Scattering and pairing by exchange interactions
Quantum interactions exchanging different types of particles play a pivotal rôle in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspective. Here, we consider a system made of two fermions and one boson, in order to study the effect of such an off-diagona...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425100832/type/journal_article |
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| author | Jean-Bernard Bru Walter de Siqueira Pedra Alan Ramer dos Santos |
| author_facet | Jean-Bernard Bru Walter de Siqueira Pedra Alan Ramer dos Santos |
| author_sort | Jean-Bernard Bru |
| collection | DOAJ |
| description | Quantum interactions exchanging different types of particles play a pivotal rôle in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspective. Here, we consider a system made of two fermions and one boson, in order to study the effect of such an off-diagonal interaction term, having in mind the physics of cuprate superconductors. Additionally, our model also includes a generalized Hubbard interaction (i.e., a general local repulsion term for the fermions). Regarding pairing, exponentially localized dressed bound fermion pairs are shown to exist, and their effective dispersion relation is studied in detail. Scattering properties of the system are derived for two channels: the unbound and bound pair channels. We give particular attention to the regime of very large on-site (Hubbard) repulsions because this situation is relevant for cuprate superconductors. |
| format | Article |
| id | doaj-art-85d36a7c316a4160ac26e4e9edef4cc8 |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-85d36a7c316a4160ac26e4e9edef4cc82025-08-20T03:58:18ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.10083Scattering and pairing by exchange interactionsJean-Bernard Bru0https://orcid.org/0000-0001-9159-9407Walter de Siqueira Pedra1https://orcid.org/0000-0002-8014-4076Alan Ramer dos Santos2https://orcid.org/0009-0008-1623-3884Departamento de Matemáticas & EHU Quantum center, Facultad de Ciencia y Tecnología, https://ror.org/000xsnr85Universidad del País Vasco / Euskal Herriko Unibertsitatea, UPV/EHU , Apartado 644, 48080 Bilbao, Spain; https://ror.org/03b21sh32BCAM - Basque Center for Applied Mathematics , Mazarredo, 14, 48009 Bilbao, Spain https://ror.org/01cc3fy72IKERBASQUE, Basque Foundation for Science , Plaza Euskadi 5, 48009 Bilbao, Spain; E-mail:https://ror.org/03b21sh32BCAM - Basque Center for Applied Mathematics , Mazarredo, 14, 48009 Bilbao, Spain Departamento de Matemática, Instituto de Ciências Matemáticas e da Computação, https://ror.org/036rp1748Universidade de São Paulo , Avenida Trabalhador São-carlense, 400, 13566-590 São Carlos - SP, Brazil; E-mail:https://ror.org/03b21sh32BCAM - Basque Center for Applied Mathematics , Mazarredo, 14, 48009 Bilbao, Spain Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, https://ror.org/036rp1748Universidade de São Paulo , Rua do Matão 1010, CEP 05508-090 São Paulo - SP, Brazil; E-mail:Quantum interactions exchanging different types of particles play a pivotal rôle in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspective. Here, we consider a system made of two fermions and one boson, in order to study the effect of such an off-diagonal interaction term, having in mind the physics of cuprate superconductors. Additionally, our model also includes a generalized Hubbard interaction (i.e., a general local repulsion term for the fermions). Regarding pairing, exponentially localized dressed bound fermion pairs are shown to exist, and their effective dispersion relation is studied in detail. Scattering properties of the system are derived for two channels: the unbound and bound pair channels. We give particular attention to the regime of very large on-site (Hubbard) repulsions because this situation is relevant for cuprate superconductors.https://www.cambridge.org/core/product/identifier/S2050509425100832/type/journal_article47B9381Q10 |
| spellingShingle | Jean-Bernard Bru Walter de Siqueira Pedra Alan Ramer dos Santos Scattering and pairing by exchange interactions Forum of Mathematics, Sigma 47B93 81Q10 |
| title | Scattering and pairing by exchange interactions |
| title_full | Scattering and pairing by exchange interactions |
| title_fullStr | Scattering and pairing by exchange interactions |
| title_full_unstemmed | Scattering and pairing by exchange interactions |
| title_short | Scattering and pairing by exchange interactions |
| title_sort | scattering and pairing by exchange interactions |
| topic | 47B93 81Q10 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425100832/type/journal_article |
| work_keys_str_mv | AT jeanbernardbru scatteringandpairingbyexchangeinteractions AT walterdesiqueirapedra scatteringandpairingbyexchangeinteractions AT alanramerdossantos scatteringandpairingbyexchangeinteractions |