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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Dephasing rate SP formula ： ウィキペディア英語版 Dephasing rate SP formula The SP formula for the dephasing rate $\backslash Gamma\_$ of a particle that moves in a fluctuating environment unifies various results that have been obtained, notably in condensed matter physics, with regard to the motion of electrons in a metal 〔B. Altshuler, A. Aronov, and D. Khmelnitskii, J. Phys. C 15, 7367 (1982)〕 〔H. Fukuyama and E. Abrahams, Phys. Rev. B 27, 5976 (1983)〕 〔S. Chakravarty and A. Schmid, Phys. Rep. 140, 193 (1986)〕 .〔A. Stern, Y. Aharonov, and Y. Imry, Phys. Rev. A 41, 3436 (1990)〕 The general case requires to take into account not only the temporal correlations but also the spatial correlations of the environmental fluctuations .〔D. Cohen, Phys. Rev. E 55, 1422 (1997); Phys. Rev. Lett. 78, 2878 (1997)〕 These can be characterized by the spectral form factor $\backslash tilde(q,\backslash omega)$, while the motion of the particle is characterized by its power spectrum $\backslash tilde(q,\backslash omega)$. Consequently at finite temperature the expression for the dephasing rate takes the following form that involves "S" and "P" functions: 〔D. Cohen, J. Phys. A 31, 8199 (1998)〕 〔D. Cohen and Y. Imry, Phys. Rev. B 59, 11143 (1999)〕 〔Y. Imry, Introduction to Mesoscopic Physics (Oxford University Press, 2002)〕 $$ \Gamma_ \ = \ \int d \int \frac \,\tilde(,\omega) \, \tilde(-,-\omega) Due to inherent limitations of the semiclassical (stationary phase) approximation the physically correct procedure is to use the non-symmetrized quantum versions of $\backslash tilde(q,\backslash omega)$ and $\backslash tilde(q,\backslash omega)$. The argument is based on the analogy of the above expression with Fermi-golden-rule calculation of the transitions which are induced by the system-environment interaction. ==Derivation== It is most illuminating to understand the SP formula in the context of the DLD model, which describes motion in dynamical disorder. In order to derive the dephasing rate formula from first principles, a purity-based definition of the dephasing factor can be adopted.〔D. Cohen and B. Horovitz, J. Phys. A 40, 12281 (2007); Europhys. Lett. 81, 30001 (2008)〕 The purity $P(t)=e^$ describes how a quantum state becomes mixed due to the entanglement of the system with the environment. Using perturbation theory, one recovers at finite temperatures at the long time limit $F(t)=\backslash Gamma\_t$ where the decay constant is given by the dephasing rate formula with non symmetrized spectral functions as expected. There is a somewhat controversial possibility to get power law decay of $P(t)$ at the limit of zero temperature.〔D.S. Golubev and A.D. Zaikin, Phys. Rev. Lett. 81, 1074 (1998).〕 The proper way to incorporate Pauli blocking in the many-body dephasing calculation,〔F. Marquardt, J. von Delft, R.A. Smith, and V. Ambegaokar, Phys. Rev. B 76, 195331 (2007)〕 within the framework of the SP formula approach, has been clarified as well.〔D. Cohen, J. von Delft, F. Marquardt and Y. Imry, Phys. Rev. B 80, 245410 (2009)〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dephasing rate SP formula」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.