Title: Diffusion equations in inhomogeneous solid having arbitrary gradient concentration
Author(s):

	Y. Bilotsky (Aalto University, School of Chemical Technology, Materials Processing, PO Box 16200 FI-00076 AALTO Finland) ,
	M. Gasik (Aalto University, School of Chemical Technology, Materials Processing, PO Box 16200 FI-00076 AALTO Finland) ,
	B. Lev (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine, 14-b Metrolohichna St., 03143 Kyiv, Ukraine)

A quantum kinetic equation is obtained for an inhomogeneous solid having arbitrary gradient concentration and chemical potential. We find, starting from nonequilibrium statistical operator, a new equation to describe atom migration in solid states. In continuous approximation, this equation turns into a non-linear diffusion equation. We derive conditions for which this equation can be reduced to Fick's or Cahn equation.

Key words: nonequilibrium statistical operator, solid state, diffusion process
PACS: 23.23.+x, 56.65.Dy

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