The effect of local phases of wave function on transmission of a quantum particle through two dimensional clusters

We investigate the relationship between the transport properties ofordered and disordered two dimensional quantum percolation systemsand the spatial variations of the phase of the wave function. Whileoften only the spatial variations of the probability amplitudes arestudied in relation to localization and transport properties, ourstudy illustrates how crucial a role the phase variation plays. Ourinvestigation based on many different energies of the incidentparticle over the entire accessible range suggests that systems withmany neighboring sites with phase differences of ~π turn outto be those with minimal transmission, even if the probabilityamplitudes alone appear to suggest high transmission, whereas thosewith neighboring sites with ~2π, zero or small phasedifferences typically lead to high transmission. By calculatingassociated momentum distribution of the states we have shown that alow(high) transmitting state results from the equal(unequal)contribution from +<InlineEquation ID="IEq1"> <EquationSource Format="TEX"> $\overrightarrow{k}$ </EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX"> $-\overrightarrow{k}$ </EquationSource> </InlineEquation> fouriercomponents. We have alsoexplored the effect of replacing diluted sites in percolation bythose with couplings that are non-zero but smaller than the onebetween undiluted sites (thus introducing finite couplinginhomogeneities instead of infinite barriers), and found that theresulting transmission can be higher or lower compared with the casewith dilution (normal, infinite barriers). Furthermore, it can behigher or lower even compared with the ordered case (uniformcouplings). Copyright Springer 2008