Dynamic correlation mechanism

T. Yanai and G. K. L. Chan, Canonical transformation theory for dynamic correlations in multireference problems, in Reduced-Density-Matrix Mechanics With Application to Many-Electron Atoms and Molecules, A Special Volume of Advances in Chemical Physics, Volume 134 (D.A. Mazziotti, ed.), Wiley, Hoboken, NJ, 2007. 

Richter D, Farago B, Butera R, Fetters LJ, Huang JS, Ewen B (1993) On the origin of entanglement constraints. Macromolecules 26(4) 795—804 Rice SA, Gray P (1965) Statistical mechanics of simple liquids. Wiley, New York Ronca G (1983) Frequency spectrum and dynamic correlation of concentrated polymer liquids. J Chem Phys 79(2) 1031-1043... 

In many investigations dynamic-mechanical properties have been determined not so much to correlate mechanical properties as to study the influence of polymer structure on thermo-mechanical behaviour. For this purpose, complex moduli are determined as a function of temperature at a constant frequency. In every transition region (see Chap. 2) there is a certain fall of the moduli, in many cases accompanied by a definite peak of the loss tangent (Fig. 13.22). These phenomena are called dynamic transitions. The spectrum of these damping peaks is a characteristic fingerprint of a polymer. Fig. 13.23 shows this for a series of polymers. 

In Papers II and III, the centroid-based theory was significantly extended to treat perhaps one of the most challenging problems in condensed matter theory—the computation of general real-time quantum correlation functions (A(f)5(0)). Consistent with the general theme of this research, the properties of dynamical correlation functions were explored using the centroid-based perspective of quantum statistical mechanics. To be more specific, in one approach, real-time dynamical information was extracted with the help of the centroid-constrained formalism for imaginary-time... 

In Section VI, we discuss future prospects of the study on reactions from multidimensional Hamilton chaos. We point out the possibility that dynamical correlation among processes of crossing over barriers can be revealed by synthesizing the above two ideas, that is, intersections of stable and unstable manifolds and Arnold webs. We suggest that these studies would shed a new light on the mechanism of protein folding and molecular functions. 

Based on the discussions in Sections IV and V, we can envisage a possible mechanism for dynamical correlation. See Figure 3.25 for schematic explanations for this. Here, we suggest that there exist three levels of dynamical correlation. 

Structure is interpreted based on the concept of free energy, that is, the concept of equihbrium statistical mechanics. However, if the folding processes take place far from equilibrium, the concept of equilibrium statistical mechanics cannot be applied. On the other hand, from our point of view, the funnel-like structure would give a typical example where the strong dynamical correlation exists. If we can analyze how stable and unstable manifolds intersect in the folding processes, we can have an alternative explanation concerning the funnel, which is a future project from our approach. 

Another example is the mechanism where efficiency of reactions is affected by the surrounding molecules. Suppose that, depending on the surrounding molecules, intersection of the stable and unstable manifolds of a reaction changes between (a) and (b) or between (b) and (c). Then, these molecules can enhance or decrease the reaction rate by switching the level of dynamical correlation. Moreover, when the surrounding molecules induce bifurcation of reaction paths, their existence can trigger new reactions. These possibilities would offer a clue to understand molecular functions from a dynamical point of view. 

A complete answer to this question will be given when the tube is derived from more basic equations such as eqn (5.84) by a kind of mean field approximation. This will require a new development of statistical mechanics since the tube is a dynamical concept rather than static. (Notice that the mean force acting on the polymer vanishes if it is averaged over a time longer than r, so that the average of the surrounding field must be taken over a finite time.) Perhaps the tube is better understood as representing the effect of dynamical correlation of the environment rather than the usual mean field. 

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