PDE and Applied Analysis SeminarㅣDynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons

분야Field
날짜Date	2022-11-16 ~ 2022-11-16	시간Time	15:00 ~ 16:00
장소Place		초청자Host
연사Speaker	Jacky Chong	소속Affiliation	Peking University
TOPIC	PDE and Applied Analysis SeminarㅣDynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons
소개 및 안내사항Content	Dynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons Abstract: In this talk, we study the effective (mean-field) dynamics of a many- body bosonic system and obtain a quantitative bound on the error between the exact and effective dynamics. More precisely, we consider a system of N interacting bosons where the particles experience a short range two-body interaction given by N −1 vN (x) = N3β−1 v(Nβx), which scales to a δ function, where 0 < β < 1 and v is a non-negative spherically symmetric function. Our main result is the extension of the local-in-time Fock space norm approximation of the exact dynamics of quasifree states proven in M. Grillakis and M. Machedon, Comm. PDEs., 42, 24(2017) for 0 < β < 2 3 to a global-in-time approximation for 0 < β < 1. Our extension allows for a more general set of initial data that includes coherent states. The key ingredients in establishing the Fock space approximation are the work of Grillakis and Machedon on the local well-posedness theory for the time-dependent Hartree–Fock– Bogoliubov (HFB) system in M. Grillakis and M. Machedon, Comm. PDEs., 44, 1431(2019) and a global-in-time estimate for the HBF system in J. Chong, M. Grillakis, M. Machedon, and Z. Zhao, Comm. PDEs., 46, 2015(2021). This is a joint work with Z. Zhao, Ann. Henri Poincaré (2021). The talk will be delivered in English. Zoom link: https://postech-ac-kr.zoom.us/j/96428451691?pwd=YTdPQTMrd1JlVUlzUkk0ZUZkRVM2dz09 Meeting ID: 964 2845 1691 Password: PDEAA

학회명Field	PDE and Applied Analysis SeminarㅣDynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons
날짜Date	2022-11-16 ~ 2022-11-16	시간Time	15:00 ~ 16:00
장소Place		초청자Host
소개 및 안내사항Content	Dynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons Abstract: In this talk, we study the effective (mean-field) dynamics of a many- body bosonic system and obtain a quantitative bound on the error between the exact and effective dynamics. More precisely, we consider a system of N interacting bosons where the particles experience a short range two-body interaction given by N −1 vN (x) = N3β−1 v(Nβx), which scales to a δ function, where 0 < β < 1 and v is a non-negative spherically symmetric function. Our main result is the extension of the local-in-time Fock space norm approximation of the exact dynamics of quasifree states proven in M. Grillakis and M. Machedon, Comm. PDEs., 42, 24(2017) for 0 < β < 2 3 to a global-in-time approximation for 0 < β < 1. Our extension allows for a more general set of initial data that includes coherent states. The key ingredients in establishing the Fock space approximation are the work of Grillakis and Machedon on the local well-posedness theory for the time-dependent Hartree–Fock– Bogoliubov (HFB) system in M. Grillakis and M. Machedon, Comm. PDEs., 44, 1431(2019) and a global-in-time estimate for the HBF system in J. Chong, M. Grillakis, M. Machedon, and Z. Zhao, Comm. PDEs., 46, 2015(2021). This is a joint work with Z. Zhao, Ann. Henri Poincaré (2021). The talk will be delivered in English. Zoom link: https://postech-ac-kr.zoom.us/j/96428451691?pwd=YTdPQTMrd1JlVUlzUkk0ZUZkRVM2dz09 Meeting ID: 964 2845 1691 Password: PDEAA

성명Field	PDE and Applied Analysis SeminarㅣDynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons
날짜Date	2022-11-16 ~ 2022-11-16	시간Time	15:00 ~ 16:00
소속Affiliation	Peking University	초청자Host
소개 및 안내사항Content	Dynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons Abstract: In this talk, we study the effective (mean-field) dynamics of a many- body bosonic system and obtain a quantitative bound on the error between the exact and effective dynamics. More precisely, we consider a system of N interacting bosons where the particles experience a short range two-body interaction given by N −1 vN (x) = N3β−1 v(Nβx), which scales to a δ function, where 0 < β < 1 and v is a non-negative spherically symmetric function. Our main result is the extension of the local-in-time Fock space norm approximation of the exact dynamics of quasifree states proven in M. Grillakis and M. Machedon, Comm. PDEs., 42, 24(2017) for 0 < β < 2 3 to a global-in-time approximation for 0 < β < 1. Our extension allows for a more general set of initial data that includes coherent states. The key ingredients in establishing the Fock space approximation are the work of Grillakis and Machedon on the local well-posedness theory for the time-dependent Hartree–Fock– Bogoliubov (HFB) system in M. Grillakis and M. Machedon, Comm. PDEs., 44, 1431(2019) and a global-in-time estimate for the HBF system in J. Chong, M. Grillakis, M. Machedon, and Z. Zhao, Comm. PDEs., 46, 2015(2021). This is a joint work with Z. Zhao, Ann. Henri Poincaré (2021). The talk will be delivered in English. Zoom link: https://postech-ac-kr.zoom.us/j/96428451691?pwd=YTdPQTMrd1JlVUlzUkk0ZUZkRVM2dz09 Meeting ID: 964 2845 1691 Password: PDEAA

성명Field	PDE and Applied Analysis SeminarㅣDynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons
날짜Date	2022-11-16 ~ 2022-11-16	시간Time	15:00 ~ 16:00
호실Host		인원수Affiliation	Jacky Chong
사용목적Affiliation		신청방식Host	Peking University
소개 및 안내사항Content	Dynamical Hartree–Fock–Bogoliubov Approximation of Interacting Bosons Abstract: In this talk, we study the effective (mean-field) dynamics of a many- body bosonic system and obtain a quantitative bound on the error between the exact and effective dynamics. More precisely, we consider a system of N interacting bosons where the particles experience a short range two-body interaction given by N −1 vN (x) = N3β−1 v(Nβx), which scales to a δ function, where 0 < β < 1 and v is a non-negative spherically symmetric function. Our main result is the extension of the local-in-time Fock space norm approximation of the exact dynamics of quasifree states proven in M. Grillakis and M. Machedon, Comm. PDEs., 42, 24(2017) for 0 < β < 2 3 to a global-in-time approximation for 0 < β < 1. Our extension allows for a more general set of initial data that includes coherent states. The key ingredients in establishing the Fock space approximation are the work of Grillakis and Machedon on the local well-posedness theory for the time-dependent Hartree–Fock– Bogoliubov (HFB) system in M. Grillakis and M. Machedon, Comm. PDEs., 44, 1431(2019) and a global-in-time estimate for the HBF system in J. Chong, M. Grillakis, M. Machedon, and Z. Zhao, Comm. PDEs., 46, 2015(2021). This is a joint work with Z. Zhao, Ann. Henri Poincaré (2021). The talk will be delivered in English. Zoom link: https://postech-ac-kr.zoom.us/j/96428451691?pwd=YTdPQTMrd1JlVUlzUkk0ZUZkRVM2dz09 Meeting ID: 964 2845 1691 Password: PDEAA