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ECE615_Lecture_17

ECE615_Lecture_17 - Lecture 17 Density Matrix Calculation...

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(1) Lecture 17 ( 29 ( 29 (1) (0) ˆ ( ) exp ( ), exp t nm nm nm nm nm nm i t i t dt V t i t ρ ϖ γ ρ ϖ γ -∞ - = - + + ɶ Density Matrix Calculation of the Linear Susceptibility ˆ ˆ ( ) ( ) V t E t μ = - ɶ (0) =0 for nm n m ρ ( ( ) ( )exp p p p E t E i t ϖ ϖ = - ɶ ( (0) (0) (0) ˆ ˆ ˆ ˆ , nv vm nv vm nm v V V V ρ ρ ρ = - (omit the vector signs) (2) (3) 1 ( (0) (0) ( ) nv vm nv vm v E t μ ρ ρ μ = - - ɶ ( (0) (0) ( ) mm nn nm E t ρ ρ μ = - - ɶ ( 29 ( 29 ( 29 (1) (0) (0) ( ) exp ( )exp t nm mm nn nm nm nm nm nm i t i t E t i t dt ρ ρ ρ ϖ γ μ ϖ γ -∞ = - - + + ɶ
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( 29 (1) (0) (0) ( ) ( ) nm mm nn nm p p i t E ρ ρ ρ μ ϖ = - ( 29 ( 29 ( 29 exp exp t nm nm nm p nm i t i t dt ϖ γ ϖ ϖ γ -∞ × - + - + ( 29 ( 29 ( ( 29 ( 29 ( 29 exp exp exp t nm p nm p nm nm nm p nm nm p nm i t i t i t i i ϖ ϖ γ ϖ ϖ γ ϖ ϖ γ ϖ ϖ γ -∞ - + - × - + = - + - + ( 29 (1) (0) (0) ( ) ( ) nm mm nn nm p p i t E ρ ρ ρ μ ϖ = - (0) (0) (0) ρ ρ - (4) (5) 2 ( ( 29 (1) 1 (0) ( )exp ( ) nm p p nm mn p nm p nm E i t t i μ ϖ ϖ ρ ϖ ϖ γ - - = - - mn mm nn ( (1) (1) ˆ ˆ ( ) tr nm nm nm t μ
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