Abstract
This article presents a tutorial introduction to a recently developed real-time renormalization group method [1].It describes nonequilibrium properties of discrete quantum systems coupled linearly to an environment.We illustrate the technique by a simple and exactly solvable model:A quantum dot consisting of a single non-degenerate level coupled to two reservoirs.The article is intended for advanced students.Besides elementary quantum mechanics and statistical mechanics, it requires knowledge of second quantization and Wick’s theorem.The latter topics can be learned easily from standard textbooks,see e.g.Ref.[2].
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References
H. Schoeller and J. König, cond-mat/9908404.
A.L. Fetter and J.D. Walecka,”Quantum Theory of Many Particle Systems”, (McGraw-Hill, New York,1971).
P.W. Anderson, J.Phys.C 3, 2346 (1970);K.G.Wilson,Rev.Mod.Phys. 47,773 (1975).
H.R. Krishnamurthy, J.W. Wilkins, and K.G. Wilson, Phys.Rev. B 21,1003(1980);Phys.Rev.21,1043 (1980).
T.A. Costi, A.C. Hewson, and V. Zlatić, J.Phys. C 6, 2519 (1994).
S.D. Glazek and K.G. Wilson, Phys.Rev. D 48, 5863 (1993);F.Wegner, Ann.Physik (Leipzig),3, 77 (1994).
P. Joyez, V. Bouchiat, D. Esteve, C. Urbina, and M.H. Devoret, Phys.Rev.Lett. 79, 1349 (1997).
D. Goldhaber-Gordon et al.,Nature (London), 391, 156 (1998);Phys.Rev.Lett. 81, 5225 (1998); S.M.Cronenwett et al.,Science 281,540 (1998);J.Schmid et al., Physica B 256–258,182 (1998); F.Simmel et al.,Phys.Rev.Lett.83,804 (1999).
H. Schoeller, in ‘Mesoscopic Electron Transport’,eds.L.L. Sohn et al.(Kluwer 1997),p.291; J.König,”Quantum Fluctuations in the Single-Electron Transistor ”, Shaker (Aachen,1999).
J. König and H. Schoeller, Phys.Rev.Lett.81,3511 (1998).
C. Caroli et al., J.Phys.C 4, 916 (1971); J.Phys.C 5,21 (1972).
A.C. Hewson, The Kondo Problem to Heavy Fermions, (Cambridge University Press,1993).
I. Affleck and A.W.W. Ludwig, Nucl.Phys. B 360, 641 (1991).
K. Blum, Density Matrix Theory and Applications,2nd edition (Plenum Press, 1996).
E. Fick and G. Sauermann, The Quantum Statistics of Dynamic Processes, (Springer,1990).
C.W. Gardiner,Quantum noise, Springer Series in Synergetics 56,(Springer-Verlag,Berlin,1991).
S.E. Barnes, J.Phys.F:Metal Phys.6,1375 (1976);7, 2637 (1977).
F. Kuczera, H. Schoeller, J. König, and G. Schön,submitted to Europhys.Lett..
T. Pohjola, J. König, H. Schoeller, and G. Schön, Phys.Rev.B 59,7579 (1999).
M. Keil and H. Schoeller,preprint 1999.
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Schoeller, H. (1999). An Introduction to Real-Time Renormalization Group. In: Brandes, T. (eds) Low-Dimensional Systems. Lecture Notes in Physics, vol 544. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46438-7_7
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DOI: https://doi.org/10.1007/3-540-46438-7_7
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