Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry

被引：0

作者：

Kubu, Ondrej ^{[1
]}

Reyes, Daniel ^{[2
,3
]}

Tempesta, Piergiulio ^{[2
,3
]}

Tondo, Giorgio ^{[4
]}

机构：

[1] Czech Tech Univ, Fac Nucl Sci & Phys Engn, Dept Phys, Prague, Czech Republic

[2] Inst Ciencias Matemat ICMAT, C Nicolas Cabrera 13-15, Madrid 28049, Spain

[3] Univ Complutense Madrid, Fac Ciencias Fis, Dept Fis Teor, Madrid 28040, Spain

[4] Univ Trieste, Dipartimento Matemat Informat & Geosci, Trieste, Italy

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2024年 / 480卷 / 2301期

关键词：

integrable systems; Haantjes geometry; magnetic systems; St & auml; ckel systems; SEPARATION; VARIABLES;

D O I：

10.1098/rspa.2024.0076

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional (3D) Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically. In addition, the underlying St & auml;ckel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field.

引用

页数：24

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