Coherence classical

Consequently, in considering what properties of a system favor coherence, the mass or size of the species will be less important than the underlying classical coherence. We know that a harmonic oscillator is coherent classically because the oscillators of each ensemble component have the same frequency and quantum mechanically because all energy spacings are equal. Hence coherence is favored by harmonic behavior regardless of the system size. 

Fig. 12. Predicted variation of the second moment for low density polyethylene of draw ratio 5-7, based on the coherent classical rotation model (after Folkes and Ward).

A comprehensive discussion of wavepackets, classical-quantum correspondence, optical spectroscopy, coherent control and reactive scattering from a unified, time dependent perspective. 

The generalized Prony analysis can extract a great variety of information from the ENDyne dynamics, such as the vibrational energy vib arrd the frequency for each normal mode. The classical quantum connection is then made via coherent states, such that, say, each nomral vibrational mode is represented by an evolving state... 

Panel). Most of the basic processes were established almost a century and a half ago, but a coherent theoretical explanation was not available until the publication in 1938 of the classic paper by R, W. Gurney and N. F. Mott. (Pwc. Roy. Soc. A164, 151-67 (1938)). Since then the subject has stimulated a vast amount of fundamental research in wide areas of solid-state chemistry and physics. 

Electron Nuclear Dynamics (48) departs from a variational form where the state vector is both explicitly and implicitly time-dependent. A coherent state formulation for electron and nuclear motion is given and the relevant parameters are determined as functions of time from the Euler equations that define the stationary point of the functional. Yngve and his group have currently implemented the method for a determinantal electronic wave function and products of wave packets for the nuclei in the limit of zero width, a "classical" limit. Results are coming forth protons on methane (49), diatoms in laser fields (50), protons on water (51), and charge transfer (52) between oxygen and protons. 

Classical dynamics is studied as a special case by analyzing the Ehrenfest theorem, coherent states (16) and systems with quasi classical dynamics like the rigid rotor for molecules (17) and the oscillator (18) for various particle systems and for EM field in a laser. 

Usually, at least several hundreds of fringes are measured and characterized. Taking the classical example of X-ray diffraction, coherent domains are defined by the stacks of polyaromatic layers (Figure 2). The coherent domains are distinguished from the single layers and their relative... 

As an alternative to QDs, silicon can be doped with single atom impurities, in particular phosphorus, which acts as an electron donor. Donors can be implanted individually with a precision of about 10 nm. Either the 31P nuclear spin or the unpaired electron can be used as qubits [63, 64]. An advantage of silicon is its widespread use in current electronics, meaning that QC might profit from methods and technologies already developed for their classical cousins . Also, spins in silicon can attain extremely high coherence times experiments on 28 Si-enriched silicon show spin coherence times T2 exceeding 10 s [65]. The read-out and coherent manipulation of individual spin qubits in silicon have been recently achieved [66]. 

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