Metastable state dynamics

Within this general framework there have been many different systems modelled and the dynamical, statistical prefactors have been calculated. These are detailed in [42]. For a binary mixture, phase separating from an initially metastable state, the work of Langer and Schwartz [48] using die Langer theory [47] gives the micleation rate as... 

The dynamic behavior of nonisothermal CSTRs is extremely complex and has received considerable academic study. Systems exist that have only a metastable state and no stable steady states. Included in this class are some chemical oscillators that operate in a reproducible limit cycle about their metastable... 

Needless to say, tunneling is one of the most famous quantum mechanical effects. Theory of multidimensional tunneling, however, has not yet been completed. As is well known, in chemical dynamics there are the following three kinds of problems (1) energy splitting due to tunneling in symmetric double-well potential, (2) predissociation of metastable state through... 

Chodera, J.D., Singhal, N., Pande, V.S., Dill, K.A., Swope, W.C. Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics. J. Chem. Phys. 2007, 126, 155101-17. 

The absolute instability of the "metastable" states in the framework of classical elasticity manifests itself in dynamics as well. The associated elastodynamical problem reduces to a solution of the nonlinear wave equation = o (uJu . It is convenient to rewrite it as a mixed type first order system... 

It is crucial to attain high coherence time T. In the beam experiments that time is just the time of flight through the region with the electric held. For a gas-dynamic molecular source the typical time of flight is 1 — 10 ms. On the other hand, for the PbO experiment in vapor cell T is close to the lifetime of the excited (metastable) state a(l), T 0.1 Ills. So, the beam experiments have advantage in the coherence time. 

In particular, irregular vibrational spectra with Wignerian level spacing statistics have been observed this last decade for a number of highly excited molecules [3-7]. On the other hand, many recent works have characterized the reactive dynamics in terms of quantum resonances, which allows a rigorous definition of metastable states with finite lifetimes and hence of dissociation rates [4, 8-10]. 

By contrast, in heavy-light-heavy molecules such as HMuH, C1HC1, or IHI, a very extended elliptic island exists in the classical phase space [150]. In such cases, the elliptic island may be the support of several metastable states that can be obtained by Bohr-Sommerfeld quantization. Their lifetime is determined by dynamical tunneling from inside the elliptic island to the outside regions. 

A relaxation process will occur when a compound state of the system with large amplitude of a sparse subsystem component evolves so that the continuum component grows with time. We then say that the dynamic component of this state s wave function decays with time. Familiar examples of such relaxation processes are the a decay of nuclei, the radiative decay of atoms, atomic and molecular autoionization processes, and molecular predissociation. In all these cases a compound state of the physical system decays into a true continuum or into a quasicontinuum, the choice of the description of the dissipative subsystem depending solely on what boundary conditions are applied at large distances from the atom or molecule. The general theory of quantum mechanics leads to the conclusion that there is a set of features common to all compound states of a wide class of systems. For example, the shapes of many resonances are nearly the same, and the rates of decay of many different kinds of metastable states are of the same functional form. 

In many cases of physical interest (e.g., a decay, photoionization, or predissociation) the dynamic and the dissipative subsystems correspond to degenerate (or quasidegenerate) states of the same zero-order Hamiltonian. For future purposes, it will be useful to establish the way in which a metastable state decays in this case. Let the total Hamiltonian for the system be given by... 

We turn now to study the properties of the metastable state in more detail. We, therefore, concentrate on the long-time behavior, i.e., t > f0, and defer the discussion of the short-time dynamics to a later section. Figure 1.3 shows snapshots of the probability density of the evolving wave packet at different... 

The interpretation of final state distributions following the decay of metastable states is a very interesting topic. If the intermediate complex lives longer than an internal period, the memory on the parent molecule in the electronic ground state will be essentially erased and the product state distributions will no longer reflect the initial wavefunction. As we will show in Section 10.3, they instead reflect the wavefunction in the transition state of the upper electronic state and the dynamics in the exit channel following the transition region. 

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