Closed-Form Expectation Values of the Damped Kerr Oscillator

• URL: http://arxiv.org/abs/2607.24842v1
• Date: Fri, 24 Jul 2026 15:09:47 GMT
• Title: Closed-Form Expectation Values of the Damped Kerr Oscillator
• Abstract summary: We specialize to coherent-state initial conditions, obtaining explicit time-dependent expressions for arbitrary normally ordered expectation values.<n>The closed-form solution provides an efficient alternative to numerical simulation while remaining free of Fock-space truncation error.<n>We note an extension of the underlying Lie-algebraic structure that may provide a useful starting point for obtaining exact solutions to a broader class of open quantum optical systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We derive a closed-form analytical expression for the expectation values of a damped Kerr nonlinear oscillator initialized in a coherent state. Starting from the exact Liouville-space solution of the Lindblad master equation, we specialize to coherent-state initial conditions, obtaining explicit time-dependent expressions for arbitrary normally ordered expectation values. The resulting expressions depend only on the system parameters and the initial coherent-state amplitude, requiring neither numerical integration nor evolution in a truncated Fock space. We verify the analytical expressions against master-equation simulations over a range of nonlinear interaction strengths. The closed-form solution provides an efficient alternative to numerical simulation while remaining free of Fock-space truncation error. Finally, we note an extension of the underlying Lie-algebraic structure that may provide a useful starting point for obtaining exact solutions to a broader class of open quantum optical systems.

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