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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2408.03309 |
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| _version_ | 1866908709604556800 |
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| author | Zhang, Xilin |
| author_facet | Zhang, Xilin |
| contents | This work introduces a unified emulation framework for studying continuum physics in finite quantum systems. Using a reduced basis method, we construct powerful emulators for the inhomogeneous Schrödinger equation that operate in a combined parameter space of complex energy ($E$) and other inputs ($\bmθ$). Within the space, the emulators simultaneously perform analytical continuation in $E$ -- extracting continuum physics from numerically simpler bound-state-like calculations -- and interpolate this entire process across $\bmθ$. This yields a small, non-Hermitian system whose properties (e.g., resonances and scattering observables) can be rapidly predicted for any $\bmθ$. Crucially, the complex-$E$ emulation provides a pathway to compute continuum observables for complex systems where advanced bound-state methods exist but direct continuum calculations are yet to be developed, while the $\bmθ$-emulation enables rapid parameter-space exploration and can be adapted to accelerate other existing continuum calculations. Demonstrations with two- and three-body systems highlight the method's effectiveness and suggest its connection to (near-)optimal rational approximation. This Letter presents the key results, with further details reserved for a companion paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03309 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-Like Calculations Zhang, Xilin Nuclear Theory High Energy Physics - Phenomenology Atomic Physics Chemical Physics Computational Physics This work introduces a unified emulation framework for studying continuum physics in finite quantum systems. Using a reduced basis method, we construct powerful emulators for the inhomogeneous Schrödinger equation that operate in a combined parameter space of complex energy ($E$) and other inputs ($\bmθ$). Within the space, the emulators simultaneously perform analytical continuation in $E$ -- extracting continuum physics from numerically simpler bound-state-like calculations -- and interpolate this entire process across $\bmθ$. This yields a small, non-Hermitian system whose properties (e.g., resonances and scattering observables) can be rapidly predicted for any $\bmθ$. Crucially, the complex-$E$ emulation provides a pathway to compute continuum observables for complex systems where advanced bound-state methods exist but direct continuum calculations are yet to be developed, while the $\bmθ$-emulation enables rapid parameter-space exploration and can be adapted to accelerate other existing continuum calculations. Demonstrations with two- and three-body systems highlight the method's effectiveness and suggest its connection to (near-)optimal rational approximation. This Letter presents the key results, with further details reserved for a companion paper. |
| title | Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-Like Calculations |
| topic | Nuclear Theory High Energy Physics - Phenomenology Atomic Physics Chemical Physics Computational Physics |
| url | https://arxiv.org/abs/2408.03309 |