2024/11/11 by Xilin Zhang, Zhang, Xilin · 1 citation
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Nuclear Theory (nucl-th) #Quantum Mechanics and Non-Hermitian Physics #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.2411.06712
openalex publication_date 2024/11/11 · openalex created_date 2024/11/15 · openalex updated_date 2026/08/01
This work applies a reduced basis method to study the continuum physics of a finite quantum system -- either few or many-body. Specifically, I develop reduced-order models, or emulators, for the underlying inhomogeneous Schrödinger equation and train the emulators against the equation's bound-state-like solutions at complex energies. The emulators rapidly and accurately interpolate and extrapolate the matrix elements of the Hamiltonian resolvent operator (Green's function) across a parameter space that includes both complex energy and other real-valued physical inputs in the Schrödinger equation. The spectra, discretized and compressed as the result of emulation, and the associated resolvent matrix elements (or amplitudes), have the defining characteristics of non-Hermitian quantum mechanics calculations, featuring complex eigenenergies with negative imaginary parts and branch cuts moved below the real axis in the complex energy plane. Therefore, one now has a method that extracts continuum physics from bound-state-like calculations and emulates those extractions in the input parameter space. Building on a prior Letter [arXiv:2408.03309], this article provides the full theoretical details, a comprehensive analysis of the method's performance, and a brief discussion of how it can be coupled with existing continuum approaches to perform emulations in their input parameter spaces.