Third order transitions physical meaning

PHYSICAL MEANING OF AN APPARENT THIRD ORDER TRANSITION... 

The existence of an apparent third order transition above Tg was noted independently by Boyei and by Hocker et a1. No attempt at a physical explanation was made in either case. It was noted in the first instance that there was a discontinuity in d HIdT in the second case, a discontinuity in d VIdP. This current DSC data on polystyrene, as well as similar results on a number of polymers, when coupled with the data discussed in ref. 21 and Fig. 1, suggests that at least preliminary discussions of the physical meaning of a third order transition are in order. 

Here another source of a conceptual problem of the seeond order-approach appears. The standard formulation of the J-O theory, even if extended by the dynamic coupling model, is based on the single configuration approximation. This means that in such a description all the eleetron correlation effects are neglected and it is well known that the transition amplitude strongly depends on them. At this point also the spin-orbit interactions should be taken into consideration as possibly important in the description of the spectroscopic patterns of the lanthanides. In the case of all of these possibly important physical mechanisms there is a demand for an extension of the standard Judd-Ofelt formulation. The transition amplitude in equation (10.17) has to be modified by the third-order contributions that originate from various perturbing operators introduced in addition to the crystal field potential that plays a... 

It is possible to identify all of these different contributions to the intensity parameters when deriving their tensorial form explicitly at the second, third, or even higher orders of perturbation approach. It is impossible however to go backwards and select parts of fitted parameters and assign to them a particular physical meaning or interpretation. In general, the parameters Tlx represent the overall picture of possibly important mechanisms that affect the/ <—> f transition amplitudes, without any specification about the order of perturbation, since this particular formalism does not play any role at the point of numerical analysis of their fitted values. 

In addition to expectation values and transition moments, we have a third class of important physical properties, which we refer to as second-order response properties. To develop some understanding for the meaning of and theoretical methods for studying these responses, let us investigate the response of a state 0> corresponding to H to an external time-independent one-cicetron perturbation (a//i)... 

RMD Simulation of Chemical Nucleation (22). A series of microscopic computer experiments was performed using the cooperative isomerization model (Eq. 2). This system was selected for the trial simulations for several reasons First, only two chemical species are involved, so that a minimal number of particles is needed. Second, the absence of buffered chemicals (e.g., A and B in the Trimolecular reaction of the next section) eliminates the need for creation or destruction of particles in order to maintain constant populations (19., 22j. Third, the dynamical model of the cooperative mean-field interaction can be examined as a convenient means of introducing cubic or higher nonlinearity into molecular models based on binary collisions. Finally, the need for a microscopic simulation is most apparent for transitions between multi -pie macroscopic states. Indeed, the characterization of spatially localized fluctuations is of obvious importance to the understanding of nucleation phenomena. As for the equilibrium vapor-liquid and liquid-solid transitions, detailed simulations at the molecular level should provide deep physical insight into chemical nucleation processes whkh is unattainable from theory, higher-level simulation, or experiment. 

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