Critical Dynamics in Nonhermitian Many-body System

Recently, there are observations on critical phenom-

ena in photon condensate in dye-filled microcavity, indi-

cating possible exceptional points in the collective sys-

tem dynamics. To understand the generic mechanism,

we consider a driven-dissipative, two-component photon-

polariton condensate and study the nonlinear dynamics in the collective fluctuations. We find a novel exceptional point associated

with the coalescence of eigenmodes as the mixture of am-

plitude and phase modes, featuring a transition between

exponential and oscillatory behavior in correlation dy-

namics. Meanwhile, the gap closure is found in the massive mode

when the system approaches the critical exceptional point (CEP) in

the collective emission spectrum. Along the way, we find

that instability can happens at finite momentum k other

than the uniform one at zero-k.