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Open Quantum Systems Decoherence
Quantum Simulation
Multivariable Painleve'-II equation: connection formulas for asymptotic solutions
arXiv
Authors: N. A. Sinitsyn
Year
2026
Paper ID
35822
Status
Preprint
Abstract Read
~2 min
Abstract Words
89
Citations
N/A
Abstract
It is shown that a generalization of the Painlevé-II equation (P-II) to a system of coupled equations with symmetry breaking terms is integrable. A Lax pair for this system is used to relate the asymptotic behavior of the solutions at different infinities via an asymptotically exact WKB approach. The analysis relies on an exact solution of the quantum mechanical Demkov-Osherov model (DOM). An application to the problem of unstable vacuum decay during a second order phase transition provides precise scaling of the number of excitations, including subdominant contributions.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- It is shown that a generalization of the Painlevé-II equation (P-II) to a system of coupled equations with symmetry breaking terms is integrable.
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