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arXiv:2412.00812 · Physical review. D/Physical review. D.

Toward extracting scattering phase shift from integrated correlation functions. III. Coupled channels

Peng Guo, Frank X. Lee

Published Mar 10, 2025• 6 citations
arXivHTMLPDF

Abstract

The formalism developed in the preceding papers that connects integrated correlation function of a trapped two-particle system to infinite volume scattering phase shift is further extended to coupled-channel systems in the present work. Using a trapped nonrelativistic two-channel system as an example, a new relation is derived that retains the same structure as in the single channel, and has explicit dependence on the phase shifts in both channels but not on the inelasticity. The relation is illustrated by a exactly solvable coupled-channel quantum mechanical model with contact interactions. It is further validated by path integral Monte Carlo simulation of a quasi-one-dimensional model that can admit general interaction potentials. In all cases, we found rapid convergence to the infinite volume limit as the trap size is increased, even at short times, making it potentially a good candidate to overcome signal-to-noise issues in Monte Carlo applications.

DOI
10.1103/physrevd.111.054506

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In present work, a relation that connects the integrated correlation function of a trapped two-particle system to infinite volume particles scattering phase shift is derived. It has the potential to provide an alternative approach for extracting two-particle scattering phase shift from integrated correlation function in lattice simulation at small Euclidean time region. Both (i) perturbation calculation of 1+1 dimensional lattice Euclidean field theory model of fermions interacting with a contact interaction and (ii) Monte Carlo simulation of a 1D exactly solvable quantum mechanics model are carried out to test the proposed relation. In contrast to conventional two-step approach of extracting energy levels from temporal correlation function in lattice simulation at large Euclidean time first and then applying Lüscher formula to convert energy levels into scattering phase shifts, we show that the difference of integrated correlation functions between interacting and noninteracting trapped systems converges rapidly to infinite volume limit that is given in terms of scattering phase shifts at small Euclidean time region.
In present work, a relation that connects the integrated correlation function of a trapped two-particle system to infinite volume particles scattering phase shift is derived. It has the potential to provide an alternative approach for extracting two-particle scattering phase shift from integrated correlation function in lattice simulation at small Euclidean time region. Both (i) perturbation calculation of (1+11+11+1)-dimensional lattice Euclidean field theory model of fermions interacting with a contact interaction and (ii) Monte Carlo simulation of a 1D exactly solvable quantum mechanics model are carried out to test the proposed relation. In contrast to conventional two-step approach of extracting energy levels from temporal correlation function in lattice simulation at large Euclidean time first and then applying L\"uscher formula to convert energy levels into scattering phase shifts, we show that the difference of integrated correlation functions between interacting and noninteracting trapped systems converges rapidly to infinite volume limit that is given in terms of scattering phase shifts at small Euclidean time region.
In the present work, a relativistic relation that connects the difference of interacting and noninteracting integrated two-particle correlation functions in finite volume to infinite volume scattering phase shift through an integral is derived. We show that the difference of integrated finite volume correlation functions converges rapidly to its infinite volume limit as the size of the periodic box is increased. The fast convergence of our proposed formalism is illustrated by analytic solutions of a contact interaction model, the perturbation theory calculation, and also the Monte Carlo simulation of a complex ϕ 4 lattice field theory model. Published by the American Physical Society 2024
We investigate the feasibility of extracting infinite volume scattering phase shift on quantum computers in a simple one-dimensional quantum mechanical model, using the formalism established in Ref.~\cite{Guo:2023ecc} that relates the integrated correlation functions (ICF) for a trapped system to the infinite volume scattering phase shifts through a weighted integral. The system is first discretized in a finite box with periodic boundary conditions, and the formalism in real time is verified by employing a contact interaction potential with exact solutions. Quantum circuits are then designed and constructed to implement the formalism on current quantum computing architectures. To overcome the fast oscillatory behavior of the integrated correlation functions in real-time simulation, different methods of post-data analysis are proposed and discussed. Test results on IBM hardware show that good agreement can be achieved with two qubits, but complete failure ensues with three qubits due to two-qubit gate operation errors and thermal relaxation errors.
Based on an established relation that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral, we propose to extract the infinite volume scattering phase shifts through quantum simulation of the integrated correlation functions of trapped two-particle systems on quantum computers. The integrated correlation function can be computed by an ancilla-based algorithm. The proposal is demonstrated with a simple contact interaction fermion model.
The energy spectrum of two short-range interacting particles in a harmonic potential trap has previously been related to free-space scattering phase shifts. But the existing formula for systems with a nonzero interaction range is exact only in the limit of an infinitely shallow trap. Here I provide a systematically improved formula---describing the low-energy dynamics---that enables the use of finite traps. This paves the way for extracting nuclear scattering phase shifts from ab initio nuclear many-body structure calculations, a long-sought goal in nuclear physics. The derivation establishes effective field theory as a powerful framework for studying the connection between structure information of a trapped system (with two or more subclusters) and continuum physics in the fields of both nuclear and condensed-matter physics.