous systems.
Quantum particles and Gaussian model on graphs
Vezzani A
2000
Abstract
A quantum particle on a general discrete structure with a local external potential is described by a generalized tight-binding Hamiltonian on a graph. Here, we show that this model can be naturally mapped on a classical statistical model (the Gaussian model) on the same graph. This equivalence provides not only a powerful technical tool for model solving, but it also puts into evidence general fundamental properties of quantum inhomogeneous systems.File in questo prodotto:
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