  Non-Hermitian classical and open quantum systems near an exceptional point
(EP) are known to undergo strong deviations in their dynamical behavior under
small perturbations or slow cycling of parameters as compared to Hermitian
systems. Such a strong sensitivity is at the heart of many interesting
phenomena and applications, such as the asymmetric breakdown of the adiabatic
theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions
and photonic catastrophe. Like for Hermitian systems, the sensitivity to
perturbations on the dynamical evolution can be captured by Loschmidt echo and
fidelity after imperfect time reversal or quench dynamics. Here we disclose a
rather counterintuitive phenomenon in certain non-Hermitian systems near an EP,
namely the deceleration (rather than acceleration) of the fidelity decay and
improved Loschmidt echo as compared to their Hermitian counterparts, despite
large (non-perturbative) deformation of the energy spectrum introduced by the
perturbations. This behavior is illustrated by considering the fidelity decay
and Loschmidt echo for the single-particle hopping dynamics on a tight-binding
lattice under an imaginary gauge field.
