Abstract
The classical Hall effect resulting from the impact of external magnetic and electric fields on the non-Markovian dynamics of charge carriers is studied. The dependence of the tangent of the Hall angle on the magnetic field is derived and compared with the experimental data for Zn. The method is proposed to determine experimentally the memory time in a system.
Similar content being viewed by others
References
S.V. Vonsowsky,Magnetism (Nauka Publishers, Moscow, 1971)
Ch. Kittel,Quantum Theory of Solids (John Wiley & Sons, Inc., USA, 1987)
V.V. Dodonov, V.I. Man’ko, Sov. J. Theor. Math. Phys. 65, 1 (1985)
L. Langer, et al., Phys. Rev. Lett. 76, 479 (1996)
L. Jacak, P. Hawrylak, A. Wojs,Quantum Dots (Springer-Verlag, Berlin, Heidelberg, New York, 1997)
W.D. Heiss, R.G. Nazmitdinov, Phys. Rev. B 55, 16310 (1997)
W.D. Heiss, R.G. Nazmitdinov, Pis’ma v ZhETF 68, 870 (1998)
M. Dineykhan, R.G. Nazmitdinov, Phys. Rev. B 55, 13707 (1997)
R.G. Nazmitdinov, N.S. Simonovic, J.M. Rost, Phys. Rev. B 65, 155307 (2002)
Yu. Demidenko, A. Kuzyk, V. Lozovski, O. Tretyak, J. Phys. Condense. Matter 16, 543 (2004)
A. Matulis, E. Anisimovas, J. Phys. Condense. Matter 17, 3851 (2005)
N.G. van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981)
C.W. Gardiner,Quantum Noise (Springer, Berlin, 1991)
U. Weiss,Quantum Dissipative Systems (Wold Scientific, Singapore, 1999)
D. Zubarev, V. Morozov, G. Röpke, inStatistical mechanics of nonequilibrium processes (Academie Verlag, Berlin, 1997) Vol. 2, p. 52
H.J. Carmichael,An open system approach to quantum optics (Springer, Berlin, 1993)
Yu.L. Klimontovich,Statistical theory of open systems (Kluwer Academic Publishers, Dordrecht, 1995)
A.O. Caldeira, A.J. Leggett, Phys. Rev. Lett. 46, 211 (1981)
A.O. Caldeira, A.J. Leggett, Phys. Rev. Lett. 48, 1571 (1982)
A.O. Caldeira, A.J. Leggett, Ann. Phys. 149, 374 (1983)
V.V. Dodonov, V. I. Man’ko, Density Matrices and Wigner Functions of Quasiclassical Quantum Systems, in Proc. Lebedev Phys. Inst. of Sciences, edited by A.A. Komar (Nova Science, Commack, NY, 1987), Vol. 167
K. Lindenberg, B.J. West,The Nonequilibrium Statistical Mechanics of Open and Closed Systems (VCH Publishers, Inc., New York, 1990)
K. Lindenberg, B.J. West, Phys. Rev. A 30, 568 (1984)
A. Isar, A. Sandulescu, H. Scutaru, E. Stefanescu, W. Scheid, Int. J. Mod. Phys. E 3, 635 (1994)
H.P. Breuer, F. Petruccione,The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)
G.W. Ford, J.T. Lewis, R.F. O’Connell, Phys. Rev. A 36, 1466 (1987)
G.W. Ford, J.T. Lewis, R.F. O’Connell, Phys. Rev. A 37, 4419 (1988)
G.Y. Hu, R.F. O’Connell, Physica A 151, 33 (1988)
G.Y. Hu, R.F. O’Connell, Phys. Rev. B 36, 5798 (1987)
X.L. Li, G.W. Ford, R.F. O’Connell, Phys. Rev. A 41, 5287 (1990)
X.L. Li, G.W. Ford, R.F. O’Connell, Phys. Rev. A 42, 4519 (1990)
X.L. Li, G.W. Ford, R.F. O’Connell, Physica A 193, 575 (1993)
X.L. Li, G.W. Ford, R.F. O’Connell, Phys. Rev. E 53, 3359 (1996)
S. Dattagupta, J. Singh, Phys. Rev. Lett. 79, 961 (1997)
Th.M. Nieuwenhuizen, A.E. Allahverdyan, Phys. Rev. E 66, 036102 (2002)
Z. Kanokov, Yu.V. Palchikov, G.G. Adamian, N.V. Antonenko, W. Scheid, Phys. Rev. E 71, 016121 (2005)
Sh.A. Kalandarov, Z. Kanokov, G.G. Adamian, N.V. Antonenko, Phys. Rev. E 75, 0311115 (2007)
G.G. Adamian, N.V. Antonenko, Z. Kanokov, V.V. Sargsyan, Theor. Math. Phys. 145, 1443 (2005)
V.V. Sargsyan, Z. Kanokov, G.G. Adamian, N.V. Antonenko, Phys. Rev. C 77, 024607 (2008)
V.V. Sargsyan, Z. Kanokov, G.G. Adamian, N.V. Antonenko, Phys. Part. Nuclei 41, 175 (2010)
R.A. Kuzyakin, V.V. Sargsyan, G.G. Adamian, N.V. Antonenko, Phys. Rev. A 83, 062117 (2011)
R.A. Kuzyakin, V.V. Sargsyan, G.G. Adamian, N.V. Antonenko, Phys. Rev. A 84, 032117 (2011)
K. Wen, F. Sakata, Z.-X. Li, X.-Z. Wu, Y.-X. Zhang, S.-G. Zhou, Phys. Rev. Lett. 111, 012501 (2013)
D. Lacroix, V.V. Sargsyan, G.G. Adamian, N.V. Antonenko, Eur. Phys. J. B 88, 89 (2015)
V.V. Sargsyan, D. Lacroix, G.G. Adamian, N.V. Antonenko, Phys. Rev. A 95, 032119 (2017)
V.V. Sargsyan, D. Lacroix, G.G. Adamian, N.V. Antonenko, Phys. Rev. A 90, 022123 (2014)
V.V. Sargsyan, D. Lacroix, G.G. Adamian, N.V. Antonenko, Phys. Rev. A 96, 012114 (2017)
H.W. Lewis, Phys. Rev. 92, 1149 (1953)
H.W. Lewis, Phys. Rev. 100, 641 (1955)
E.S. Borovik, Doklady Acad. Nauk S.S.S.R. 70, 601 (1950)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Abdurakhmanov, I.B., Adamian, G.G., Antonenko, N.V. et al. Non-Markovian feature of the classical Hall effect. Eur. Phys. J. B 91, 223 (2018). https://doi.org/10.1140/epjb/e2018-90385-0
Received:
Published:
DOI: https://doi.org/10.1140/epjb/e2018-90385-0