Coupling linear

To verify effectiveness of NDCPA we carried out the calculations of absorption spectra for a system of excitons locally and linearly coupled to Einstein phonons at zero temperature in cubic crystal with one molecule per unit cell (probably the simplest model of exciton-phonon system of organic crystals). Absorption spectrum is defined as an imaginary part of one-exciton Green s function taken at zero value of exciton momentum vector... 

The same relations (11) and (12) hold for the Gibbs free energy in the (N, p,T) ensemble. Equation (11) is also valid for a quanmm mechanical system. Note that for a linear coupling scheme such as Eq. (10), the first term on the right of Eq. (12) is zero the matrix of second derivatives can then be shown to be definite negative, so that the free energy is a concave function of the Xi. 

The free energy derivatives are also related to the coefficients in a Taylor expansion of the free energy with respect to X. In the case of linear coupling, we let Eba = XdJ-a — Up,)lkT in Eq. (9) we obtain... 

The most general problem should be that of a particle in a nonseparable potential, linearly coupled to an oscillator heat bath, when the dynamics of the particle in the classically accessible region is subject to friction forces due to the bath. However, this multidimensional quantum Kramers problem has not been explored as yet. 

Of particular interest is the model of a bath as a set of harmonic oscillators qj with frequencies cOj, which are linearly coupled to the tunneling coordinate... 

Coupled—Pair Functional (ACPF) and Coupled Electron Pair Approximation (CEPA). The simplest form of CEPA, CEPA-0, is also known as Linear Coupled Cluster Doubles (LCCD). 

A transition linearly coupled to the phonon field gradient will experience, from the perturbation theory perspective, a frequency shift and a drag force owing to phonon emission/absorption. Here we resort to the simplest way to model these effects by assuming that our degree of freedom behaves like a localized boson with frequency (s>i. The corresponding Hamiltonian reads... 

Linear coupling approximation, geometric phase theory, 3... 

We are currently extending our study to other wavelengths, especially in the transparent region of the film, X > 7000 angstroms. By examining the linear coupling coefficients and mode shape as a function of wavelength, we should be able, once A0 vs. X is measured, to determine the X 3) Vs. X. 

Instead of this nonlinear coupling, a linear coupling provides an exactly solvable model with the Hamiltonian (S.P. Kim et.al., 2000 2002 2001)... 

As is shown below for the solute, the linear term can be included in the quadratic term by redefining the fluctuation operator. G(m s) is a rectangular matrix obtained from the second cross-derivatives coupling the solute to the solvent l(s m) is a vector obtained by similar procedures from the (dGm(X)/dRs)(n) linear coupling. How to actually perfonn such operation is not directly important now. We assume that, in principle, such operations are feasible. 

For a local sensitivity analysis, Eq. (2.69) may be differentiated with respect to the parameters a to yield a set of linear coupled equations in terms of the elementary sensitivity coefficients, cXM /daj. 

The strategy, usually adopted to achieve a theoretical description of this complex dynamics, is to describe the influence of the solvent environment on the electron-transfer reaction within linear response theory [5, 26, 196, 197] as linear coupling to a bath of harmonic oscillators. Within this model, all properties of the bath enter through a single function called the spectral density [5, 168]... 

Ky represent the frequency and the linear coupling of the yth vibrational mode, respectively. Here, we consider specifically an Ohmic bath described by the spectral density... 

In the usual coupled-cluster hierarchy, MP2 energy functional, while linearized coupled-cluster single-doubles (L-... 

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