Associate Professor Jon Links

Associate Professor

Mathematics
Faculty of Science
jrl@maths.uq.edu.au
+61 7 336 52400

Overview

Dr Jon Links's research interests are in: Lie Algebras, Quantised Algebras, Knot Theory, Exactly Solvable Models, Algebraic Bethe Ansatz, Models of Correlated Electrons and Models of Bose-Einstein Condensates.

He received his PhD from the University of Queensland in 1993. His current research projects are in the fields of:

* BCS Model

* Models of Bose-Einstein Condensates

Qualifications

  • Bachelor of Science (Honours), The University of Queensland
  • Doctor of Philosophy, The University of Queensland
  • Bachelor of Science, Australian National University

Publications

View all Publications

Supervision

View all Supervision

Available Projects

  • The study of few-body problems has a long history, and has offered up significant mathematical challenges arising from apparently simple physical systems. Recent progress in the manipulation of ultracold quantum systems, with a high degree of precision, has reignited interest in quantum few-body problems. In the case of integrable quantum systems, there is a wealth of mathematical machinery which has been developed to extract their exact solutions. This project will apply such integrablilty techniques to gain new insights into quantum few-body systems. Examples include bosonic multi-well tunneling models, multi-species fermionic tunneling models, and open fermionic systems.

  • Richardson-Gaudin equations arise in both the study of integrable quantum systems, and polynomial solutions of second-order differential equations. In the integrable systems setting, they have a close connection to the representation theory of certain infinite-dimensional Lie algebras. In the differential equation setting, the structure of the equations is invariant under Moebius transformations, and particular instances gives rise to symmetries. This project will investigate the consequences of these invariances and symmetries for the corresponding representation theory.

  • Quantum integrable systems are well-studied, through a variety of mathematical methods, due to the existence of exact solutions for their eigenvalue spectra. A perennial question is whether such solutions are complete. This project will extend some recent results on the topic to prove new completeness results for a particular class of integrable systems associated with the names of Richardson and Gaudin

View all Available Projects

Publications

Book Chapter

  • Foerster, A., Links, J. R. and Zhou, H. (2003). Exact solvability in contemporary physics. In A. Kundu (Ed.), Classical and Quantum Nonlinear Integrable Systems (pp. 208-233) Bristol: Taylor & Francis Group.

Journal Article

Conference Publication

  • Shen, Yibing and Links, Jon (2015). Richardson - Gaudin form of Bethe Ansatz solutions for an atomic-molecular Bose-Einstein condensate model. In: Journal of Physics: Conference Series. 30th International Colloquium on Group Theoretical Methods in Physics (Group30), Ghent, Belgium, (012068.1-012068.6). 14-18 July 2014. doi:10.1088/1742-6596/597/1/012068

  • Birrell, A., Isaac, P. S. and Links, J. (2013). Exactly solvable BCS-BEC crossover Hamiltonians. In: Symmetries and Groups in Contemporary Physics. The XXIX International Colloquium on Group-Theoretical Methods in Physics, Tianjin, China, (161-166). 20-26 August 2012. doi:10.1142/9789814518550_0018

  • Moghaddam, Amir , Links, Jon and Zhang, Yao-Zhong (2013). Exactly solvable, non-Hermitian BCS Hamiltonian. In: Chengming Bai , Jean-Pierre Gazeau and Mo-Lin Ge, Symmetries and Groups in Contemporary Physics: Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in Physics. XXIX International Colloquium on Group-Theoretical Methods in Physics, Tianjin, China, (627-630). 20-26 August 2012.

  • Links, Jon, Foerster, Angela, