Evolution of Fractal Patterns during a Classical-Quantum Transition

A. P. Micolich; R. P. Taylor; A. G. Davies; J. P. Bird; R. Newbury; T. M. Fromhold; A. Ehlert; H. Linke; L. D. Macks; W. R. Tribe; E. H. Linfield; D. A. Ritchie; J. Cooper; Y. Aoyagi; P. B. Wilkinson

doi:10.1103/PhysRevLett.87.036802

Evolution of Fractal Patterns during a Classical-Quantum Transition

A. P. Micolich, R. P. Taylor, A. G. Davies, J. P. Bird, R. Newbury, T. M. Fromhold, A. Ehlert, H. Linke, L. D. Macks, W. R. Tribe, E. H. Linfield, D. A. Ritchie, J. Cooper, Y. Aoyagi, and P. B. Wilkinson

Phys. Rev. Lett. 87, 036802 – Published 29 June 2001

Abstract

We investigate how fractals evolve into nonfractal behavior as the generation process is gradually suppressed. Fractals observed in the conductance of semiconductor billiards are of particular interest because the generation process is semiclassical and can be suppressed by transitions towards either fully classical or fully quantum-mechanical conduction. Investigating a range of billiards, we identify a “universal” behavior in the changeover from fractal to nonfractal conductance, which is described by a smooth evolution rather than deterioration in the fractal scaling properties.

Received 14 December 2000

DOI:https://doi.org/10.1103/PhysRevLett.87.036802

Authors & Affiliations

A. P. Micolich¹, R. P. Taylor^1,*, A. G. Davies², J. P. Bird³, R. Newbury⁴, T. M. Fromhold⁵, A. Ehlert⁴, H. Linke¹, L. D. Macks², W. R. Tribe², E. H. Linfield², D. A. Ritchie², J. Cooper⁶, Y. Aoyagi⁶, and P. B. Wilkinson⁵

¹Materials Science Institute, Physics Department, University of Oregon, Eugene, Oregon 97403-1274
²Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom
³Center for Solid State Research, Arizona State University, Tempe, Arizona 85287-6206
⁴School of Physics, University of New South Wales, Sydney, NSW 2052, Australia
⁵School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
⁶Semiconductor Laboratory, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan