Hidden Hermiticity of the Jaynes-Cummings Projected Liouvillian

• URL: http://arxiv.org/abs/2604.25801v2
• Date: Thu, 30 Apr 2026 18:07:41 GMT
• Title: Hidden Hermiticity of the Jaynes-Cummings Projected Liouvillian
• Abstract summary: We prove that the generator of quantum memory is pseudo-Hermitian.<n>The effect is genuine, not a block-diagonal artefact.<n>We show that the Jaynes-Cummings point sits inside a symmetry-protected pseudo-Hermitian phase.
• Score: 1.8867357521563244
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Jaynes-Cummings model has been studied for six decades, yet its Nakajima-Zwanzig projected Liouvillian QLQ hides an unexpected structure: although manifestly non-Hermitian, its spectrum is purely real across all numerically accessible parameters. We resolve this anomaly by constructing a positive-definite metric eta > 0 such that (QLQ)^dag eta = eta (QLQ), proving that the generator of quantum memory is pseudo-Hermitian. The effect is genuine, not a block-diagonal artefact: the Delta N = 0 and Delta N = +/- 2 sectors remain strongly non-Hermitian, yet the global spectrum is protected by eta. Building on Ng and Rabani's identification of exceptional-point physics in QLQ, we show that the Jaynes-Cummings point sits inside a symmetry-protected pseudo-Hermitian phase. Under continuous deformation toward the full Rabi model this protection breaks and re-enters, producing a U(1) -> complex -> Z_2 phase structure bracketed by exceptional-point boundaries. The result supplies a structural reason for Hardy-space analyticity of the memory kernel in the canonical quantum-optical model and identifies a phase transition between oscillatory and genuinely dissipative quantum memory.

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