Toward Universality in Similarity Renormalization GroupEvolved Few-body Potential Matrix Elements
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2015
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ndltd-OhioLink-oai-etd.ohiolink.edu-osu14207360212021-08-03T06:28:51Z Toward Universality in Similarity Renormalization GroupEvolved Few-body Potential Matrix Elements Dainton, Brian Physics Improvements in many-body methods have identified the need for better few-body potentials as input. There are a wide variety of input potentials, which all accurately describe few-body systems, and all must be transformed with similarity renormalization group (SRG) transformations before they are computationally efficient enough to be used in certain many-body calculations. It was realized that modern realistic 2-body potentials with very different matrix elements evolve under SRG transformations to the same universal low-energy shape. Understanding the requirements for universality in evolved potential matrix elements can aid in the construction of better potentials for the many-body problem. Furthermore, understanding the precision of few-body evolution is a key step to setting error bars on theoretical predictions.We first examine how the universality of two-nucleon interactions evolved using similarity renormalizationgroup (SRG) transformations correlates with T-matrix equivalence, with the ultimate goalof gaining insight into universality for three-nucleon forces. Because potentials are fit to low-energy data, they are (approximately) phase equivalent only up to a certain energy, and we find universality in evolved potentials up to the corresponding momentum. More generally, we find universality in local energy regions, reflecting a local decoupling by the SRG. The further requirements for universality in evolved potential matrix elements are exploredusing two simple alternative potentials. In agreement with observations made previously for Lee-Suzuki transformations, regions of universal potential matrix elements are restricted to where half-on-shell T-matrix equivalence holds.To continue the study in the 3-body sector, we create a simple 1-D spinless boson ``theoretical laboratory'' for a dramatic improvement in computational efficiency. We introduce a basis-transformation, harmonic oscillator (HO) basis, which is used for current many-body calculations and discuss the imposed truncations. We confirm that evolution to universal low-energy 2-body potential matrix elements is the same for 1-D bosons as 3-D fermions, and show that a further simplification of using positive-valued eigenvalues rather than phase-shifts is valid. When SRG evolving in a HO-basis, we show that the evolved matrix elements, once transformed back into momentum-representation, differ from those when evolving with momentum representation. This is because the generator in each basis is not exactly the same due to the truncation. In the 2-body sector, this can be avoided by increasing the basis size, but it remains unclear whether this is possible in the 3-body sector, as computational power required is greatly increased for three-body evolution.In our efforts to study universal matrix elements in the 3-body sector by observing momentum representation matrix elements, we observe oscillations much like those appearing from truncation errors in the 2-body sector. We can identify that the spectator particle adds strength in far-off diagonal potential matrix elements of the embedded 2-body potential, thus truncation errors appear in 3-body HO-basis evolution at much higher values of the decoupling scale than expected from 2-body calculations. With a better understanding of the source of errors in 3-body input potentials, we hope to gain further insight into how to make progress towards precision nuclear many-body calculations. 2015-05-14 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1420736021 http://rave.ohiolink.edu/etdc/view?acc_num=osu1420736021 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
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NDLTD |
| language |
English |
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NDLTD |
| topic |
Physics |
| spellingShingle |
Physics Dainton, Brian Toward Universality in Similarity Renormalization GroupEvolved Few-body Potential Matrix Elements |
| author |
Dainton, Brian |
| author_facet |
Dainton, Brian |
| author_sort |
Dainton, Brian |
| title |
Toward Universality in Similarity Renormalization GroupEvolved Few-body Potential Matrix Elements |
| title_short |
Toward Universality in Similarity Renormalization GroupEvolved Few-body Potential Matrix Elements |
| title_full |
Toward Universality in Similarity Renormalization GroupEvolved Few-body Potential Matrix Elements |
| title_fullStr |
Toward Universality in Similarity Renormalization GroupEvolved Few-body Potential Matrix Elements |
| title_full_unstemmed |
Toward Universality in Similarity Renormalization GroupEvolved Few-body Potential Matrix Elements |
| title_sort |
toward universality in similarity renormalization groupevolved few-body potential matrix elements |
| publisher |
The Ohio State University / OhioLINK |
| publishDate |
2015 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=osu1420736021 |
| work_keys_str_mv |
AT daintonbrian towarduniversalityinsimilarityrenormalizationgroupevolvedfewbodypotentialmatrixelements |
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1719437668309270528 |