Memory-losing dynamics

IV. Geometry Behind the Memory-Losing Dynamics Inter-Basin Mixing... 

A geometry that can actually materialize such a memory-losing dynamics is studied in Section IV. We here propose a notion of inter-basin mixing that is responsible for the Markov-type stochastic appearance of molecular structures in the above memory-losing isomerization dynamics. An extension of the Liapunov exponent to quantify the time scale to reach inter-basin mixing is also proposed [10]. 

IV. GEOMETRY BEHIND THE MEMORY-LOSING DYNAMICS INTER-BASIN MIXING... 

First, do dynamical correlations exist in processes involving multiple saddles, such as structural changes of macromolecules in clusters and proteins In the conventional theory, it is supposed that consecutive processes of going over saddles take place independent of one another. In other words, the system loses its memory of the past immediately, since the vibrational relaxation within a well is assumed to be much faster than the escape from it and multistep processes are conventionally assumed to be Markov processes. To the contrary, when the characteristic time scale of IVR is comparable to that of the reaction, the system can keep dynamical correlations as it goes over successive saddles. 

Fig. 25.1. Analysis of the catalytic activity of CalB at the single-moiecuie ievei. (a) Detection of single enzymatic turnover events of the enzyme CaiB. The fluorogenic substrate BCECF-AM is hydrolyzed by CalB yielding the highly fluorescent dye BCECF. (b) Proposed reaction scheme explaining dynamic disorder. The enzyme interconverts between different conformations with the rate constants Oa, b. Each conformation hydrolyzes the substrate with its own rate constant fci. If conformational changes are slower than the catalytic reaction, a certain conformation performs several turnover cycles before it switches into another conformation. While subsequent turnovers in one conformation are correlated, the system loses its memory after a conformational change...

The sequence of passages across the (first-rank) saddles linking the successive distinct basins on multibasin energy surfaces is dynamically independent that is, local equilibrium is attained quickly in each basin before the system goes to the next so the system loses all dynamical memories. 

We have already argued (Section 7.4.2) that the Markovian nature of the system evolution implies that the relaxation dynamics of the bath is much faster than that of the system. The bath loses its memory on the timescale of interest for the system dynamics. Still the timescale forthe bath motion is not unimportant. If, for example, the sign of Rf) changes infinitely fast, it makes no effect on the system. Indeed, in order for a finite force R to move the particle it has to have a finite duration. It is convenient to introduce a timescale tb, which characterizes the bath motion, and to consider an approximate picture in which Rf) is constant in the interval [t, t -I- Tb], while Rff and Rff are independent Gaussian random variables if... 

In essence, the DPS approach reduces the problem of global kinetics to a discrete space of stationary points. Phenomenological rate constants can then be extracted under the assumption of Markovian dynamics within this space, which requires that the system has time to equilibrate between transitions and lose any memory of how it reached the current minimum. The Markovian assumption is therefore an essential part of the framework. However, we can regroup the stationary points into states whose members are separated by low barriers so that the Markov property is likely to be better obeyed between the groups (Section 14.2.3). 

At short times, the orientation of the central water molecule is fixed by the H bonds to its neighbors. It performs oscillations around the HB direction that are nearly harmonic. This dynamic behavior is described by Cj (t). At longer times, the bonds break, the cage begins to relax, and the particle can reorient itself, losing its memory of its initial orientation. Thus, the first-order rotational correlation function eventually decays to zero by a stretched exponential relaxation. The RCM model demonstrates that the higher order correlation functions are thus determined from Ci(r)[98] and that in the decoupling approximation Fh(<2, t) = FiiQ, t)FR Q, t). The Fh(<2, ) can be written... 

Nonvolatile ferroelectric random access memory (FRAM) devices Dynamic random access memory (DRAM) and static random access memory (SRAM) devices based on semiconductor technology are volatile that is, they wiU lose stored information when the power fails. Nonvolatile devices such as CMOS (complementary metal oxide semiconductors) and EEPROMs (electrically erasable read-only memories) are forbiddingly expensive for mass-produced electronic devices. As described above (see Section 8.3), the magnitude and direction of polarization of a ferroelectric ceramics can be reversed by applying an external electric field, and this method is used by FRAMs to store (or erase) data. As the materials have a nonlinear hysteresis curve, the polarization remains in the same state when the voltage is switched off (i.e., the information originally stored is maintained). In addition, FRAMs may be radiation-hardened for use in harsh environments such as outer space (Scott and Paz de Araujo, 1989). 

---