Still, if you go through Rammer then this chapter by Kleinert nicely summarizes everything without dropping too many details. The newest edition of Altland and Simons has two chapters on classical and quantum systems out of equilibrium, but I was fairly disappointed with their treatment considering the rest of the book is fantastic. As for quantum transport, where this formalism is frequently employed, I can recommend Di Ventra as an undergrad-level introductory book and this book by Datta for some other interesting topics. Weiss is excellent for dissipative open systems, although this field opens up a whole new can of worms so you might want to avoid at first.

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Rammer and Smith's review article "Quantum field-theoretical methods in transport theory of metals" Rev. For researchers who study condensed matter physics i. Haug and A. Tatara, H. Kohno, and J. Shibata : Microscopic approach to current-driven domain wall dynamics Phys. Ryndyk, R. Gutierrez, B.

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Song, and G. The above articles will be reliable and readable. On top of them, one can learn important details from the sophisticated manuscripts by Alex Kamenev:. Although as far as I know I have listed the relevant articles, I guess I have missed a lot of other important papers. Please forgive me if I have. I hope my contribution helps someone to learn Keldysh formalism. Last, let me remark the points of Keldysh formalism which I have learned by the above articles; thanks to the Schwinger-Keldysh closed time path, the Schwinger-Keldysh formalism i. Therefore, within the perturbative theory via Schwinger-Keldysh or contour-ordered Green's functions, the formalism can deal with an arbitrary time-dependent Hamiltonian and treat the system out of the equilibrium.

On top of this, this formalism is applicable to systems at finite temperature; the well-known Matsubara formalism i. That is, the Schwinger-Keldysh formalism includes the Matsubara formalism and information about finite temperature is contained in the greater and lesser Green's functions.

Consequently we can treat non-equilibrium phenomena at finite temperature thanks to the Schwinger-Keldysh formalism. This will be the strong point of the formalism. Finally, this slide of mine also contains useful references, as does this indroductory presentation , both written by me.

## Quantum Statistical Mechanics by Leo P. Kadanoff, Gordon Baym | Waterstones

This answer contains some additional resources that may be useful. Please note that answers which simply list resources but provide no details are strongly discouraged by the site's policy on resource recommendation questions. This answer is left here to contain additional links that do not yet have commentary. Botermans and R.

Malfliet, Quantum transport theory of nuclear matter, Physics Reports , Calzetta and B. Hu, Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation, Phys. D 37 , Chou, Z. Su, B. Hao, and L. Yu, Equilibrium and nonequilibrium formalisms made unified, Physics Reports , Ivanov, J.

Knoll, and D. A , If it is still of interest, next to all the excellent suggestions above there is a book from which I found rather helpful as it makes some neat observations I could not find in other texts:.

## Quantum statistical mechanics : Green's function methods in equilibrium and nonequilibrium problems

Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Good reading on the Keldysh formalism Ask Question. Asked 8 years, 1 month ago. Active 2 years, 7 months ago. Viewed 10k times. In the context of condensed matter physics I recommend the following books even though various techniques also apply outside this regime : Rammer's Quantum Field Theory of Non-Equilibrium States.

See, e. Why they have to be that form? Discuss the advantage and disadvantage of both. Explain the meaning of slide 54 from first line to the second line. The equations can be derived quickly. The integral is along the contour.

Absence of this term is consistent with adiabatic switch-on from Feynman diagrammatic expansion. This expression can be proving to be real, no need to take Re. Above equation works for general nonlinear case. Typically, 10 to 20 iterations should be already converged. For real fortran codes, see And why we need to define Heisenberg operator starting at the same point?

Derive the integral form of equation from the differential form for GLC slide 79 and state clearly the implicit assumption made for the validity of the integral form. Derive the contour ordered Dyson equation, slides Derive the two different forms of Keldysh equations on bottom of slide Derive the Meir-Wingreen formula and the Caroli formula slide. Verify the results on slide for 1D chain. Note that 4 is cancelled by c ; 7 by d. Fetter and J. AI t etc. For a proof, see Rammer.

The Dyson equation here is wrong — one need to subtract the disconnected part, which is not zero. For a more systematic exposition of the Feynman-diagrammatic expansion, see Fetter and Welecka. Wang, X. Ni, and J. Jiang, Phys. B 80, The number in front of the diagrams represents extra combinatorial factor. The famous WG method the first term in the expansion for coulomb interaction.

Derive the Hedin equations for the electron-phonon system. I have not understood the derivation or have not spend time try. A smart student in the audience should try and give a presentation. Quantum Transport.

Outline: What is Computational Electronics? Interaction between atoms and the lattice properties of crystals. Wavefunction Quantum mechanics acknowledges the wave-particle duality of matter by supposing that, rather than traveling along a definite path, a particle. No friction. No air resistance. Perfect Spring Two normal modes. Similar presentations.

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