Diagonalisation of quantum observables on regular lattices and general graphs

Diagonalisation of quantum observables on regular lattices and general graphs

Quantum Walks on Regular Graphs and Eigenvalues

We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of S+(U3), a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We find the eigenvalues of S+(U) and S+(U2) for regular graphs and show that S+(U2) = S+(U)2 + I.

Regular quantum graphs

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way incoming and outgoing channels at vertex scattering processes are connected. Symmetry properties of the quantum graph as well as its spectral statistics depend o...

Lattices associated with distance-regular graphs

Let L be a finite set associated with cliques of a distance-regular graph of order (s, t), with d-cliques of Johnson graphs and antipodal distance-regular graphs of diameter d, respectively. If we partially order L by the ordinary inclusion, three families of finite atomic lattices are obtained. This article discusses their geometricity, and computes their characteristic polynomials. c © 2007 E...

Quantum transport on two-dimensional regular graphs

Abstract. We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem can be treated in a large measure analytically. Some of these results carry over to graphs which obey open boundary conditions (OBCs), such as cylind...