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Volumn 78, Issue 16, 2008, Pages

Stochastic time-dependent current-density-functional theory: A functional theory of open quantum systems

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EID: 54449095208     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.165105     Document Type: Article
Times cited : (44)

References (49)
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    • This assumption is needed in the proof of the theorem of S-TDCDFT (see Ref.).
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    • Here, remember that dxx- x-dx dx/2x- (dx) 2 /8 x3 + which follows from the standard Taylor expansion of the function x for x 0.
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    • In calculating the time evolution with the SSE we make use of the techniques discussed in Sec. 5.
    • In calculating the time evolution with the SSE we make use of the techniques discussed in Sec. 5.
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    • We expect that, for noninteracting particles, the deviation between the dynamics obtained via the density-matrix equation and the SSE scales as 1/m if m is the number of independent runs on which we average the SSE.
    • We expect that, for noninteracting particles, the deviation between the dynamics obtained via the density-matrix equation and the SSE scales as 1/m if m is the number of independent runs on which we average the SSE.
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    • The initial state is pure and the bath is selecting only a particular state thus forcing the system toward another pure state. Moreover, we can prove that if the system evolves from the ground state, the stochastic part vanishes on this state and then the boson gas remains in the ground state of the interacting Hamiltonian.
    • The initial state is pure and the bath is selecting only a particular state thus forcing the system toward another pure state. Moreover, we can prove that if the system evolves from the ground state, the stochastic part vanishes on this state and then the boson gas remains in the ground state of the interacting Hamiltonian.
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    • Only the dynamics obtained from the SSE is reported in Fig. 6.
    • Only the dynamics obtained from the SSE is reported in Fig. 6.


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