Signature of exceptional point phase transition in Hermitian systems

Exceptional point (EP) is a spectral singularity in non-Hermitian systems. The passing over the EP leads to phase transition, which endows system with unconventional features that find wide range of applications. However, need using dissipation and amplification limits possible applications systems EP. In this work, we demonstrate an existence signature exceptional transition Hermitian are free from amplification. We consider composite including both two coupled oscillators their environment consisting only several tens degrees freedom. show dynamics such occurs at coupling strength between corresponding system. This manifests itself even non-Markovian regime collapses revivals energy occur. Thus, occurring all time. discuss experimental scheme observe regime.