To $\mathcal{PT}$ or not to $\mathcal{PT}$: Noise-induced escape and nonlinear-damping stabilization in a parity-time dimer

• URL: http://arxiv.org/abs/2608.14468v1
• Date: Fri, 14 Aug 2026 16:48:56 GMT
• Title: To $\mathcal{PT}$ or not to $\mathcal{PT}$: Noise-induced escape and nonlinear-damping stabilization in a parity-time dimer
• Abstract summary: Parity-time systems exhibit long-lived excitations by balancing gain and loss in coupled resonators.<n>We show that Hamiltonian Duffing nonlinearity restricts the $mathcalPT$-unbroken phase to a finite, nonattracting region of phase space.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Parity-time ($\mathcal{PT}$) symmetric systems exhibit long-lived excitations by balancing gain and loss in coupled resonators, driving extensive theoretical interest and diverse experimental realizations. Realistic physical implementations, however, inevitably introduce nonlinearities and noise. This mandates a rigorous reevaluation of their global long-time dynamics. In this work, we show that Hamiltonian Duffing nonlinearity restricts the $\mathcal{PT}$-unbroken phase to a finite, nonattracting region of phase space. Consequently, unavoidable fluctuations drive first-passage escape into runaway trajectories. This renders the linearly $\mathcal{PT}$-unbroken phase a purely transient phenomenon. We then recover global stochastic stability by introducing two-photon loss on the gain oscillator. This nonlinear damping explicitly breaks exact $\mathcal{PT}$ symmetry while supplying genuine phase-space attraction, generating a bistable regime where a low-amplitude orbit mimicking the original linear state coexists with a high-amplitude limit cycle. Thus, we establish a revised origin for stability in non-Hermitian experiments: the observed long-time stochastic stability is governed by inherent restoring dissipation rather than the spectral $\mathcal{PT}$ symmetry itself.

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