Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session X8: 50 Years of Anderson Localization |
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Sponsoring Units: FHP Chair: David Thouless, University of Washington Room: 414/415 |
Thursday, March 19, 2009 2:30PM - 3:06PM |
X8.00001: Anderson localization in the seventies and beyond Invited Speaker: Little attention was paid to Anderson's challenging paper on localization for the first ten years, but from 1969 onwards it generated a lot of interest. Around that time a number of challenging questions were raised by the community, on matters such as the existence of a sharp distinction between localized and extended states, or between conductors and insulators. For some of these questions the answers are unambiguous. There certainly are energy ranges in which states are exponentially localized, in the presence of a static disordered potential. In a one-diensional potential all states are localized. There is clear evidence, in three dimensions, for energy ranges in which states are extended and diffusive. Magnetic and spin-dependent interactions play an important part in reducing localization effects. For massive particles like electrons and atoms the lowest energy states are localized, but for massless particles like photons and acoustic phonons the lowest energy states are extended. In a one-dimensional disordered system all states are localized. Uncertainties remain. Scaling theory shows that in two-dimensional systems all states are weakly localized, and that there is no minimum metallic conductivity. The interplay between disorder and mutual interactions is still an area of uncertainty, which is very important for electronic systems. Optical and dilute atomic systems provide experimental tests which allow interaction to be much less important. The quantum Hall effect provided a system where states on the Fermi surface are localized, but non-dissipative currents flow in response to an electric field. [Preview Abstract] |
Thursday, March 19, 2009 3:06PM - 3:42PM |
X8.00002: Tests of Localization in Metals and Semiconductors Invited Speaker: The metal-Insulator transition has been a subject of study for decades. It is now well known that entering the critical region of the transition the characteristics of a highly correlated system dominate. The dimensionality of the system is also very important. In this talk I will reminisce about the concepts and experiments to test models, explore systems, and investigate the role of dimensionality. Mott's concept of a minimum metallic conductivity drove my own thinking until the landmark paper of Abrahams, Anderson. Licciardello and Ramankrishnan. A series of careful experiments testing the notions of weak localization followed this paper and provided critical tests of the concept. I will describe some of those experiments and the things we learned from this work. [Preview Abstract] |
Thursday, March 19, 2009 3:42PM - 4:18PM |
X8.00003: Anderson Localization of Light Invited Speaker: Photonic lattices are excellent model systems for studying wave localization due to disorder. The recent progress on Anderson Localization of light will be reviewed, including the additional effects of nonlinearity, with an emphasis on the universal features common to all wave systems in nature. [Preview Abstract] |
Thursday, March 19, 2009 4:18PM - 4:54PM |
X8.00004: Anderson Localization and Mesoscopics Invited Speaker: I will review certain trends developed within the last thirty years of research on Anderson Localization with emphasis on the description of the Anderson transition in terms of the entire distribution function of the conductance mesoscopic fluctuations, and on the role of electron-electron interactions. [Preview Abstract] |
Thursday, March 19, 2009 4:54PM - 5:30PM |
X8.00005: Direct observation of Anderson localization of matter-waves in an optical disorder Invited Speaker: In 1958, P.W. Anderson predicted the localization$^{1}$ of electronic wave functions in disordered crystals, and the resulting absence of diffusion. It has been realized later that Anderson Localization is ubiquitous in wave physics$^{2}$, and this has prompted an intense activity to observe it with light, microwaves, sound waves, and electron gases, but to our knowledge there was no direct observation of exponential spatial localization of matter-waves (electrons or others). We have observed directly$^{3}$ exponential localization of the wave function of ultracold atoms released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle. We will present this work, and the prospects of extending that experimental scheme to quantum gases in higher dimensions (2D and 3D), and with controlled interactions. We will also discuss its significance in the rapidly growing field of quantum simulators. \newline 1 Anderson, P.W. \textit{Absence of diffusion in certain random lattices}. Phys. Rev. \textbf{109}, 1492-1505 (1958). \newline 2 Van Tiggelen, B. \textit{Anderson localization of waves}. In \textit{Wave diffusion in complex media 1998}, edited by J.P. Fouque, Les Houches Lectures (Kluwer, Dordrecht, 1999). \newline 3 Juliette Billy, Vincent Josse, Zhanchun Zuo, Alain Bernard, Ben Hambrecht, Pierre Lugan, David Cl\'{e}ment, Laurent Sanchez-Palencia, Philippe Bouyer$^{ }${\&} Alain Aspect. \textit{Direct observation of Anderson localization of matter-waves in a controlled disorder} Nature$,$ 453, 891 (2008). \newline Work published back to back with a related work in the Inguscio's group in Florence: G. Roati et al., Nature$,$ 453, 895 (2008). [Preview Abstract] |
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