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Simulation of Crystalline Nanoporous Materials and the Computation of Adsorption/Diffusion Properties
Published in T. Grant Glover, Bin Mu, Gas Adsorption in Metal-Organic Frameworks, 2018
The fluctuation–dissipation theorem relies on the assumption that the response of a system in thermodynamic equilibrium to a small applied force is the same as its response to a spontaneous fluctuation [317]. Therefore, the theorem connects the linear response relaxation of a system from a prepared nonequilibrium state to its statistical fluctuation properties in equilibrium. Often the linear response takes the form of one or more exponential decays. Close to equilibrium linear response theory (and linear irreversible thermodynamics) provide a relatively complete treatment [91].
The spontaneous emission rate determination of a molecule near a perfect conductive wall
Published in Molecular Physics, 2021
Hossein Falinejad, Maryam Akhgar
In the Fermi's golden rule, by expanding the electric field operator in frequency space, the spontaneous emission rate of an excited atom or molecule can be written in terms of the electric field operator correlation function (relation (13)). Therefore, using the explicit form of the electric field operator and then taking the expectation value in vacuum state is the natural way for evaluating the electric field correlation function and then the spontaneous emission rate determination. In this paper by using the vector potential operator expressions (3), (4) and the commutation relations (5) and (6), the spontaneous mission rate of an exited molecule near a perfect conductive wall is evaluated. The electric field correlation function (as given by (29)) can also be written in terms of the imaginary part of the vector potential Green function (via Fluctuation-Dissipation theorem and Kubo’s Formula in statistical mechanics). In this paper also by using the required vector potential Green function, the spontaneous emission rate of an excited molecule in vicinity a perfect conductive wall is evaluated. The field quantizationn approach and the Green function approach give the same expression for the spontaneous emission rate near the conductive wall, and therefore the consistency between the two approaches (in this particular problem) is shown.
Adiabatic and nonadiabatic dynamics in classical mechanics for coupled fast and slow modes: sudden transition caused by the fast mode against the slaving principle
Published in Molecular Physics, 2018
The adiabatic dynamics attained as above seems quite natural. Looking obvious, the formalism can be applied to a nontrivial problems if we take a really macroscopic system as the slow subsystem and the fast mode is chose in a microscopic dynamics of molecular level. As in the fluctuation-dissipation theorem in statistical mechanics, we can attain some insight about the macro-micro relationship in mechanics as in the dynamics of friction. We show such an example in Appendix 1.
Statistical quasi-particle theory for open quantum systems
Published in Molecular Physics, 2018
Hou-Dao Zhang, Rui-Xue Xu, Xiao Zheng, YiJing Yan
Gaussian bath covers the Caldeira–Leggett model [50,51], which is widely adopted in the study of decoherence problems. It covers also the electronic transfer coupling model that is commonly used in quantum transport and quantum impurity physics research [52]. The simplification of Gaussian bath is rooted at the underlying Gaussian–Wick's theorem. This is concerned with the thermodynamical average, , over the equilibrium canonical ensembles of the bare bath at a given temperature [26–28]. The extension to nonequilibrium grand canonical ensembles for bath reservoirs in the presence of bias chemical potentials is rather trivial [33,44]. Apparently, one could always set the total composite Hamiltonian in the form of HT = HS + hB + HSB, with the system-and-bath coupling the form of Equation (2.1) satisfying . The Gaussian–Wick's statistical thermodynamics with zero means is then completely characterised by the second cumulants. Involved are simply the interacting bath correlation functions. These are further related to the bath hybridisation spectral densities via the fluctuation–dissipation theorem [27,28], owing to the underlying detailed-balance relation [25]. In other words, the above bath characterisation completely determines the influences of linearly coupling environments on the reduced system dynamics; cf. Section 2.3. This is also the reason for the Feynman–Vernon influence functional path integral formalism being exact in the present bath model [26,27]. It is worth to note that the path integral formalism adopts the initial factorisation ansatz, , for the total system-and-bath density operator. As the differential-equation counterpart to the influence functional path integral theory, the HEOM formalism would in principle also suffer this problem. On the other hand, the DEOM construction formally starts with an arbitrary initial ρT(t0).