Lecture 23 - ( 29 ( 29 ( 29 = Φ- & 142 43 describes...

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Unformatted text preview: ( 29 ( 29 ( 29 = Φ- & 142 43 describes non-instantaneous responses ' t B t t t F t dt r for a generalized field , the response for the property is F B ( 29 ( 29 ( 29 ϖ ϖ ϖ χ ϖ χ ϖ- = = Φ t t B F e t dt i after effect function (describes a possible delay between the perturbation and the response) measure electric current flowing as a response to a Field. σ r ur J electric current, conductivity tensor, E applied field α α α α α α α α α = xx xy xz x x y yx yy yz y z zx zy zz z J E J E J E ϖ to find dependence, we look into - field, and average over a period of time when Field is on t dependent ( 29 ( 29 ( 29 ( 29 = Φ- r 142 43 2 describes non-instantaneous responses ' +O E Laplace- convolution t J t t t E t dt ( 29 ( 29 ϖ ϖ ϖ ϖ σ ϖ- = = uuuuur r r J where each component is given by i t E x e x t ( 29 ( 29 = - & r r consider the field as a perturbation, the interaction between total dipole moment and field t M E t h ( 29 ( 29 = - or (for the interaction on the direction) t M E t a a h a ( 29 Ψ + = Ψ h t t H = H h i H o ( 29 ( 29 ϖ ψ ψ ψ- Ψ = = m t m m m m m m t t e E o i a H ( 29 ( 29 ( 29 ( 29 = = = (only one state is populated) 1 0 for m if the perturbation is small, n m k k t t n t a a a a ( 29 ( 29 ϖ ϖ ψ ψ-- Ψ = + n m t t n m m n m t e t e i i a ( 29 ( 29 ( 29 ϖ ϖ ψ ψ-- = - ' where ' ' m n t t m m n t e t dt i a i h G = G charges current in the direction J charge x velocity b b b ( 29 ( 29 ( 29 Ψ Ψ Ψ the expectation value of the current J for the state t t J t b b ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ψ ψ ψ ψ ψ ψ---- Ψ Ψ = + + + ' ' ' ' ' ......
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This note was uploaded on 05/29/2011 for the course CHM 6461 taught by Professor Bowers during the Spring '08 term at University of Florida.

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Lecture 23 - ( 29 ( 29 ( 29 = Φ- & 142 43 describes...

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