Phase transition at exceptional point in Hermitian systems

T. T. Sergeev, A. A. Zyablovsky, E. S. Andrianov, Yu. E. Lozovik

Published 2022-07-05Version 1

Exceptional point (EP) is a spectral singularity in non-Hermitian systems. The passing over the EP leads to a phase transition which endows the system with unconventional features that find a wide range of applications. However, the need of using the dissipation and amplification limits the possible applications of systems with the EP. In this work, the concept of phase transitions at the EP is expanded to Hermitian systems which are free from dissipation and amplification. It is considered a composite Hermitian system including both two coupled subsystems and their environment consisting only of several tens degrees of freedom such that the energy can return from the environment to the subsystems. It is shown that the dynamics of such a Hermitian system demonstrates a clear phase transition. It occurs at the critical coupling strength between subsystems corresponding to the EP in the non-Hermitian system. This phase transition manifests itself even in the non-Markovian regime of the system dynamics in which collapses and revivals of the energy occur. A photonic circuit is proposed for observing the EP phase transition in systems free from dissipation and amplification. The obtained results extend the range of practical applications of the EP phenomena to Hermitian systems.