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<p>To study the uncertainty quantification of resonant states in open quantum systems, we developed a Bayesian framework by integrating a reduced basis method (RBM) emulator with the Gamow coupled-channel (GCC) approach. The RBM, constructed via eigenvector continuation and trained on both bound and resonant configurations, enables the fast and accurate emulation of resonance properties across the parameter space. To identify the physical resonant states from the emulator’s output, we introduce an overlap-based selection technique that effectively isolates true solutions from background artifacts. By applying this framework to unbound nucleus <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(^6\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>6</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Be, we quantified the model uncertainty in the predicted complex energies. The results demonstrate relative errors of 17.48% in the real part and 8.24% in the imaginary part, while achieving a speedup of four orders of magnitude compared with the full GCC calculations. To further investigate the asymptotic behavior of the resonant-state wavefunctions within the RBM framework, we employed a Lippmann–Schwinger (L–S)-based correction scheme. This approach not only improves the consistency between eigenvalues and wavefunctions but also enables a seamless extension from real-space training data to the complex energy plane. By bridging the gap between bound-state and continuum regimes, the L–S correction significantly enhances the emulator’s capability to accurately capture continuum structures in open quantum systems.</p>

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Bayesian analysis of Gamow resonances with reduced basis methods: from eigenvector continuation to post-emulation corrections

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • Ruo-Yu Cheng,
  • Zhi-Cheng Xu

摘要

To study the uncertainty quantification of resonant states in open quantum systems, we developed a Bayesian framework by integrating a reduced basis method (RBM) emulator with the Gamow coupled-channel (GCC) approach. The RBM, constructed via eigenvector continuation and trained on both bound and resonant configurations, enables the fast and accurate emulation of resonance properties across the parameter space. To identify the physical resonant states from the emulator’s output, we introduce an overlap-based selection technique that effectively isolates true solutions from background artifacts. By applying this framework to unbound nucleus \(^6\) 6 Be, we quantified the model uncertainty in the predicted complex energies. The results demonstrate relative errors of 17.48% in the real part and 8.24% in the imaginary part, while achieving a speedup of four orders of magnitude compared with the full GCC calculations. To further investigate the asymptotic behavior of the resonant-state wavefunctions within the RBM framework, we employed a Lippmann–Schwinger (L–S)-based correction scheme. This approach not only improves the consistency between eigenvalues and wavefunctions but also enables a seamless extension from real-space training data to the complex energy plane. By bridging the gap between bound-state and continuum regimes, the L–S correction significantly enhances the emulator’s capability to accurately capture continuum structures in open quantum systems.