Abstract
Within the framework of microscopic fluctuation-dissipation theory, we obtain the stochastic equation describing the Brownian motion of an electron in the phonon field of the crystal lattice. An expression for the Green’s function of the phonon field is found in general form and for the case of linear phonon-variable interaction of an electron with the phonon field with allowance for the potential screening of crystal-lattice nuclei. An expression for the phonon drag acting on a conduction electron in the lattice field is found and analyzed with allowance for the interaction. Frequency dependence of the coefficient of the phonon drag acting on a conduction electron is studied and the contribution of the electron-phonon interaction to the effective mass of a charge carrier is determined.
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REFERENCES
E. G. Maksimov, D. Yu. Savrasov, and S. Yu. Savrasov, Physics-Uspekhi, 40, No.4, 337 (1998).
G. N. Bochkov and G. F. Efremov, Nonlinear Stochastic Models of the Processes and Systems [in Russian], Gorky State University, Gorky (1978).
G. F. Efremov and V. A. Kazakov, Radiophys. Quantum Electron., 22, 86 (1979).
G. F. Efremov and A. Yu. Smirnov, Sov. Phys. JETP, 53, 547 (1981).
G. F. Efremov, Stochastic Equations for Open Quantum Systems [in Russian], Gorky State University, Gorky (1982).
J. Schwinger, J. Math. Phys., 2, 407 (1961).
J. Schwinger, in: The Browinian Motion of a Quantum Oscillator (collected papers) [Russian translation], Inostrannaya Literatura, Moscow (1962).
R. Senitzky, Phys. Rev., 119, 670 (1960).
R. Senitzky, Phys. Rev., 124, 642 (1961).
V. F. Gantmakher and I. B. Levinson, Carrier Scattering in Metals and Semiconductors, North-Holland, Amsterdam (1987).
A. A. Abrikosov, Fundamentals of the Theory of Metals, Elsevier Science Publ. (1988).
A. A. Abrikosov, L. P. Gor’kov, and I. Ye. Dzyaloshinskii, Quantum Field Theoretical Methods in Statistical Physics, Pergamon Press, Oxford (1965).
P. C. Martin and J. S. Schwinger, in: Phys. Rev., 115, 1342 (1959).
L. Kadanov and G. Baym, Quantum Statistical mechanics, Benjamin/Cummings, London (1962).
L. V. Keldish, Sov. Phys. JETP, 20, 1018 (1965).
G. F. Efremov, Sov. Phys. JETP, 83, No.5, 896 (1996).
G. G. Efremov and V. V. Sharkov, Sov. Phys. JETP, 98, No.2, 171 (2004).
G. F. Efremov, L. D. Mourokh, and A. Yu. Smirnov, Phys. Lett. A, 175, 89 (1993).
A. Yu. Smirnov, Ann. Phys., 264, 1 (1998).
A. Yu. Smirnov, Phys. Rev. E, 56, 1484 (1997).
A. Yu. Smirnov and L. G. Mourokh, Phys. Lett. A, 231, 429 (1997).
V. I. Puller, L. G. Mourokh, N. J. M. Horing, and A. Yu. Smirnov, in: Topical Problems in Statistical Radiophysics (Malakhov’s Compendium) [in Russian] (2002), Vol. 1, No.1, p. 63.
G. F. Efremov, O. V. Mareeva, D. A. Vorobiev, and V. V. Sharkov, Topical Problems in Statistical Radiophysics (Malakhov’s Compendium) [in Russian] (2003), Vol. 2, p. 5.
G. F. Efremov and O. V. Mareeva, Vestnik NNGU, 1(20), 114 (1999).
S. I. Pekar, Research in Electron Theory of Crystals, US AEC Report AEC-tr-5575, Washington, DC (1963).
A. S. Davydov, Solid State Theory [in Russian], Nauka, Moscow (1976).
A. A. Abrikosov, An Introduction to the Theory of Normal Metals, Suppl. 12 of Solid State Physics, Academic, London (1972), p. 16.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 3, pp. 249–268, March 2005.
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Efremov, G.F., Mareeva, O.V. & Vorobiev, D.A. Statistical Theory of the Phonon Drag Force Acting on a Conduction Electron. Radiophys Quantum Electron 48, 222–239 (2005). https://doi.org/10.1007/s11141-005-0063-0
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DOI: https://doi.org/10.1007/s11141-005-0063-0