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Electrical current through extended and localized states from the quantum Boltzmann equation

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  • Van Vliet, Carolyn M.
  • Van Weert, Christiaan G.
  • Marshak, Alan H.

Abstract

The fundamental equation for current flow in isothermal inhomogeneous systems, such as in electron devices, is J(r)=(σ/q)∇μ(r), where μ = ξ - qφ is the electrochemical potential or quasi-Fermi level, ξ is the chemical potential, and φ is the electrical potential. The two parts lead to drift and diffusion current. In the present paper we consider current flow involving arbitrary one electron states |ζ), where |ζ) may be an extended Bloch type state or a localized state, the total current being ponderomotive plus collisional current. Using the quantum mechanical Boltzmann equation derived previously by one of us, we show that the above thermodynamic result for J remains valid for any type of current when an exact second quantization formalism is used.

Suggested Citation

  • Van Vliet, Carolyn M. & Van Weert, Christiaan G. & Marshak, Alan H., 1985. "Electrical current through extended and localized states from the quantum Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 134(1), pages 249-264.
    • Handle: RePEc:eee:phsmap:v:134:y:1985:i:1:p:249-264
    DOI: 10.1016/0378-4371(85)90165-7
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    1. Kerkvliet, Benedict J., 1978. "Popular Uprisings in the Philippines, 1840–1940. By David R. Sturtevant. (Ithaca, N.Y.: Cornell University Press, 1976. Pp. 317. $17.50.)," American Political Science Review, Cambridge University Press, vol. 72(2), pages 771-772, June.
    2. Kerkvliet, Benedict J., 1980. "Reflections from Captivity: Phan Boi Chau's “Prison Notes” and Ho Chi Minh's “Prison Diary.” Edited by David G. Marr. Translated by Christopher Jenkins, Tran Khanh Tuyet, and Huynh Sanh Thong. (Athens," American Political Science Review, Cambridge University Press, vol. 74(1), pages 253-254, March.
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