Closed-Form Expectation Values of the Damped Kerr Oscillator
Source: Originally published on arXiv quant-ph on July 29, 2026.
arXiv:2607.24842v1 Announce Type: new 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 numeric...
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