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Advances in Condensed Matter Physics
Volume 2011 (2011), Article ID 104843, 16 pages
Two-Dimensional Electron Systems in Magnetic Fields: The Current Equipartition Law
Physics Laboratory, The Jikei University School of Medicine, 8-3-1 Kokuryo-cho, Chofu, Tokyo182-8570, Japan
Received 15 March 2011; Revised 9 July 2011; Accepted 30 August 2011
Academic Editor: Sergio E. Ulloa
Copyright © 2011 Tsuyoshi Ueta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- C. W. J. Beenakker and H. Van Houten, “Billiard model of a ballistic multiprobe conductor,” Physical Review Letters, vol. 63, no. 17, pp. 1857–1860, 1989.
- K. Kawamura, T. Ueta, and H. Sawano, “Fraunhoffer diffraction of electrons in anisotropic media,” Japanese Journal of Applied Physics, Part 1, vol. 31, no. 2, pp. 317–326, 1992.
- M. Saito, M. Takatsu, M. Okada, and N. Yokoyama, “Analysis of the angular distribution of electrons injected through a quantum point contact by use of a Greens function with a weak-magnetic-field approximation,” Physical Review B, vol. 46, no. 20, pp. 13220–13233, 1992.
- T. Ueta, “Statistical properties of quantum transport through two-dimensional random-shaped quantum dots,” Electronics and Communications in Japan, Part II, vol. 83, no. 9, pp. 42–48, 2000.
- T. Ueta, “Analysis of statistical transport properties of twodimensional random-shaped quantum dots by means of the quantized billiard model,” Denshi Joho Tsushin Gakkai Ronbunshi, vol. 83, pp. 359–631, 2000 (Japanese).
- H. Bruus and A. D. Stone, “Quantum chaos in a deformable billiard: applications to quantum dots,” Physical Review B, vol. 50, no. 24, pp. 18275–18287, 1994.
- H. U. Baranger and P. A. Mello, “Mesoscopic transport through chaotic cavities: a random S-matrix theory approach,” Physical Review Letters, vol. 73, no. 1, pp. 142–145, 1994.
- K. M. Frahm and D. L. Shepelyansky, “Quantum localization in rough billiards,” Physical Review Letters, vol. 78, no. 8, pp. 1440–1443, 1997.
- M. Büttiker, “Scattering theory of current and intensity noise correlations in conductors and wave guides,” Physical Review B, vol. 46, no. 19, pp. 12485–12507, 1992.
- R. A. Jalabert, J.-L. Pichard, and C. W. J. Beenakker, “Universal quantum signatures of chaos in ballistic transport,” Europhysics Letters, vol. 27, pp. 255–260, 1994.
- X. Yang, H. Ishio, and J. Burgdörfer, “Statistics of magnetoconductance in ballistic cavities,” Physical Review B, vol. 52, no. 11, pp. 8219–8225, 1995.
- J. P. Bird, K. Ishibashi, D. K. Ferry, Y. Ochiai, Y. Aoyagi, and T. Sugano, “Spectral characteristics of conductance fluctuations in ballistic quantum dots: the influence of finite magnetic field and temperature,” Physical Review B, vol. 52, no. 11, pp. 8295–8304, 1995.
- K.-F. Berggren, Z.-L. Ji, and T. Lundberg, “Origin of conductance fluctuations in large circular quantum dots,” Physical Review B, vol. 54, no. 16, pp. 11612–11621, 1996.
- R. Akis, D. K. Ferry, and J. P. Bird, “Magnetotransport fluctuations in regular semiconductor ballistic quantum dots,” Physical Review B, vol. 54, no. 24, pp. 17705–17715, 1996.
- I. V. Zozoulenko, R. Schuster, K.-F. Berggren, and K. Ensslin, “Ballistic electrons in an open square geometry: selective probing of resonant-energy states,” Physical Review B, vol. 55, no. 16, pp. R10209–R10212, 1997.
- I. V. Zozoulenko and K. F. Berggren, “Quantum scattering, resonant states, and conductance fluctuations in an open square electron billiard,” Physical Review B, vol. 56, no. 11, pp. 6931–6941, 1997.
