Journal article
Scattering using real-time path integrals
Physical review. C, Vol.101(6), 064001
06/04/2020
DOI: 10.1103/PhysRevC.101.064001
Abstract
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While imaginary time treatments of scattering are possible, imaginary time is not a natural framework for treating scattering problems. More importantly, quantum algorithms for calculating path integrals require real-time evolution.
Purpose: We test a recently introduced method for performing direct calculations of scattering observables using real-time path integrals in order to understand the challenges facing real-time path integral calculations of scattering observables.
Method: The computations are based on a new interpretation of the path integral as the expectation value of a potential functional on cylinder sets of continuous paths with respect to a complex probability distribution. The method can in principle be applied to arbitrary short-range potentials.
Results: The method is applied to compute matrix elements of Moller wave operators applied to narrow wave packets. These are used to calculate half-shell sharp-momentum transition matrix elements for one-dimensional potential scattering. The calculations for half-shell transition operator matrix elements converge to the numerical solution of the Lippmann-Schwinger equation.
Conclusions: This work presents a proof in principle that scattering observables can be computed using real-time Feynman path integrals. While the computational method is not efficient, it can be improved. It provides a laboratory for studying quantum computational algorithms that are applicable to scattering problems.
Details
- Title: Subtitle
- Scattering using real-time path integrals
- Creators
- W. N. Polyzou - University of IowaEkaterina Nathanson - Georgia Gwinnett College
- Resource Type
- Journal article
- Publication Details
- Physical review. C, Vol.101(6), 064001
- DOI
- 10.1103/PhysRevC.101.064001
- ISSN
- 2469-9985
- eISSN
- 2469-9993
- Publisher
- Amer Physical Soc
- Number of pages
- 23
- Grant note
- DESC0016457 / U.S. Department of Energy, Office of Science; United States Department of Energy (DOE)
- Language
- English
- Date published
- 06/04/2020
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984428676802771
Metrics
5 Record Views