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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 Semiconductor Bloch equations ： ウィキペディア英語版 Semiconductor Bloch equations The semiconductor Bloch equations〔 Lindberg, M.; Koch, S. W. (1988). "Effective Bloch equations for semiconductors". ''Physical Review B'' 38 (5): 3342–3350. doi:(10.1103%2FPhysRevB.38.3342 )〕 (abbreviated as SBEs) describe the optical response of semiconductors excited by coherent classical light sources, such as lasers. They are based on a full quantum theory, and form a closed set of integro-differential equations for the quantum dynamics of microscopic polarization and charge carrier distribution.〔 Schäfer, W.; Wegener, M. (2002). ''Semiconductor Optics and Transport Phenomena''. Springer. ISBN 3540616144. 〕〔 Haug, H.; Koch, S. W. (2009). ''Quantum Theory of the Optical and Electronic Properties of Semiconductors'' (5th ed.). World Scientific. p. 216. ISBN 9812838848. 〕 The SBEs are named after the structural analogy to the optical Bloch equations that describe the excitation dynamics in a two-level atom interacting with a classical electromagnetic field. As the major complication beyond the atomic approach, the SBEs must address the many-body interactions resulting from Coulomb force among charges and the coupling among lattice vibrations and electrons. The SBEs are one of the most sophisticated and successful approaches to describe optical properties of semiconductors originating from the classical light–matter interaction, once the many-body effects are systematically included. ==Background== The optical response of a semiconductor follows if one can determine its macroscopic polarization $\backslash mathbf$ as a function of the electric field $\backslash mathbf$ that excites it. The connection between $\backslash mathbf$ and the microscopic polarization $P\_$ is given by $$ \mathbf = \mathbf\, \sum_} + \operatorname\;, where the sum involves crystal-momenta $\backslash hbar$ of all relevant electronic states. In semiconductor optics, one typically excites transitions between a valence and a conduction band. In this connection, $\backslash mathbf$ is the dipole matrix element between the conduction and valence band and $P\_\_\}$ by using the Heisenberg equation of motion $$ \mathrm \hbar \frac t} \langle \hat}," TITLE="\hat_ \rangle\;. Due to the many-body interactions within $\backslash hat\_\}$ couples to new observables and the equation structure cannot be closed. This is the well-known BBGKY hierarchy problem that can be systematically truncated with different methods such as the cluster-expansion approach.〔Kira, M.; Koch, S. W. (2011). ''Semiconductor Quantum Optics''. Cambridge University Press. ISBN 978-0521875097.〕 At operator level, the microscopic polarization is defined by an expectation value for a single electronic transition between a valence and a conduction band. In second quantization, conduction-band electrons are defined by fermionic creation and annihilation operators $\backslash hat^\backslash dagger\_\_^\backslash dagger\_\_\}\; =\; \backslash langle\; \backslash hat^\backslash dagger\_\_\}\; =\; \backslash langle\; \backslash hat^\backslash dagger\_\_\}$ term) or vice versa ($P\_\_^\backslash dagger\_\_\_^\backslash dagger\_\_\_^\backslash dagger\_\{v,\; \backslash mathbf\{k\}\}\; \backslash rangle$ that are left to the valence band due to optical excitation processes. 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「Semiconductor Bloch equations」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.