Crossover localization

Single chains confined between two parallel purely repulsive walls with = 0 show in the simulations the crossover from three- to two-dimensional behavior more clearly than in the case of adsorption (Sec. Ill), where we saw that the scaling exponents for the diffusion constant and the relaxation time slightly exceeded their theoretical values of 1 and 2.5, respectively. In sufficiently narrow slits, D density profile in the perpendicular direction (z) across the film that the monomers are localized in the mid-plane z = Djl so that a two-dimensional SAW, cf. Eq. (24), is easily established [15] i.e., the scaling of the longitudinal component of the mean gyration radius and also the relaxation times exhibit nicely the 2 /-exponent = 3/4 (Fig. 13). 

A quantitative analysis of scattering data, originating from the crossover regime between short-time Rouse motion and local reptation, needs explicit consideration of the initial Rouse motion neglected by de Gennes. Ronca [50] proposed an effective medium approach, where he describes the time-dependent... 

Q-dependence of the plateau levels. The results for the model parameters are given in Table 3. The crossover time xe = 15 ns (T = 492 K) calculated with Eq. (41b) agrees well with the observed spectral shape in dividing the initial fast decay from the plateau-like behavior at longer times. Figure 25 (lower part) compares the experimental spectra for times longer than xe with the local... 

Characteristic Rouse times for chains with bending elasticity Terminal time for reptation Crossover time Rouse, local reptation Characteristic Rouse times for the all-rotational model Rouse time... 

We next consider the effective force balance for all >N variables, while treating the system as an unconstrained system. For simplicity, we consider the case in which the crossover from ballistic motion to diffusion occurs at a timescale much less than any characteristic relaxation time for vibrations of the hard coordinates, so that the vibrations are overdamped, but in which the vibrational relaxation times are much less than any timescale for the diffusion of the soft coordinates. In this case, we may assume local equilibration of all 3N momenta at timescales of order the vibration time. Repeating the analysis of the Section V.A, while now treating all 3N coordinates as unconstrained, yields an effective force balance... 

Fig. 1. Modified periodic table showing the itinerant vs. localized character of unsaturated transition shells. Bonding is contrasted to magnetic moment formation, to illustrate the band-like vs. atomic-like behaviour of wavefunctions. The dashed region represents the crossover between the two situations (from Ref. 1)...

On the basis of the known electronic properties of actinides (which have been discussed elsewhere in this book), theoreticians had distinguished the 5f itinerant behaviour of light actinide metals from the 5 f localized behaviour of heavy actinide metals from Am on. The crossover, presented often as a Mott transition, had been predicted to occur between Pu and Am metal, due to the localized character of the 5f state in the latter. Photoemission spectroscopy demonstrates this phenomenon directly with the observation of a 5 f multiplet away from the Fermi level. The detailed description of this peak is certainly complicated, as often happens for response of localized states in photoemission on the other hand (Fig. 17) the contrast to the emission of Pu metal is convincing. 

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