  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, we demonstrate an existence
of signature of exceptional point phase transition in Hermitian systems that
are free from dissipation and amplification. We consider a composite Hermitian
system including both two coupled oscillators and their environment consisting
only of several tens of degrees of freedom. We show that the dynamics of such a
Hermitian system demonstrate a transition, which occurs at the coupling
strength between oscillators corresponding to the EP in the non-Hermitian
system. This transition manifests itself even in the non-Markovian regime of
the system dynamics in which collapses and revivals of the energy occur. Thus,
we demonstrate that the phase transition occurring at the passing over the EP
in the non-Hermitian system manifests itself in the Hermitian system at all
time. We discuss the experimental scheme to observe the signature of EP phase
transition in the non-Markovian regime.
