2009.05.01-ECE659-L42-notes

2009.05.01-ECE659-L42-notes - Equation ( 29 ( 29 E r r a a...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 42: Summing Up Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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H s Σ 2 Σ 1 Σ [ ] 1 n in G EI H G G G - + = - - Σ = Σ E 1 μ 2 2 γ 1 Newton’s Law: , , p r p t dr E dt dp = ∇ a a a a D(E) Statistical Mechanics Equilibrium Problems Non-equilibrium Problems E dt = -∇ , 1 T dS dE E = Boltzman Equation ( 29 , , f r k t a a Newton’s Law + scattering (Entropic forces)
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Quantum Mechanics ( 29 r ψ Schrodinger Equation NEGF Quantum Boltzman Equation (Schrodinger Equation + scattering) Landauer Model dynamics Channel thermodynamics Contact Works well when coupling of levels is low Photons 2 2 4 2 2 E m c p c = + Schrodinger Equation r photons Maxwell’s quation Applications: small devices, large device in low bias Multi-particle Schrodinger Equation ( 29 1 2 , ,. .. 1 exp B r r d i H dt H N Z k T μ ρ Ψ Ψ = Ψ - = - for photons
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Unformatted text preview: Equation ( 29 ( 29 E r r a a 1 photon/s ? ? Air Glass a + b * i = Multi-electron Schrodinger Equation ( 29 1 2 , ,. .. r r This becomes an operator in second quantization [ ] 1 n in n G EI H G G G G -+ + =-- = = * t ( 29 ( 29 ( 29 ( 29 1 2 2 1 1 2 a r b r a r b r r r =-= = if * cannot be measured can be measured In case of photons, the - sign is replaced by a + sign so many photons can be in a single state, which gives a big magnitude for electric field, that can be measured...
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2009.05.01-ECE659-L42-notes - Equation ( 29 ( 29 E r r a a...

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