Superpositional transition

An alternative perspective is as follows. A 5-frmction pulse in time has an infinitely broad frequency range. Thus, the pulse promotes transitions to all the excited-state vibrational eigenstates having good overlap (Franck-Condon factors) with the initial vibrational state. The pulse, by virtue of its coherence, in fact prepares a coherent superposition of all these excited-state vibrational eigenstates. From the earlier sections, we know that each of these eigenstates evolves with a different time-dependent phase factor, leading to coherent spatial translation of the wavepacket. 

State I ) m the electronic ground state. In principle, other possibilities may also be conceived for the preparation step, as discussed in section A3.13.1, section A3.13.2 and section A3.13.3. In order to detemiine superposition coefficients within a realistic experimental set-up using irradiation, the following questions need to be answered (1) Wliat are the eigenstates (2) What are the electric dipole transition matrix elements (3) What is the orientation of the molecule with respect to the laboratory fixed (Imearly or circularly) polarized electric field vector of the radiation The first question requires knowledge of the potential energy surface, or... 

Hamiltonian does not give rise to any crystalline order in the system. By employing models hke this, the quench-rate and chain-length dependence of the glass transition temperature, as well as time-temperature superposition, similar to experiments [23], were investigated in detail. 

Another important characteristic aspect of systems near the glass transition is the time-temperature superposition principle [23,34,45,46]. This simply means that suitably scaled data should all fall on one common curve independent of temperature, chain length, and time. Such generahzed functions which are, for example, known as generalized spin autocorrelation functions from spin glasses can also be defined from computer simulation of polymers. Typical quantities for instance are the autocorrelation function of the end-to-end distance or radius of gyration Rq of a polymer chain in a suitably normalized manner ... 

By exploiting the fact that such rules obey an additive superposition principle -namely, that if >add is the global transition function, then + ob) = (<7a) +... 

Quantum Cellular Automata (QCA) in order to address the possibly very fundamental role CA-like dynamics may play in the microphysical domain, some form of quantum dynamical generalization to the basic rule structure must be considered. One way to do this is to replace the usual time evolution of what may now be called classical site values ct, by unitary transitions between fe-component complex probability- amplitude states, ct > - defined in sncli a way as to permit superposition of states. As is standard in quantum mechanics, the absolute square of these amplitudes is then interpreted to give the probability of observing the corresponding classical value. Two indepcuidently defined models - both of which exhibit much of the typically quantum behavior observed in real systems are discussed in chapter 8.2,... 

Figure 15-3 shows the optical absorption spectrum of a MEH-PPV/C60 film with different C, content compared to the optical absorption spectrum of the components alone. The peak at 2.5 eV is identified as the n-n absorption of MEH-PPV and is clearly observed along with the first dipole-allowed transition in C(l0 (at 3.75 eV). The spectrum is a simple superposition of the two components. Further-... 

We use a7r/2 — vr — vr/2 pulse sequence to coherently divide, deflect and finally recombine an atomic wavepacket. The first vr/2 pulse excites an atom initially in the l,p) state into a coherent superposition of states l,p) and 2,p + hkeff). If state 2) is stable against spontaneous decay, the two parts of the wavepacket will drift apart by a distance hkT/m in time T. Each partial wavepacket is redirected by a vr pulse which induces the transitions... 

The WLF equation can be widely applied, and demonstrates the equivalence of time and temperature, the so-called time-temperature superposition principle, on the mechanical relaxations of an amorphous polymer. The equation holds up to about 100° above the glass transition temperature, but after that begins to break down. 

The description of states participating in a spin-state transition as electronic isomers with discrete nuclear configurations, in particular different metal-ligand distances, requires that separate electronic and vibrational spectra of the two spin states exist. Indeed, a superposition of the individual vibrational spectra of the two states is in general observed, the relative contribution of the states being a function of temperature [41, 139, 140, 141, 142]. This observation sets a lower limit for the spin-state lifetime longer than the nuclear vibrational period, i.e.,... 

Most Mossbauer spectra are split because of the hyperfine interaction of the absorber (or source) nuclei with their electron shell and chemical environment which lifts the degeneracy of the nuclear states. If the hyperfine interaction is static with respect to the nuclear lifetime, the Mossbauer spectrum is a superposition of separate lines (i), according to the number of possible transitions. Each line has its own effective thickness t i), which is a fraction of the total thickness, determined by the relative intensity W of the lines, such that t i) = Wit. 

Time-cure superposition is valid for materials which do not change their relaxation exponent during the transition. This might be satisfied for chemical gelation of small and intermediate size molecules. However, it does not apply to macromolecular systems as Mours and Winter [70] showed on vulcanizing polybutadienes. 

In microphase-separated systems, ESR spectra may consist of a superposition of two contributions, from nitroxides in both fast and slow-tumbling regimes. Such spectra provide evidence for the presence of two types of domains with different dynamics and transition temperatures. This case was detected for a HAS-derived nitroxide radical in heterophasic polyfacrylonitrile-butadiene-styrene) (ABS) as shown in Figure 5, the fast and slow components in the ESR spectrum measured represent nitroxide radicals located in butadiene-rich (B-rich) and styrene/acrylonitrile-rich (SAN-rich) domains, respectively [40]. These two components were determined by deconvoluting the ESR spectrum of HAS-NO measured at 300 K. 

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