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
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).
PACS: 64.60.ah – Percolation / 72.15.Rn – Localization effects (Anderson or weak localization) / 05.60.Gg – Quantum transport
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008