Abstract
We report a microscopic derivation of a quantum transport equation for Bloch electrons of metals based on the Dyson equation for the nonequilibrium Keldysh Green's function. Effects of the periodic lattice potential and external electromagnetic fields are taken into account from the beginning by expanding Green's function in terms of modified Wannier functions with the Peierls phase. We then introduce a Wigner representation of Green's function in terms of the crystal momentum and carry out the first-order gradient expansion of the Dyson equation. These procedures enable us to obtain a gauge-invariant quantum transport equation which can describe nonequilibrium evolutions of electrons in metals beyond the semiclassical Boltzmann equations and the linear response theory.
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