The nuclear many-body problem is conceptualized in an infinite-dimensional Hilbert space, but computationally solved in a finite one. Thus, the predictive power of microscopic calculations relies on the truncated representation of the infinite-dimensional space as well as leveraging advanced computational methods. My dissertation research focuses on three problems related to computational nuclear physics: exploring aspects of nuclear structure, efficiently solving the large sparse matrix-eigenvalue problem and improving the construction of the many-body basis in the no-core configuration-interaction (NCCI) framework.
I) Elliott’s rotational SU(3) model, and its later extension, the symplectic Sp(3, R) model, both played a foundational role in improving the description of nuclear rotational spectral bands. My study of several beryllium isotopes, and 20Ne uses the decomposition of no-core shell-model wavefunctions into symmetry defined subspaces to show the Sp(3, R) picture provides a more consistent description of rotational band structure.
II) Solving the non-relativistic many-body Schrödinger equation is often cast as a large sparse Hamiltonian eigenvalue problem. State-of-the-art NCCI calculation dimensions can exceed several billion and typically require supercomputers and thousands of core hours to compute small numbers of low-lying eigenstates. Thus, there is strong motivation for ways to reduce computational costs. In this research, I augment the block Lanczos algorithm using a bootstrapped pivot to significantly reduce the number of Hamiltonian-matrix multiplications typically dominating the algorithm’s total time-to-solution. My results demonstrate significant speedup in time-to-solution, often by a factor of two or more, and up to ten, can be achieved through the use of bootstrapping.
III) In NCCI, the many-body basis is historically constructed from antisymmeterized products of harmonic oscillator (HO) single-particle wavefunctions. However, one often needs many HO antisymmeterized products states to produce accurate theoretical predictions of the properties of low-lying nuclear states. Alternative choices of single-particle basis which provide better descriptions of nuclear observables relative to the problem dimension and underlying basis parameters motivate continued explorations. In this research, I explore the use of a natural orbital (NO) single-particle basis, that is, one which diagonalizes the one-body density matrix of a reference many-body state, as a means of improving the description of energy, electromagnetic transitions and radii calculations relative to the problem dimension for select sd-shell nuclei.
","abstract_html":"<p>The nuclear many-body problem is conceptualized in an infinite-dimensional Hilbert space, but computationally solved in a finite one. Thus, the predictive power of microscopic calculations relies on the truncated representation of the infinite-dimensional space as well as leveraging advanced computational methods. My dissertation research focuses on three problems related to computational nuclear physics: exploring aspects of nuclear structure, efficiently solving the large sparse matrix-eigenvalue problem and improving the construction of the many-body basis in the no-core configuration-interaction (NCCI) framework.</p> <p>I) Elliott’s rotational SU(3) model, and its later extension, the symplectic Sp(3, <em>R</em>) model, both played a foundational role in improving the description of nuclear rotational spectral bands. My study of several beryllium isotopes, and 20Ne uses the decomposition of no-core shell-model wavefunctions into symmetry defined subspaces to show the Sp(3, <em>R</em>) picture provides a more consistent description of rotational band structure.</p> <p>II) Solving the non-relativistic many-body Schrödinger equation is often cast as a large sparse Hamiltonian eigenvalue problem. State-of-the-art NCCI calculation dimensions can exceed several billion and typically require supercomputers and thousands of core hours to compute small numbers of low-lying eigenstates. Thus, there is strong motivation for ways to reduce computational costs. In this research, I augment the block Lanczos algorithm using a <em>bootstrapped</em> pivot to significantly reduce the number of Hamiltonian-matrix multiplications typically dominating the algorithm’s total time-to-solution. My results demonstrate significant speedup in time-to-solution, often by a factor of two or more, and up to ten, can be achieved through the use of bootstrapping.</p> <p>III) In NCCI, the many-body basis is historically constructed from antisymmeterized products of harmonic oscillator (HO) single-particle wavefunctions. However, one often needs many HO antisymmeterized products states to produce accurate theoretical predictions of the properties of low-lying nuclear states. Alternative choices of single-particle basis which provide better descriptions of nuclear observables relative to the problem dimension and underlying basis parameters motivate continued explorations. In this research, I explore the use of a natural orbital (NO) single-particle basis, that is, one which diagonalizes the one-body density matrix of a reference many-body state, as a means of improving the description of energy, electromagnetic transitions and radii calculations relative to the problem dimension for select <em>sd</em>-shell nuclei.</p>","abstract_has_math":false,"creators":["Zbikowski, Ryan M"],"institution":null,"degree_name":"Computational Science Joint PhD with San Diego State University, PhD","degree_level":"Open Access Dissertation","degree_discipline":"Institute of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Fridolin Weber","Peter Blomgren","Marina Chugunova & Ali Nadim"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-01-01T08:00:00Z","date_published":"2024-01-01T08:00:00Z","updated_at":"2026-07-24T01:40:36Z","subjects":["Computational Physics","Computational Science","Lanczos Algorithm","Nuclear Structure"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarship.claremont.edu/cgu_etd/816","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Fridolin Weber","Peter Blomgren","Marina Chugunova & Ali Nadim"]},{"key":"dc:creator","label":"Author","values":["Zbikowski, Ryan M"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2024-07-17T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Institute of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Computational Science Joint PhD with San Diego State University, PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computational Physics","Computational Science","Lanczos Algorithm","Nuclear Structure"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarship.claremont.edu/cgu_etd/816"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The nuclear many-body problem is conceptualized in an infinite-dimensional Hilbert space, but computationally solved in a finite one. Thus, the predictive power of microscopic calculations relies on the truncated representation of the infinite-dimensional space as well as leveraging advanced computational methods. My dissertation research focuses on three problems related to computational nuclear physics: exploring aspects of nuclear structure, efficiently solving the large sparse matrix-eigenvalue problem and improving the construction of the many-body basis in the no-core configuration-interaction (NCCI) framework.
