Dynamic field

Griffin RG, Prisner TF (2010) High field dynamic nuclear polarization-the renaissance. Phys Chem Chem Phys 12 5737-5740... 

Kim, S.P. and F.C. Khanna. Thermo Field Dynamics of Time-Dependent Boson and Fermion System, quant-ph, 0308053, (unpublished). 

Basically, two fundamental approaches are used (I) continuum or field dynamics and (2) kinetic theory and nonequilibrium statistical mechanics. The study of fluids tends to be quite complex. 

This section introduced a methodology to move from a verbal description of biocomplexity to its numerical representation. In future studies it will be necessary to take into consideration bottom relief, climate trends, ice field dynamics, detailed components of the trophic pyramid, bottom sediments, and the structure of currents. Also, it will be necessary to add to Formula (6.31) elements describing anthropogenic impacts on the ecosystem considered in a socio-economic sense. 

Thus, we see that in order to obtain the mean field equations of motion, the density matrix of the entire system is assumed to factor into a product of subsystem and environmental contributions with neglect of correlations. The quantum dynamics then evolves as a pure state wave function depending on the coordinates evolving in the mean field generated by the quantum density. As we have seen in the previous sections, these approximations are not valid and no simple representation of the quantum-classical dynamics is possible in terms of single effective trajectories. Consequently, in contrast to claims made in the literature [54], quantum-classical Liouville dynamics is not equivalent to mean field dynamics. 

Fig. 3 Forward rate coefficient kAB(t) as a function of time for f3 = 1.0. The upper (blue) curve is the adiabatic rate, the purple curve is the result obtained by Tully s surface-hopping algorithm, the middle (black) curve is the quantum master equation result, the green curve is the QCL result, and the lowest dashed line (grey) is the result using mean-field dynamics.

P. E. Fielding and C. J. Fielding, Dynamics of lipoprotein transport in the circulatory system. Biochemistry of Lipids, Lipoproteins and Membranes (D. E. Vance and J. Vance eds.), Elsevier, New York, 1991, pp. 427-459. 

In a given work computer simulations devoted to study of nanostructure of abovementioned cryogenic amorphous phases of ice, mechanisms of their transformations, and properties to accumulate methane and hydrogen was realized within the theoretical concepts thermo field dynamics [5] and quantum-field chemistry [6-9]. We developed two models of nanostructures corresponding to HDA-ice and LDA-ice, respectively. Some computations of energetic barriers locking molecules CH4 and H2 inside of amorphous ice were fulfilled. 

Umezawa H., Matsumoto H., Tachiki M. (1982) Thermo field dynamics and condensed states. Amsterdam - New-York - Oxford North-Holland Publishing Company. 

Grinstein, F. F., E. Gutmark, and T. P. Parr. 1995. Near-field dynamics of subsonic, free square jets. A computational and experimental study. J. Physics Fluids 1 1483— 97. 

A large class of time-dependent quantum problems involves strongly interacting coupled fields requiring self-consistent non-perturbative and non-adiabatic approaches. We present here a general framev ork for analyzing these, based on Liouvillean Quantum Field Dynamics. Thus a multifunctional extension of the time-dependent density functional approach to many-body problems is... 

The nature of media effects relates to the fact that, since the microscopic displacement field is the net field to which molecules of the medium are exposed, it corresponds to a fundamental electric field dynamically dressed by interaction with the surroundings. The quantized radiation is in consequence described in terms of dressed photons or polaritons. A full and rigorous theory of dressed optical interactions using noncovariant molecular quantum electrodynamics is now available [25-27], and its application to energy transfer processes has been delineated in detail [10]. In the present context its deployment leads to a modification of the quantum operators for the auxiliary fields d and h, which fully account for the influence of the medium—the fundamental fields of course remain unchanged. Expressions for the local displacement electric and the auxiliary magnetic field operators [27], correct for all microscopic interactions, are then as follows... 

It will be demonstrated below that, within the LCT approach, many aspects of the combined particle/field dynamics can be understood in the classical limit. The temporal change of a quantity A (not explicitly depending on time) is given by... 

Nevertheless, the coupled vibrational-rotational-field dynamics has not been investigated in much detail. An exception is the work of Hornung and de Vivie-Riedle [204], who studied this interplay in connection with optimal control theory (OCT) [17, 42]. With respect to experiment, the new technique of polarization shaping [205-208] is directly connected to the angular motion. 

Buck, M., BouguetBonnet, S., Pastor, R.W., MacKereU, A.D. Importance of the GMAP correction to the CHARMM22 protein force field Dynamics of hen lysozyme. Biophys. J. 2006, 90, L36-8. 

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