By Joseph Maciejko

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This quantity collects jointly the lectures and papers provided on the joint Los Alamos nationwide Laboratory - Commissariat a l'Energie Atomique assembly, held at Cadarache fortress, in Provence (France), April 22-26, 1985. approximately 100 contributors got here from either laboratories and from different linked French businesses.

- Nonlinear dynamics of surface-tension-driven instabilities
- Statistical physics of phase transitions
- A History of Thermodynamics
- The arrow of time in cosmology and statistical physics
- Further Remarks on the Second Law of Thermodynamics in General Relativity
- Introduction to the renormalization group and critical phenomena

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A 8, 214 (1975). 11. Yu. A. Kukharenko and S. G. Tikhodeev, Zh. Eksp. Teor. Fiz 83, 1444 (1982) [Sov. Phys. JETP 56, 831 (1982)]. 12. M. Wagner, Phys. Rev. B 44, 6104 (1991). 13. H. -P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer-Verlag, Berlin, 1998). 14. A. Kamenev, cond-mat/0109316 (2001); cond-mat/0412296 (2004). 15. A. M. Zagoskin, Quantum Theory of Many-Body Systems (Springer, New York, 1998). 16. J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986). ˇ cka, and B.

31), the equilibrium piece will give a vanishing contribution and only G< 1 in Eq. 32) will give a nonvanishing contribution to the current. We therefore obtain j = e2 d3 p (2π)3 ∂nF dω vp (vp · E) − 2π ∂ω A(p, ω)Λ(p, ω) from which the conductivity tensor is easily extracted, σµν = e2 m2 d3 p (2π)3 dω ∂nF pµ pν − 2π ∂ω A(p, ω)Λ(p, ω) which is equivalent to the Kubo formula result. 3 One-Band Electrons with Spin-Orbit Coupling 51 where λ(p) is odd in p in general due to time-reversal symmetry, but for simplicity we neglect higher-order terms and assume it is only linear in p.

For pedagogical reasons, let us first derive the expression from the usual perturbation expansion of the S-matrix and the subsequent application of Wick’s theorem, and then obtain it from the path integral method which is more transparent. 2 Perturbation Expansion for the Mixed Green’s Function As explained, we define the unperturbed Hamiltonian as the first two terms of Eq. 1), † † H= kα ckα ckα + HC [{dn }, {dn }], kα and the perturbation as the tunneling term, tkα,n c†kα dn + t∗kα,n d†n ckα .

### An Introduction to Nonequilibrium Many-Body Theory by Joseph Maciejko

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