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In this talk I will discuss the application of the real-time renormalization group method in the Laplace representation [1] to the study of the time evolution in quantum impurity models. This method allows to determine an effective Liouvillian which governs the time dynamics of the reduced density matrix of a quantum impurity. I will review our recent results for the Kondo model [2], the interacting resonant level model [3,4], and various relations to the spin-boson model, focusing on qualitatively new features which arise in the time evolution of observables beyond the Markovian approximation. An outlook is presented for the application of the method to the description of the time evolution in the strong coupling regime.
[1] H. Schoeller, Eur. Phys. J. Special Topics 168, 179 (2009). [2] M. Pletyukhov, D. Schuricht, and H. Schoeller, PRL 104, 106801 (2010). [3] C. Karrasch, S. Andergassen, M. Pletyukhov, D. Schuricht, L. Borda, V. Meden, and H. Schoeller, EPL 90, 30003 (2010). [4]S. Andergassen, M. Pletyukhov, D. Schuricht, H. Schoeller, L. Borda, arXiv:1010.5666, to be published in Phys. Rev. B. |
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