I) Elliott’s rotational SU(3) model, and its later extension, the symplectic Sp(3, R) model, both played a foundational role in improving the description of nuclear rotational spectral bands. My study of several beryllium isotopes, and 20Ne uses the decomposition of no-core shell-model wavefunctions into symmetry defined subspaces to show the Sp(3, R) picture provides a more consistent description of rotational band structure.
II) Solving the non-relativistic many-body Schrödinger equation is often cast as a large sparse Hamiltonian eigenvalue problem. State-of-the-art NCCI calculation dimensions can exceed several billion and typically require supercomputers and thousands of core hours to compute small numbers of low-lying eigenstates. Thus, there is strong motivation for ways to reduce computational costs. In this research, I augment the block Lanczos algorithm using a bootstrapped pivot to significantly reduce the number of Hamiltonian-matrix multiplications typically dominating the algorithm’s total time-to-solution. My results demonstrate significant speedup in time-to-solution, often by a factor of two or more, and up to ten, can be achieved through the use of bootstrapping.
III) In NCCI, the many-body basis is historically constructed from antisymmeterized products of harmonic oscillator (HO) single-particle wavefunctions. However, one often needs many HO antisymmeterized products states to produce accurate theoretical predictions of the properties of low-lying nuclear states. Alternative choices of single-particle basis which provide better descriptions of nuclear observables relative to the problem dimension and underlying basis parameters motivate continued explorations. In this research, I explore the use of a natural orbital (NO) single-particle basis, that is, one which diagonalizes the one-body density matrix of a reference many-body state, as a means of improving the description of energy, electromagnetic transitions and radii calculations relative to the problem dimension for select sd-shell nuclei.
"]},{"key":"dc:title","label":"Title","values":["Computational Approaches to the Nuclear Many-Body Problem"]}]}],"canonical_facts":{"dc:contributor":["Fridolin Weber","Peter Blomgren","Marina Chugunova & Ali Nadim"],"dc:creator":["Zbikowski, Ryan M"],"dc:date.available":["2024-07-17T07:00:00Z"],"dc:description.abstract":["The nuclear many-body problem is conceptualized in an infinite-dimensional Hilbert space, but computationally solved in a finite one. Thus, the predictive power of microscopic calculations relies on the truncated representation of the infinite-dimensional space as well as leveraging advanced computational methods. My dissertation research focuses on three problems related to computational nuclear physics: exploring aspects of nuclear structure, efficiently solving the large sparse matrix-eigenvalue problem and improving the construction of the many-body basis in the no-core configuration-interaction (NCCI) framework.
I) Elliott’s rotational SU(3) model, and its later extension, the symplectic Sp(3, R) model, both played a foundational role in improving the description of nuclear rotational spectral bands. My study of several beryllium isotopes, and 20Ne uses the decomposition of no-core shell-model wavefunctions into symmetry defined subspaces to show the Sp(3, R) picture provides a more consistent description of rotational band structure.
II) Solving the non-relativistic many-body Schrödinger equation is often cast as a large sparse Hamiltonian eigenvalue problem. State-of-the-art NCCI calculation dimensions can exceed several billion and typically require supercomputers and thousands of core hours to compute small numbers of low-lying eigenstates. Thus, there is strong motivation for ways to reduce computational costs. In this research, I augment the block Lanczos algorithm using a bootstrapped pivot to significantly reduce the number of Hamiltonian-matrix multiplications typically dominating the algorithm’s total time-to-solution. My results demonstrate significant speedup in time-to-solution, often by a factor of two or more, and up to ten, can be achieved through the use of bootstrapping.
III) In NCCI, the many-body basis is historically constructed from antisymmeterized products of harmonic oscillator (HO) single-particle wavefunctions. However, one often needs many HO antisymmeterized products states to produce accurate theoretical predictions of the properties of low-lying nuclear states. Alternative choices of single-particle basis which provide better descriptions of nuclear observables relative to the problem dimension and underlying basis parameters motivate continued explorations. In this research, I explore the use of a natural orbital (NO) single-particle basis, that is, one which diagonalizes the one-body density matrix of a reference many-body state, as a means of improving the description of energy, electromagnetic transitions and radii calculations relative to the problem dimension for select sd-shell nuclei.
"],"dc:identifier":["https://scholarship.claremont.edu/cgu_etd/816"],"dc:subject":["Computational Physics","Computational Science","Lanczos Algorithm","Nuclear Structure"],"dc:title":["Computational Approaches to the Nuclear Many-Body Problem"],"thesis:degree_discipline":["Institute of Mathematical Sciences"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Computational Science Joint PhD with San Diego State University, PhD"]},"updated_at":"2026-07-24T01:40:36Z"}