Genesis, selected applications, and future prospects of the mode coupling theory

The decade of 1960–1970 was a very exciting one when the critical phenomena attracted world's best minds. At that time, very little was understood about the mysterious ways in which large-scale critical fluctuations affect both static and dynamic behavior of systems near criticality as were revealed by the wealth of experimental findings accumulated since the end of the last century. The mode coupling theory (MCT) originated in this decade as a promising approach to dynamic critical phenomena. By 1980, however, the mystery of critical phenomena was largely solved thanks to the renormalization group idea among others. Starting the mid-1970s, a new life was imbued to MCT when the theory was successfully applied to liquid dynamics, and then to glass transitions in the 1980s. Further applications are being made to problems in chemical physics like polymer dynamics. These developments are briefly reviewed together with future prospects.