9780030839931, Chapter 13, Problem 4P

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Chapter 13, Problem 4P Problem The response of the conduction electrons to an electric field E(r, t) = Re [E(q, (13.73) Which depends on position as well as time, requires some special consideration. Such a field will in general include a spatially varying charge density p(r, t) = e δn(r, t), δn(r, t) = Re [δn(q, (13.74) Since electrons are conserved in collisions, the local equilibrium distribution appearing in the relaxation-time approximation (13.3) must correspond to a density equal to the actual instantaneous local density n(r, t). Thus even at uniform temperature one must allow for a local chemical potential of the form µ(r, t) = µ + δµ(r, t), t) = Re [δµ(q, (13.75) where w) is chosen to satisfy (to linear order in E) the condition δn(q, w) = δµ(q, w). (13.76) (a) Show, as a result, that at uniform temperature Eq. (13.22) must be replaced by43 g(r, k, t) = + Re [δg(q, k, δg(q, w) = ( (δµ(q, - - ev(k) q v(k)] E(q, w) (13.77) (b) By constructing the induced current and charge densities from the distribution function (13.77), show that the choice (13.75) of w) is precisely what is required to insure that the equation of continuity (local charge conservation) = wp(q, (13.78) is satisfied (c) show that if no charge density is induced, then the current is t) = Re E(q. = e² ( - (1/t) - - Show that a sufficient condition for (13.79) to be valid is that the electric field E be perpendicular to a plane of mirror symmetry in which the wave vector q lies. Step-by-step solution There is no solution to this problem yet. Get help from a Chegg subject expert. Ask an expert