Anderson localization from classical trajectories

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Piet W. Brouwer
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA

Alexander Altland
Institut für Theoretische Physik, Zülpicher Strasse 77, 50937 Köln, Germany

Received 7 February 2008; revised 6 June 2008; published 5 August 2008

Weshow that Anderson localization in quasi-one-dimensional conductors with ballistic electrondynamics, such as an array of ballistic chaotic cavities connectedvia ballistic contacts, can be understood in terms of classicalelectron trajectories only. At large length scales, an exponential proliferationof trajectories of nearly identical classical action generates an abundanceof interference terms, which eventually leads to a suppression oftransport coefficients. We quantitatively describe this mechanism in two differentways: the explicit description of transition probabilities in terms ofinterfering trajectories, and an hierarchical integration over fluctuations in theclassical phase space of the array cavities.

URL:	http://link.aps.org/doi/10.1103/PhysRevB.78.075304
DOI:	10.1103/PhysRevB.78.075304
PACS:	05.45.Mt; 73.20.Fz; 73.23.-b 05.45.Mt Quantum chaos; semiclassical methods 73.20.Fz Weak or Anderson localization (surface/interface states) 73.23.-b Electronic transport in mesoscopic systems YEAR: 2008
KEYWORDS:	Anderson model, ballistic transport, chaos, phase space methods

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P. W. Anderson, Phys. Rev. 109, 1492 (1958).
E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
Exceptions to this rule include various one- and two-dimensional electron systems of non-Wigner-Dyson symmetry [see A. Altland and M. R. Zirnbauer, Phys. Rev. B 55, 1142 (1997)], and two-dimensional systems with spin-orbit scattering.
K. Ensslin and P. M. Petroff, Phys. Rev. B 41, 12307 (1990).
R. Blümel and U. Smilansky, Phys. Rev. Lett. 60, 477 (1988).
R. A. Jalabert, H. U. Baranger, and A. D. Stone, Phys. Rev. Lett. 65, 2442 (1990).
K. Richter and M. Sieber, Phys. Rev. Lett. 89, 206801 (2002).
S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, Phys. Rev. Lett. 93, 014103 (2004).
S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, Phys. Rev. E 72, 046207 (2005).
S. Heusler, S. Müller, P. Braun, and F. Haake, Phys. Rev. Lett. 96, 066804 (2006).
R. S. Whitney and P. Jacquod, Phys. Rev. Lett. 96, 206804 (2006).
P. W. Brouwer and S. Rahav, Phys. Rev. B 74, 075322 (2006).
I. L. Aleiner and A. I. Larkin, Phys. Rev. E 55, R1243 (1997).
S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, Phys. Rev. Lett. 98, 044103 (2007).
[JETP Lett. 36, 318 (1982)].
[Sov. Phys. JETP 58, 444 (1983)].
S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982).
D. L. Shepelyansky, Phys. Rev. Lett. 56, 677 (1986).
A. Altland and M. R. Zirnbauer, Phys. Rev. Lett. 77, 4536 (1996).
H. Schanz and U. Smilansky, Phys. Rev. Lett. 84, 1427 (2000).
I. L. Aleiner and A. I. Larkin, Phys. Rev. B 54, 14423 (1996).
H. U. Baranger, R. A. Jalabert, and A. D. Stone, Phys. Rev. Lett. 70, 3876 (1993).
H. U. Baranger, R. A. Jalabert, and A. D. Stone, Chaos 3, 665 (1993).
P. W. Brouwer and K. Frahm, Phys. Rev. B 53, 1490 (1996).
C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
M. R. Zirnbauer, Phys. Rev. Lett. 69, 1584 (1992).
A. V. Tartakovski, Phys. Rev. B 52, 2704 (1995).
P. W. Brouwer, Phys. Rev. B 57, 10526 (1998).
B. Rejaei, Phys. Rev. B 53, R13235 (1996).
S. Rahav and P. W. Brouwer, Phys. Rev. B 73, 035324 (2006).
P. W. Brouwer, Phys. Rev. B 76, 165313 (2007).
P. W. Brouwer and S. Rahav, Phys. Rev. B 74, 085313 (2006).
J. Müller, T. Micklitz, and A. Altland, Phys. Rev. E 76, 056204 (2007).
[JETP Lett. 62, 76 (1995)].
N. Argaman, Phys. Rev. Lett. 75, 2750 (1995).