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Nuclear Theory·nucl-th

Monday·March 13, 2023

7 papers—2 primary·5 cross-listed

All7Primary2Cross-lists5
  1. 01

    [Submitted on 10 Mar 2023]

    Introducing the Random Phase Approximation Theory

    Giampaolo Co'

    Random Phase Approximation (RPA) is the theory most commonly used to describe the excitations of many-body systems. In this article, the secular equations of the theory are obtained by using three different approaches: the equation of motion method, the Green's function perturbation theory and the time-dependent Hartree--Fock theory. Each approach emphasizes specific aspects of the theory overlooked by the other methods. Extensions of the RPA secular equations to treat the continuum part of the excitation spectrum and also the pairing between the particles composing the system are presented. Theoretical approaches which overcome the intrinsic approximations of RPA are outlined.

    Comments:
    57 pages, 6 figures
    Subjects:
    Nuclear Theory (nucl-th); Strongly Correlated Electrons (cond-mat.str-el)
    arXiv:
    2303.05801 [pdf]
    Universe(2023)·9 citations
  2. 02

    [Submitted on 10 Mar 2023]

    Eigenvector continuation for emulating and extrapolating two-body resonances

    Nuwan Yapa · Kévin Fossez · Sebastian König

    The study of open quantum systems (OQSs), i.e., systems interacting with an environment, impacts our understanding of exotic nuclei in low-energy nuclear physics, hadrons, cold-atom systems, or even noisy intermediate-scale quantum computers. Such systems often exhibit resonance states characterized by energy positions and dispersions (or decay widths), the properties of which can be difficult to predict theoretically due to their coupling to the continuum of scattering states. Dealing with this phenomenon poses challenges both conceptually and numerically. For that reason, we investigate how the reduced basis method known as eigenvector continuation (EC), which has emerged as a powerful tool to emulate bound and scattering states in closed quantum systems, can be used to study resonance properties. In particular, we present a generalization of EC that we call conjugate-augmented eigenvector continuation, which is based on the complex-scaling method and designed to predict Gamow-Siegert states, and thus resonant properties of OQSs, using only bound-state wave functions as input.

    Comments:
    12 pages, 10 figures, published version, Python code provided as ancillary files
    Subjects:
    Nuclear Theory (nucl-th); Quantum Gases (cond-mat.quant-gas)
    arXiv:
    2303.06139 [pdf]
    PRC(2023)·28 citations

Affiliations

first authorsco-authorsvia INSPIRE