Conservation global energy

Lee D and Albrecht A C 1993 On global energy conservation in nonlinear light matter interaction the nonlinear spectroscopies, active and passive Adv. Phys. Chem. 83 43-87... 

Several scenarios for global energy demand and supply by the year 2050 are discussed below. For ease of comparison, they are based on the same assumptions regarding energy demand concern for human welfare and environmental sustainability are assumed to lead to highly efficient energy consumption patterns based on increased concern for materials conservation and emphasis on non-material ("information society") types of activity. 

In the multiple copy MD [77] or locally enhance sampling (LES) [78] method, part of the system simulated is replicated multiple times, e.g. 20 copies of a peptide are simulated in the presence of 1 copy of the solvent. There are no interactions between the multiple copies. The unreplicated atoms feel the mean force of all the copies of the replicated atoms. The mean field generated by the multiple copy ensemble reduces the energy barriers but conserves the global energy minimum [78]. The number of degrees of freedom is reduced in the sense that one simulation with m copies of a subset of the atoms samples to a similar extent to m standard simulations (without multiple copies) in approximately l/m times the simulation time. Applications to peptides in solvent have shown improved sampling of phase space [79, 66]. 

The dimension of the phase space is 2N, as we have N / s and N (p s. If we still have global conservation laws (such as conservation of energy), the net dimension of the phase space is (/phasespace = 2N — (number of conservation laws). The problem is whether a KAM torus can divide the phase space (or energy surface) into two disjoint parts or not. The necessary condition for global drift of chaotic motion is... 

ON GLOBAL ENERGY CONSERVATION IN NONLINEAR LIGHT-MATTER INTERACTION THE NONLINEAR SPECTROSCOPIES, ACTIVE... 

GLOBAL ENERGY CONSERVATION IN NONLINEAR INTERACTION 57 any sth order light-matter interaction (s> 1) is given as... 

The global energy conservation condition, Eq. (4.11), is explicitly demonstrated for resonant processes up to third order (5 3), particularly for resonant passive processes, at exact resonance, where population change can be achieved at a nonquadrature level by the fields. The phase matching condition is assumed, Ak = 0. As before, the material resonance at the one-photon level is taken into account by the complex wave vector, k, = k -I-ik", whose imaginary part is absorbed into the amplitude, ,( ) = sxp[-k" r]. The electrical susceptibility is expressed in terms of the scalar Cartesian component, as given in Eq. (2.17). 

Table II can be utilized to confirm global energy conservation for the composite field/matter system for various resonant three-wave mixing processes when the resonance condition is exactly satisfied. Thus, for singly resonant sum frequency generation with = w, all s are pure imaginary when the resonance condition is exactly satisfied. Thus, according to Eqs. (3.6) and (4.9),...

It can be readily seen from Eqs. (5.2), (5.3), and (5.4), that global energy conservation as given in Eq. (4.11) is achieved in all second order (singly or doubly) resonant passive processes when the resonance conditions are exactly satisfied. 

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