Abstract
We find an analytic solution of the Smolukhovsky problem of the temperature and electric potential jumps in a metal under the action of the temperature gradient normal to the surface. We take the character of the electron energy accommodation on the surface into account. We find the analytic expressions for the electric field generated by heat processes, for the temperature distribution, and for the electric potential.
Similar content being viewed by others
REFERENCES
C. Cercignani, Theory and Application of the Boltzmann Equation, Scottish Acad. Press, Edinburgh (1975).
A. V. Latyshev, J. Appl. Math. Mech., 54, 480 (1990).
A. V. Latyshev and A. A. Yushkanov, JETP, 87, 518 (1998).
E. Lifchitz and L. Pitaevski, Cinetique Physique [in Russian] (Physique Théorique, Vol. 10, L. D. Landau and E. M. Lifchitz, eds.), Nauka, Moscow (1979); French transl., Mir, Moscow (1990).
A. V. Latyshev and A. A. Yushkanov, Tech. Phys., 48, 837 (2003).
A. A. Abrikosov, Introduction to the Theory of Normal Metals [in Russian], Nauka, Moscow (1972); English transl., North-Holland, Amsterdam (1988).
J. M. Ziman, Electrons and Phonons, Clarendon, Oxford (1960).
V. V. Vedenyapin, Kinetic Boltzmann and Vlasov Equations [in Russian], Fizmatlit, Moscow (2001).
C. E. Siewert and F. Sharipov, Phys. Fluids, 14, 4123 (2002).
M. M. R. Williams, Mathematical Methods in Particle Transport Theory, Wiley, New York (1971).
V. S. Vladimirov and V. V. Zharinov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (2000).
K. M. Case and P. F. Zweifel, Linear Transport Theory, Addison-Wesley, New York (1967).
I. K. Lifanov, Method of Singular Integral Equations and Numerical Experiment (in Mathematical Physics, Aerodynamics, and Wave Diffraction) [in Russian], TOO “Yanus,” Moscow (1995).
F. D. Gakhov, Boundary Value Problems [in Russian] (3rd ed.), Nauka, Moscow (1977); English transl., Dover, New York (1990).
L. D. Landau and E. M. Lifshitz, Statistical Physics: Part 1 [in Russian] (Course of Theoretical Physics, Vol. 5), Nauka, Moscow (1976); English transl., Pergamon, Oxford (1980).
Author information
Authors and Affiliations
Additional information
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 93–111, January, 2005.
Rights and permissions
About this article
Cite this article
Latyshev, A.V., Yushkanov, A.A. Smolukhovsky problem for electrons in a metal. Theor Math Phys 142, 79–95 (2005). https://doi.org/10.1007/s11232-005-0068-z
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11232-005-0068-z