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2009.02.18-ECE659-L16-notes

2009.02.18-ECE659-L16-notes - ECE 659 Quantum Transport...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 16: Correlation Function/Current SupriyoDatta Spring 2009 Notes prepared by SamiranGanguly
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H 1 Σ 2 Σ 1 μ 2 μ [ ] verticalbraceright 1 1 2 2 1 n in f f i G EI H G G G A i G G + - + Γ + Γ = Σ - Σ = - - Σ = Σ = - [ ] EI H s ψ - - Σ = { } 1 * * 2 2 n G ψ πψψ π ψ ψ = = ( ( 29 1 1 2 2 1 2 n G G f f G A G G + = Γ + Γ = Γ + Γ 1 2 2 * * 1 1 1 2 * * 2 1 2 2 n G ψ ψ ψ ψ ψ π ψ ψ ψ ψ = 2 [ ] { } G s ψ = The diagonal elements give electron densities [ ] { }{ } [ ] 2 n in G G s s G π + = Σ dncurlybracketlefthorizcurlybracketextdncurlybracketmidhorizcurlybracketextdncurlybracketright [ ] [ ] [ ] 1 1 1 1 1 G EI H G EI H G EI H G G - - - + - - + = - - Σ = - - Σ = - - Σ - = Σ - Σ G G G G i G G G G A G G G G i G G + + + + + + + - = Σ - Σ - = Γ = Γ = Γ = -
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Current: E H s ψ ψ ψ = + Σ + Φ dncurlybracketlefthorizcurlybracketexthorizcurlybracketextdncurlybracketmidhorizcurlybracketexthorizcurlybracketextdncurlybracketright Time dependent Schrodinger equation is then: d i dt ψ = Φ For current we need to look at
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