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Quantum scattering in the strip from ballistic to localized regimes
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QUANTUM SCATTERING IN THE STRIP:
FROM BALLISTIC TO LOCALIZED REGIMES
Robert Ge?barowski1?, Petr S?eba2,3, Karol Z?yczkowski4?, and Jakub Zakrzewski5
1Instytut Fizyki, Politechnika Krakowska im. Tadeusza Kos?ciuszki,
ul. Podchora?z?ych 1, 30–084 Krako?w, Poland.
2 Nuclear Physics Institute, Czech Academy of Sciences,
250 68 R?ez? near Prague, Czech Republic
3 Pedagogical University, Hradec Kra?love?, Czech Republic
4 Institute for Plasma Research, University of Maryland,
College Park, MD 20742, USA
5Instytut Fizyki im. Mariana Smoluchowskiego, Uniwersytet Jagiellon?ski,
ul. Reymonta 4, 30-059 Krako?w, Poland
(February 1, 2008)
Abstract
Quantum scattering is studied in a system consisting of randomly distributed
point scatterers in the strip. The model is continuous yet exactly solvable.
Varying the number of scatterers (the sample length) we investigate a transi-
tion between the ballistic and the localized regimes. By considering the cylin-
der geometry and introducing the magnetic flux we are able to study time
reversal symmetry breaking in the system. Both macroscopic (conductance)
and microscopic (eigenphases distribution, statistics of S matrix elements)
characteristics of the system are examined.
72.20.Dp,05.45.+b,72.10.Bg.
Typeset using REVTEX
?Present address: Department of Applied Mathematics and Theoretical Physics, The Queen’s
University of Belfast, Belfast BT7 1NN, Northern Ireland
?Fulbright Fellow. Permanent address: Instytut Fizyki im. Mariana Smoluchowskiego, Uniwer-
sytet Jagiellon?ski, ul. Reymonta 4, 30-059 Krako?w, Poland
1
I. INTRODUCTION
A rapid technological progress in producing small semiconductor and metallic samples,
which have the size of the electron phase coherence length, has stimulated extensive inves-
tigations of transport through disordered mesoscopic systems [1,2]. Disorder in mesoscopic
nanostructures, like for example quan
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