2009.02.09-ECE659-L12-notes

2009.02.09-ECE659-L12-notes - A q v dt x x q v A A =- = -...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 12: Cyclotron Frequency Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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S D L Vd E μ2 μ1 1 k dx E dt dk E dt = = ∇ h h k mv = h h ( 29 ( 29 ( 29 2 k qA k qA E U x m - - = + h h h h dx k qA k t m m - = = h h h h k k x k y v ( 29 dt dk q v B dt = × h h h We keep U as constant and drop it for convenience ( 29 2 , , 2 i i i k qA E i x y z m - = = 1 i i i i dx E dt k dk E dt x = = -
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We change i to j in the E expression to avoid confusion 1 i i i i dx k qA E dt k m - = = More formally 1 1 i i ij i i i i k qA E k m k qA m δ - = - = Vector notation then follows naturally j j j i j i j k qA A dk q dt m x v - = - ⋅- dhDh± ( 29 j i j j i j i i j j A dk q v A dt x dx A d qA q B dx x dt = - = - Subtracting B from A Some Tensor notations: Kronecker delta Levi-Civita tensor 1 0 ij if i j if i j = = 1 ,in cyclicorder 1 ,in anti-cyclicorder 0 or or or ijk if i j k if i j k if i j j k i k i j k ε + = - = = = = = j i i j j i j j i j j i j A dk
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Unformatted text preview: A q v dt x x q v A A =- = - Now: ( 29 , ijk i j x y y x k i j A B A B A B A B = =- H H ( 29 ( 29 , i j ijk k j k dk q v A dt q v B = = H H H so ( 29 1 k dx k qA k E dt m m dk q v B dt -= = = = + h h h h h h h h k x k y v B More generally: 1 kd qBdt dE dk = ( 29 ( 29 2 d A k qBT dE = Area in k-space Integrate over T c qB m B = = ( 29 d k qBdt v = Integrating over time T 2 2 k qBT k m T qB m = = c...
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This note was uploaded on 01/30/2011 for the course ECE 659 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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2009.02.09-ECE659-L12-notes - A q v dt x x q v A A =- = -...

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