Time-dependent perturbation theory, for

R. Dickman, I. Jensen. Time-dependent perturbation theory for nonequilibrium lattice models. Phys Rev Lett 67 2391-2394, 1991. 

Some authors have described the time evolution of the system by more general methods than time-dependent perturbation theory. For example, War-shel and co-workers have attempted to calculate the evolution of the function /(r, Q, t) defined by Eq. (3) by a semi-classical method [44, 96] the probability for the system to occupy state v]/, is obtained by considering the fluctuations of the energy gap between and 11, which are induced by the trajectories of all the atoms of the system. These trajectories are generated through molecular dynamics models based on classical equations of motion. This method was in particular applied to simulate the kinetics of the primary electron transfer process in the bacterial reaction center [97]. Mikkelsen and Ratner have recently proposed a very different approach to the electron transfer problem, in which the time evolution of the system is described by a time-dependent statistical density operator [98, 99]. 

These three factors are included in the expression derived by Robinson and Frosch from time-dependent perturbation theory, for the nonradiative energy transfer or radiationless transition probability kNR per unit time,... 

B. Simon, Convergence of time dependent perturbation theory for autoionizing states of atoms, Phys. Lett. A 36 (1976) 23. 

Supplement 4A. Time-Dependent Perturbation Theory for Radiative Transitions... 

In the framework of the Born-Oppenheimer approximation, radiationless transitions from one surface to another are impossible. (See, e.g., Michl and BonaCit -Koutecky, 1990.) It is therefore necessary to go beyond the Born-Oppenheimer approximation and to include the interaction between different electronic molecular states through the nuclear motion in order to be able to describe such transitions. Using the time-dependent perturbation theory for the rate constant of a transition between a pair of states one arrives at... 

The results we have obtained are valid for a single frequency and, if we wish to be able to perform time-dependent perturbation theory for a general perturbation of the form... 

Fujisaki, H. Zhang, Y. Straub, J. E., Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins. J. Chem. Phys. 2006, 124, 144910. 

Applicability of Time-Dependent Perturbation Theory for Electron Transfer Processes at Electrodes... 

Eight or nine of the eleven chapters in this book can be comfortably accommodated within a one-semester course. The underlying time-dependent perturbation theory for molecule-radiation interactions is emphasized early, revealing the hierarchies of multipole and multiphoton transitions that can occur. Several of the chapters are introduced using illustrative spectra from the literature. This technique, extensively used by Herzberg in his classic series of monographs, avoids excessive abstraction before spectroscopic applications are reached. Diatomic rotations and vibrations are introduced explicitly in the context of the Born-Oppenheimer principle. Electronic band spectra are examined with careful attention to electronic structure, angular momentum... 

With the formalism of the time-dependent perturbation theory for interaction between an electron and the classical radiation field, within the electric dipole and Bom-Oppenheimer approximations, the isotropic absorption cross section is given by [17]... 

Calculations of atomic and molecular hyperpolarizabilities usually proceed via time-dependent perturbation theory for the perturbed atomic states. Even for molecules of modest size, the calculation of the complete set of unperturbed wavefunctions, and exact calculation of the hyperpolarizabilities, is prohibitively difficult. Liquid crystals typically consist of organic molecules with aromatic cores, and there is considerable experimental [10] and theoretical [11, 12] evidence to indicate that the dominant contribution to the polarizabilities originates from the delocalized r-electrons in conjugated regions of these molecules. Even considering only r-electrons the calculations rapid-... 

Goldstone s original treatment of the many-body problem employed time-dependent perturbation theory for what is essentially a time-independent problem. In the Goldstone picture, time is taken to progress from the bottom to the top of the diagram. For example, the diagram ... 

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