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The Lamb shift (self-energy) of an elliptic dielectric microcavity isstudied. We show that the size of the Lamb shift, which is a small energy shiftdue to the system-environment coupling in the quantum regime, is dependent onthe geometry of the boundary conditions. It shows a global transition dependingon the eccentricity of the ellipsis. These transitions can be classified intothree types of decay channels known as whispering-gallery modes,stable-bouncing-ball modes, and unstable-bouncing-ball modes. These modes aremanifested through the Poincar\'{e} surface of section with the Husimidistribution function in classical phase space. It is found that the similarity(measured in Bhattacharyya distance) between the Husimi distributions belowcritical lines of two different modes increases as the difference of theirself-energies decreases when the quality factors of the modes are on the sameorder of magnitude.

Behavior of three modes of decay channels and their self-energies of elliptic dielectric microcavity