Complex networks and graphs provide a general description of a great variety of inhomogeneous discrete systems. These range from polymers and biomolecules to complex quantum devices, such as arrays of Josephson junctions, microbridges, and quantum wires. We introduce a technique, based on the analysis of the motion of a random walker, that allows us to determine the density of states of a general local Hamiltonian on a graph, when the potential differs from zero on a finite number of sites. We study in detail the case of the comb lattice and we derive an analytic expression for the elements of the resolvent operator of the Hamiltonian, giving its complete spectrum.
Localized states on comb lattices
Baldi G;
2004
Abstract
Complex networks and graphs provide a general description of a great variety of inhomogeneous discrete systems. These range from polymers and biomolecules to complex quantum devices, such as arrays of Josephson junctions, microbridges, and quantum wires. We introduce a technique, based on the analysis of the motion of a random walker, that allows us to determine the density of states of a general local Hamiltonian on a graph, when the potential differs from zero on a finite number of sites. We study in detail the case of the comb lattice and we derive an analytic expression for the elements of the resolvent operator of the Hamiltonian, giving its complete spectrum.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
