Effect of winding edge currents. (English) Zbl 1428.82038
Summary: We discuss persistent currents for particles with internal degrees of freedom. The currents arise because of winding properties essential for the chaotic motion of the particles in a confined geometry. The currents do not change the particle concentrations or thermodynamics, similar to the skipping orbits in a magnetic field.
MSC:
| 82C21 | Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics |
| 81V70 | Many-body theory; quantum Hall effect |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
References:
| [1] | Ceperley, D. M., Rev. Mod. Phys., 67, 279 (1995) |
| [2] | Desbois, J.; Ouvry, S., J. Stat. Mech., P05024 (2011); Desbois, J.; Ouvry, S., J. Stat. Mech., P05005 (2012) |
| [3] | Grosberg, A.; Frisch, H., J. Phys. A: Math. Gen., 36, 8955 (2003) · Zbl 1049.82077 |
| [4] | Dyakonov, M. I.; Perel, V. I., Sov. Phys. JETP Lett., 13, 467469 (1971) |
| [5] | Hirsch, J. E., Phys. Rev. Lett., 83, 18341837 (1999) |
| [6] | Zhang, S., Phys. Rev. Lett., 85, 393396 (2000) |
| [7] | Engel, H.-A.; Halperin, B. I.; Rashba, E. I., Phys. Rev. Lett., 95, 166605 (2005) |
| [8] | Tse, W.-K.; Das Sarma, S., Phys. Rev. Lett., 96, 056601 (2006) |
| [9] | Stern, N. P.; Steuerman, D. W.; Mack, S.; Gossard, A. C.; Awschalom, D. D., Nature Physics, 4, 843 (2008) |
| [10] | Jungwirth, T.; Wunderlich, J.; Olejnik, K., Nature Materials, 11, 382390 (2012) |
| [11] | Milnor, J. W., Ann. of Math., 52, 2, 248 (1950) · Zbl 0037.38904 |
| [12] | Sullivan, John M., (Discrete Differential Geometry. Discrete Differential Geometry, Oberwolfach Seminars, vol. 38 (2008), Birkhäuser), 137-161; Sullivan, John M. (2007) · Zbl 1151.53305 |
| [13] | Kühnel, W., Differential Geometry: Curves - Surfaces - Manifolds (2006), Amer. Math. Soc. |
| [14] | Spitzer, F., Trans. Amer. Math. Soc., 87, 187 (1958) · Zbl 0089.13601 |
| [15] | Zhou, Y.; Zhang, F.-C., Nature Physics, 8, 448449 (2012) |
| [16] | Thomas, L. H., Nature, 117, 514 (1926) |
| [17] | Jackson, J. D., Classical Electrodynamics (1998), Wiley Inc., p. 808 · Zbl 0114.42903 |
| [18] | Tomonaga, S.-I.; Oka, T., The Story of Spin (1997), University of Chicago Press |
| [19] | Malykin, G. B., Physics-Uspekhi, 49, 837 (2006) |
| [20] | Ritus, V. I., Physics-Uspekhi, 50, 95 (2007) |
| [21] | Zanimonskiy, Y. Y.; Stepanovsky, Yu. P., Kharkov University Bulletin, 899, 23 (2010) |
| [22] | Kessler, J., Polarized Electrons (1985), Springer, p. 299 |
| [23] | Bargmann, V.; Michel, L.; Telegdi, V. L., Phys. Rev. Lett., 2, 435 (1959) |
| [24] | Akkermans, E.; Montambaux, G., Mesoscopic Physics of Electrons and Photons (2007), Cambridge University Press |
| [25] | Lorenzo, J. R., Principles of Diffuse Light Propagation (2012), World Scientific |
| [26] | Sheng, P., Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (2006), Springer |
| [27] | Storzer, M.; Gross, P.; Aegerter, C. M.; Maret, G., Phys. Rev. Lett., 96, 063904 (2006) |
| [28] | Van Kampen, N. G., Stochastic Processes in Physics and Chemistry (2007), Elsevier, p. 464 · Zbl 0974.60020 |
| [29] | Lifshits, I. M.; Gredeskul, S. A.; Pastur, L. A., Introduction to the Theory of Disordered Systems (1988), Wiley Inc., p. 357 |
| [30] | Klyatskin, V. I., Dynamics of Stochastic Systems (2005), Elsevier: Elsevier Amsterdam, p. 212 · Zbl 1090.82002 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
