Fluctuations interactions

Nuclear spin relaxation is caused by fluctuating interactions involving nuclear spins. We write the corresponding Hamiltonians (which act as perturbations to the static or time-averaged Hamiltonian, detemiming the energy level structure) in tenns of a scalar contraction of spherical tensors ... 

The liquid phase cage model accounts for appearance in the spectrum of resolved rotational components by effective isotropization of the rapidly fluctuating interaction. This interpretation of the gas-like spectral manifestations seems to be more adequate to the nature of the liquid phase, than the impact description or the hypothesis of over-barrier rotation. Whether it is possible to obtain in the liquid cage model triplet IR spectra of linear rotators with sufficiently intense Q-branch and gas-like smoothed P-R structure has not yet been investigated. This investigation requires numerical calculations for spectra at an arbitrary value of parameter Vtv. 

Now we consider thermodynamic properties of the system described by the Hamiltonian (2.4.5) it is a generalized Hamiltonian of the isotropic Ashkin-Teller model100,101 expressed in terms of interactions between pairs of spins lattice site nm of a square lattice. Hamiltonian (2.4.5) differs from the known one in that it includes not only the contribution from the four-spin interaction (the term with the coefficient J3), but also the anisotropic contribution (the term with the coefficient J2) which accounts for cross interactions of spins a m and s m between neighboring lattice sites. This term is so structured that it vanishes if there are no fluctuation interactions between cr- and s-subsystems. As a result, with sufficiently small coefficients J2, we arrive at a typical phase diagram of the isotropic Ashkin-Teller model,101 102 limited by the plausible values of coefficients in Eq. (2.4.6). At J, > J3, the phase transition line... 

W. Parke, and A. Salyers Charge fluctuation interactions and molecular biophysics. Biophys. 9, 433 (1965). 

Table P.9.c. Low-frequency ionic-fluctuation interactions between and across anisotropic media (magnetic terms neglected)...

The motion of R1 in helices has been studied in detail, and this is the case relevant for analysis of rhodopsin. At helix surface sites where R1 has no interactions with other side chains or main-chain atoms, the motion is anisotropic and can be accurately modeled by a single order parameter (.S ) and effective correlation time (tc) (Columbus etal., 2001). This simple anisotropic motion is expected to be the same at all helical surface sites unless modulated by direct interactions of R1 with other groups in the protein and/or by local backbone fluctuations. Interactions of R1 with the environment and local backbone fluctuations are qualitatively distinguishable by their opposite effects on motion the former reduces and the latter increases the mobility relative to a noninteracting reference on the surface of a rigid helical segment. 

Numerous factors influence the bioavailability of chemicals to organisms temperature fluctuations, interactions with other pollutants, soil and sediment... 

Fluctuating Dipriles.—The varying dipoles in a aystalline material are described in terms of (more or less) anharmonic osdllations, though in some molecular crystals at higher temperatures this is a rather forced description of the movement of molecules in a rotator phase. In a fluid medium, with molecules in (more or less) regular rotation, the molecular dipole will not only fluctuate in magnitude, as well as direction, but these fluctuations interact with each other and with the fluctuations of other dipoles. 

The response to the fluctuation s increases with the wavenumber j, but the effect is small until j" approaches 1// ", i.e., until the wavelength diminishes to the order of magnitude 2nR, in the micrometer to nanometer range. It is on this same small scale that chemical fluctuations interact with the material s deformation behavior, as discussed in Chapters 14-16. 

H. Tanaka, A simple physical model of liquid-glass transition Intrinsic fluctuating interactions and random fields hidden in glass-forming liquids. J. Phys. Condens. Matter 10, L207-L214 (1998). 

One should emphasize that the coordinates describing the vibrations of an inertial polarization should be considered as the reactive coordinates equivalent to intramolecular coordinates, and in the absence of the latter, the vibrations of an inertial polarization of the medium are the only factor which provides matching of the electronic energy levels of a donor and of an acceptor. However, as shown in Ref. [10], the effect of a medium in electron transfer reactions is not reduced to matching of the electronic energies only. There are some additional effects caused by the dynamical behaviour of a medium in the electronic transfer process. One of them consists in the fact that the vibration of polarization near an acceptor produces the electric field which is the interaction, additional with respect to the direct interaction between an electron and an acceptor, leading to electron transfer to an acceptor. In some cases this fluctuational interaction exceeds the direct interaction with an acceptor. 

Fluctuating interactions with the solvent thus broaden the vibronic absorption lines of the chromophore and shift them to higher energies relative to Eg. As discussed above, however, the mean energy of interaction can shift Eg either upward or downward depending on the chromophore and the solvent. We will discuss generalized solvent coordinates further in Chaps. 5 and 10. 

Fig. 10.6 (A) A fluctuating interaction energy, V(r), with a mean value (F) of zero and a mean...

The increment ofp evolves from time t until time t, undergoing oscillations in the complex plane at frequency ojab and decaying with rate constant Yab as a result of fluctuating interactions with the surroundings. The fraction of the increment remaining at time t is ex [—(ia>ab + Ya ... 

Oscillations of fluorescence, stimulated emission and excited-state absorption have been studied by pump-probe techniques and fluorescence upconversion, and have been seen in numerous small molecules in solution (Fig. 11.7A [120, 122-124]), and also in photosynthetic bacterial reaction centers [27, 125, 126]. They typically damp out over the course of several picoseconds as a result of vibrational relaxations and dephasing. Vibrational coherences generally decay more slowly than electronic coherences because the energies of vibrational states are not coupled as strongly to fluctuating interactions with the surroundings. Vibrational dephasing also tends to be less dependent on the temperature. 

Single-chain-in-mean-field (SCMF) simulation [40-42, 86] is an approximate, computational method that retains the computational advantage of self-consistent field theory but additionally includes fluctuation effects because, in contrast to self-consistent theory, SCMF simulations aim at preserving the instantaneous description of the fluctuating interactions of a segment with its environment. In this partide-based simulation technique, one studies an ensemble of molecules in fluctuating, real, external fields. The explicit particle coordinates are the degrees of freedom and not the collective variables, densities and fields. 

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