QUASI-NORMAL-MODE EXPANSION FOR WAVES IN OPEN SYSTEMS

An open system is not conservative because energy can escape to the ou tside. As a result. the time-evolution operator is not Hermitian in th e usual sense and the eigenfunctions (factorized solutions in space an d time) are no longer normal modes but quasinormal modes (QNMs) whose frequencies omega are complex. Qausinormal-mode analysis has been a po werful tool for investigating open systems. Previous studies have been mostly system specific, and use a few QNMs to provide approximate des criptions. Here the authors review developments that lead to a unifyin g treatment. The formulation leads to a mathematical structure in clos e analogy to that in conservative, Hermitian systems. Hence many of th e mathematical tools for the latter can be transcribed. Emphasis is pl aced on those cases in which the QNMs form a complete set and thus giv e an exact description of the dynamics. In situations where the QNMs a re not complete, the ''remainder'' is characterized. Applications to o ptics in microspheres and to gravitational waves from black holes are given as examples. The second-quantized theory is sketched. Directions for further development are outlined. [S0034-6861(98)00604-7].