Abstract
We present a compact and self-contained review of the recently developed Keldysh formalism for multiple parallel worlds. The formalism has been applied to consistent quantum evaluation of the flows of informational quantities, in particular, to the evaluation of Renyi and Shannon entropy flows. We start with the formulation of the standard and extended Keldysh techniques in a single world in a form convenient for our presentation. We explain the use of Keldysh contours encompassing multiple parallel worlds. In the end, we briefly summarize the concrete results obtained with the method.
Similar content being viewed by others
References
L. V. Keldysh, Sov. Phys. JETP 20, 1018 (1965).
A. I. Larkin and Yu. N. Ovchinnikov, Sov. Phys. JETP 41, 960 (1975).
G. D. Mahan, Manyparticle Physics (Plenum, New York, 1990).
A. Kamenev and A. Levchenko, Adv. Phys. 58, 197 (2009).
A. P. Jauho, arXiv:cond-mat/0208577.
A. Kamenev, Field Theory of Non-Equilibrium Systems (Cambridge Univ. Press, Cambridge, 2011).
J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986).
A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Courier Corp., Kendallville, 1975).
Y. V. Nazarov and Y. M. Blanter, Quantum Transport. Introduction to Nanoscience (Cambridge Univ. Press, Cambridge, 2009).
Y. V. Nazarov and M. Kindermann, Eur. Phys. J. B 35, 413 (2003).
T. T. Heikkilä and Y. V. Nazarov, Phys. Rev. Lett. 102, 130605 (2009).
Y. V. Nazarov, Superlatt. Microstruct. 25, 1221 (1999).
I. Snyman and Y. V. Nazarov, Phys. Rev. B 77, 165118 (2008).
M. Buttiker, Y. Imry, R. Landauer, and S. Pinhas, Phys. Rev. B 31, 6207 (1985).
M. Buttiker, Phys. Rev. Lett. 57, 1761 (1986).
Y. V. Nazarov, arXiv:1507.03039, Physica E (submitted).
G. Jaeger, Quantum Information (Springer, Berlin, 2007).
Y. V. Nazarov, Phys. Rev. B 84, 205437 (2011).
M. H. Ansari and Y. V. Nazarov, Phys. Rev. B 91, 104303 (2015).
M. H. Ansari and Y. V. Nazarov, Phys. Rev. B 91, 174307 (2015).
M. Kindermann and S. Pilgram, Phys. Rev. B 69, 155334 (2004).
R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)
P. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959).
L. P. Pitaevskii and E. M. Lifshitz, Physical Kinetics (Butterworth–Heinemann, Oxford, 2012).
L. S. Levitov, H. W. Lee, and G. B. Lesovik, J. Math. Phys. 37, 4845 (1996).
I. Klich and L. S. Levitov, Phys. Rev. Lett. 102, 100502 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution for the JETP special issue in honor of L.V. Keldysh’s 85th birthday
The article is published in the original.
Rights and permissions
About this article
Cite this article
Ansari, M., Nazarov, Y.V. Keldysh formalism for multiple parallel worlds. J. Exp. Theor. Phys. 122, 389–401 (2016). https://doi.org/10.1134/S1063776116030134
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776116030134