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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 Quantum thermodynamics ： ウィキペディア英語版 Quantum thermodynamics Quantum thermodynamics is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics. The two independent theories address the physical phenomena of light and matter. In 1905 Einstein argued that the requirement of consistency between thermodynamics and electromagnetism...:.〔Einstein, Albert. "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt." Annalen der Physik 322, no. 6 (1905): 132-148.〕 leads to the conclusion that light is quantized obtaining the relation $E=\; h\; \backslash nu$. This paper is the dawn of quantum theory. In a few decades quantum theory became established with an independent set of rules.〔John Von Neumann. Mathematical foundations of quantum mechanics. No. 2. Princeton university press, 1955.〕 Currently quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. It differs from quantum statistical mechanics in the emphasis on dynamical processes out of equilibrium. In addition there is a quest for the theory to be relevant for a single individual quantum system. ==A dynamical view of quantum thermodynamics== There is an intimate connection of quantum thermodynamics with the theory of open quantum systems.〔() Kosloff, Ronnie. "Quantum thermodynamics: A dynamical viewpoint." Entropy 15, no. 6 (2013): 2100-2128.〕 Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics. The main assumption is that the entire world is a large closed system, and therefore, time evolution is governed by a unitary transformation generated by a global Hamiltonian. For the combined system bath scenario, the global Hamiltonian can be decomposed into: :$H=H\_S+H\_B+H\_$ where $H\_S$ is the system’s Hamiltonian, $H\_B$ is the bath Hamiltonian and $H\_$ is the system-bath interaction. The state of the system is obtained from a partial trace over the combined system and bath: $\backslash rho\_S\; (t)\; =Tr\_B\; (\backslash rho\_\; (t))$. Reduced dynamics is an equivalent description of the systems dynamics utilizing only systems operators. Assuming Markov property for the dynamics the basic equation of motion for an open quantum system is the Lindblad equation(L-GKS):〔Lindblad, G. On the generators of quantum dynamical semigroups. Comm. Math. Phys. 1976, 48, 119–130.〕〔 6. Gorini, V.; Kossakowski, A.; Sudarshan, E.C.G. Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 1976, 17, 821–825.〕 :$\backslash dot\backslash rho\_S=-()+L\_D(\backslash rho\_S)$ $H\_S$ is a (Hermitian) Hamiltonian part and $L\_D$: :$L\_D(\backslash rho\_S)=\backslash sum\_n\; \backslash left(V\_n\backslash rho\_S\; V\_n^\backslash dagger-\backslash frac\backslash left(\backslash rho\_S\; V\_n^\backslash dagger\; V\_n\; +\; V\_n^\backslash dagger\; V\_n\backslash rho\_S\backslash right)\backslash right)$ is the dissipative part describing implicitly through system operators $V\_n$ the influence of the bath on the system. The Markov property imposes that the system and bath are uncorrelated at all times $\backslash rho\_=\backslash rho\_s\; \backslash otimes\; \backslash rho\_B$. The L-GKS equation is unidirectional and leads any initial state $\backslash rho\_S$ to a steady state solution which is an invariant of the equation of motion $\backslash dot\; \backslash rho\_S(t\; \backslash rightarrow\; \backslash infty\; )\; =\; 0$.〔 The Heisenberg picture supplies a direct link to quantum thermodynamic observables. The dynamics of a system observable represented by the operator, $O$, has the form: :$\backslash frac\; =\backslash frac\; (O)\; +L\_D^$ *(O) +\frac where the possibility that the operator, $O$ is explicitly time-dependent, is included. 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「Quantum thermodynamics」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.