Activated rate processes

Berezhkovskii A M and Zitzerman V Yu 1990 Activated rate processes in a multidimensional case Physica A 166 585-621... 

Berezhkovskii A M and Zitserman V Yu 1991 Activated rate processes in the multidimensional case. Consideration of recrossings in the multidimensional Kramers problem with anisotropic friction Chem. Phys. 157 141-55... 

Berezhkovskii A M and Zitserman V Yu 1992 Multidimensional activated rate processes with slowly relaxing mode Physica A 187 519-50... 

A3.8.4 QUANTUM ACTIVATED RATE PROCESSES AND SOLVENT EFFECTS... 

Nitzan A 1988 Activated rate processes in condensed phases the Kramers theory revisited Adv. Chem. Phys. 70 489 Onuchic J N and Wolynes P G 1988 Classical and quantum pictures of reaction dynamics in condensed matter resonances, dephasing and all that J. Phys. Chem. 92 6495... 

Singh S, Krishnan R and Robinson G W 1990 Theory of activated rate processes with space-dependent friction Chem. 

Straus J B and Voth G A 1992 Studies on the influence of nonlinearity in classical activated rate processes J. Chem. Phys. 96 5460... 

See, for example, Poliak E 1986 Theory of activated rate processes a new derivation of Kramers expression J. Chem. Phys. 85 865... 

Poliak E 1990 Variational transition state theory for activated rate processes J. Chem. Phys. 93 1116 Poliak E 1991 Variational transition state theory for reactions in condensed phases J. Phys. Chem. 95 533 Frishman A and Poliak E 1992 Canonical variational transition state theory for dissipative systems application to generalized Langevin equations J. Chem. Phys. 96 8877... 

Berezhkovskii A M, Poliak E and Zitserman V Y 1992 Activated rate processes generalization of the Kramers-Grote-Hynes and Langer theories J. Chem. Phys. 97 2422... 

Poliak E, Grabert H and Hanggi P 1989 Theory of activated rate processes for arbitrary frequency dependent friction solution of the turnover problem J. Chem. Phys. 91 4073... 

Cao J and Voth G A 1996 A unified framework for quantum activated rate processes I. General theory J. Chem. Phys. 105 6856... 

B. Carmeli and A. Nitzan, Theory of activated rate processes position dependent friction, Chem. Phys. Lett. 102, 517 (1983). 

E. Poliak and P. Talkner, Transition-state recrossing dynamics in activated rate processes, Phys. Rev. E 51, 1868 (1995). 

E. Hershkovitz and E. Poliak, Multidimensional generalization of the Pollak-Grabert-Hanggi turnover theory for activated rate processes, J. Chem. Phys. 106, 7678 (1997). 

Poliak. E. Quantum theory of activated rate processes a maximum free energy approach,... 

One of the exciting new directions is the control of activated rate processes using external fields. Addition of an external field opens the way for a wide variety of new phenomena such as stochastic resonance, resonance activation, directed transport, control of the hopping distribution in surface diffusion and more. Even the addition of a constant force to the problem leads to interesting additional phenomena such as the locked to running transition, which remains a topic of ongoing research. " Quantum mechanics in the presence of external fields may differ significantly from the classical. 

Following Fey nman s original work, several authors pmsued extensions of the effective potential idea to construct variational approximations for the quantum partition function (see, e g., Refs. 7,8). The importance of the path centroid variable in quantum activated rate processes was also explored and revealed, which gave rise to path integral quantum transition state theory and even more general approaches. The Centroid Molecular Dynamics (CMD) method for quantum dynamics simulation was also formulated. In the CMD method, the position centroid evolves classically on the efiective centroid potential. Various analysis and numerical tests for realistic systems have shown that CMD captures the main quantum effects for several processes in condensed matter such as transport phenomena. 

We can understand how the observed threshold effect may arise as follows. Movement of the tie molecules in and out of the lamellae is a thermally activated rate process, and some chains will always be entering at the same time as others are leaving. The effect of the tensile stress is to bias the movement towards a greater rate of leaving. Only when a sufficient stress is applied to shift the equilibrium, such that the reduced number of tie molecules is unable to sustain the stress without breaking, will breakdown ensue. 

ACTIVATED RATE PROCESSES IN CONDENSED PHASES THE KRAMERS THEORY REVISITED... 

This chapter reviews the generalizations of the Kramers model that were develojjed during the past few years. The result of this effort, which we may call the generalized Kramers theory, provides a useful framework for the theoretical description of activated rate processes in general and of chemical reaction rates in condensed phases in particular. Some applications of this framework as well as its limitations are also discussed. In the last few years there has also been substantial progress in the study of the quantum mechanical Kramers model, which may prove useful for condensed phase tunneling reactions. This aspect of the problem is not covered by the present review. 

---