Eur. Phys. J. B 65, 555-564 (2008)
https://doi.org/10.1140/epjb/e2008-00363-x

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

Department of Physics, Purdue University, West Lafayette, IN, 47907, USA

Corresponding author: ^a islamm@uta.edu

Received: 27 August 2007
Revised: 13 June 2008
Published online: 25 September 2008

Abstract

We investigate the relationship between the transport properties of ordered and disordered two dimensional quantum percolation systems and the spatial variations of the phase of the wave function. While often only the spatial variations of the probability amplitudes are studied in relation to localization and transport properties, our study illustrates how crucial a role the phase variation plays. Our investigation based on many different energies of the incident particle over the entire accessible range suggests that systems with many neighboring sites with phase differences of ~π turn out to be those with minimal transmission, even if the probability amplitudes alone appear to suggest high transmission, whereas those with neighboring sites with ~2π, zero or small phase differences typically lead to high transmission. By calculating associated momentum distribution of the states we have shown that a low(high) transmitting state results from the equal(unequal) contribution from + and fourier components. We have also explored the effect of replacing diluted sites in percolation by those with couplings that are non-zero but smaller than the one between undiluted sites (thus introducing finite coupling inhomogeneities instead of infinite barriers), and found that the resulting transmission can be higher or lower compared with the case with dilution (normal, infinite barriers). Furthermore, it can be higher or lower even compared with the ordered case (uniform couplings).