- T. Blomquist and I. V. Zozoulenko, “Magnetoconductance fluctuations and weak localization in quantum dots: reliability of the semiclassical approach,” Physical Review B, vol. 64, no. 19, Article ID 195301, 2001.
- K. Nakamura and H. Ishio, “Quantum transport in open billiards: comparison between circle and stadium,” Journal of the Physical Society of Japan, vol. 61, no. 11, pp. 3939–3944, 1992.
- Y. Wang, J. Wang, and H. Guo, “Magnetoconductance of a stadium-shaped quantum dot: a finite-element-method approach,” Physical Review B, vol. 49, no. 3, pp. 1928–1934, 1994.
- K. Nakamura, K. Ito, and Y. Takane, “Magnetoconductance in open stadium billiard: quantum analogue of transition from chaos to tori,” Journal of the Physical Society of Japan, vol. 63, no. 9, pp. 3210–3213, 1994.
- K. Nakamura, K. Ito, and Y. Takane, “Magneto-conductance in open billiards: comparison between circle and stadium,” Journal of Physics A, vol. 27, no. 17, article 021, pp. 5889–5896, 1994.
- J. P. Bird, D. M. Olatona, R. Newbury et al., “Lead-induced transition to chaos in ballistic mesoscopic billiards,” Physical Review B, vol. 52, no. 20, pp. R14336–R14339, 1995.
- C. D. Schwieters, J. A. Alford, and J. B. Delos, “Semiclassical scattering in a circular semiconductor microstructure,” Physical Review B, vol. 54, no. 15, pp. 10652–10668, 1996.
- Y. Takane and K. Nakamura, “Influence of small-angle diffraction on the ballistic conductance fluctuations in chaotic billiards,” Journal of the Physical Society of Japan, vol. 67, no. 2, pp. 397–400, 1998.
- J. P. Bird, R. Akis, D. K. Ferry et al., “Lead-orientation-dependent wave function scarring in open quantum dots,” Physical Review Letters, vol. 82, no. 23, pp. 4691–4694, 1999.
- H. Ishio, “Resonance poles and width distribution for time-reversal transport through mesoscopic open billiards,” Physical Review E, vol. 62, no. 3, pp. R3035–R3038, 2000.
- S. Oberholzer, E. V. Sukhorukov, and C. Schönenberger, “Crossover between classical and quantum shot noise in chaotic cavities,” Nature, vol. 415, no. 6873, pp. 765–767, 2002.
- M. Planck, “Ueber das gesetz der energieverteilung im normalspectrum,” Annalen der Physik, vol. 309, pp. 553–563, 1901.
- T. Ueta, “Quantum-mechanical study of electron focusing spectrum and quantized billiard model,” Journal of the Physical Society of Japan, vol. 64, no. 12, pp. 4813–4823, 1995.
- T. Ueta, “Green's function of a charged particle in magnetic fields,” Journal of the Physical Society of Japan, vol. 61, no. 12, pp. 4314–4324, 1992.
- V. V. Dodonov, I. A. Malkin, and V. I. Man'ko, “The green function of the stationary schrödinger equation for a particle in a uniform magnetic field,” Physics Letters A, vol. 51, no. 3, pp. 133–134, 1975.
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 1970.
- T. Ueta, “Boundary element method for electron waves in uniform magnetic fields,” Engineering Analysis with Boundary Elements, vol. 17, no. 1, pp. 69–74, 1996.
- C. A. Brebbia, The Boundary Element Method for Engineers, Pentech Press, London, UK, 1978.
- R. L. Schult, H. W. Wyld, and D. G. Ravenhall, “Quantum Hall effect and general narrow-wire circuits,” Physical Review B, vol. 41, no. 18, pp. 12760–12780, 1990.
- T. Ueta, “Statistical properties of phases of transmission and reflection coefficients of two-dimensional random-shaped quantum dots,” Denshi Joho Tsushin Gakkai Ronbunshi, vol. 82, pp. 653–655, 1999 (Japanese).
- D. E. Barton and F. N. David, “Some notes on ordered random intervals,” Journal of the Royal Statistical Society, vol. 18, pp. 79–94, 1956.