Effect of Dissipation on Tunneling

A number of papers are devoted to the effect of dissipation on tunneling.81 83,103,104 Wolynes81 was one of the first to consider this problem using the Feynman path integral approach to calculate the correlation function of the reactive flux involved in the expression for the rate constant, 

A rather general method of the calculation of the tunneling taking account of the dissipation was given in Ref. 82. The cases of rather strong dissipation were considered in Refs. 81 and 82, where it was assumed that a thermodynamical equilibrium in the initial potential well exists. The case of extremely weak friction has been considered using the equations for the density matrix in Ref. 83. A quantum analogue of the Focker-Planck equation for the adiabatic and nonadiabatic processes in condensed media was obtained in Refs. 105 and 106. 

The brief review of the newest results in the theory of elementary chemical processes in the condensed phase given in this chapter shows that great progress has been achieved in this field during recent years, concerning the description of both the interaction of electrons with the polar medium and with the intramolecular vibrations and the interaction of the intramolecular vibrations and other reactive modes with each other and with the dissipative subsystem (thermal bath). The rapid development of the theory of the adiabatic reactions of the transfer of heavy particles with due account of the fluctuational character of the motion of the medium in the framework of both dynamic and stochastic approaches should be mentioned. The stochastic approach is described only briefly in this chapter. The number of papers in this field is so great that their detailed review would require a separate article. 

It should be noted that recent work has not been devoted only to the application of the theory to new processes and phenomena but has also been concerned with the basis of the theory. Therefore, new important results have been obtained also for processes which have been under theoretical investigation for many years, in particular, for electron and proton transfer reactions. These results open new directions for further investigations. 

Schmidt, Specialist Periodical Report, Electrochemistry, Vol. 5, The Chemical Society, London, 1975, p. 21. 

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