ex08 - Solid State Theory Exercise 8 FS 11 Prof. M. Sigrist...

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Unformatted text preview: Solid State Theory Exercise 8 FS 11 Prof. M. Sigrist Exercise 8.1 Bohr-van-Leeuwen-Theorem Prove the Bohr-van-Leeuwen-theorem, which states that there is no diamagnetism in classical physics. Hint: H ( p 1 ,...,p N ; q 1 ,...,q N ) is the Hamiltonian of the N-particle system with vanish- ing external magnetic field. In comparison, the Hamiltonian with applied magnetic field B is then given by H ( p 1- e/cA 1 ,...,p N- e/cA N ; q 1 ,...,q N ), where B = ∇ × A and A i = A ( q i ). The magnetization can be calculated using M =- ∂ H ∂B = 1 β ∂ log Z ∂B , (1) with the partition function Z of the system in the magnetic field. Exercise 8.2 Landau Diamagnetism Calculate the orbital part of the magnetization of the free electron gas in 3D in the limits of low temperature and small external field ( T → , H → 0). In addition, show that the magnetic susceptibility at T = 0 and H = 0 is given by χ =- 1 3 m 2 m * 2 χ P , (2) where χ P is the Pauli (spin-)susceptibility....
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This note was uploaded on 10/04/2011 for the course PHYS fs11 taught by Professor Sigrist during the Spring '11 term at Swiss Federal Institute of Technology Zurich.

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ex08 - Solid State Theory Exercise 8 FS 11 Prof. M. Sigrist...

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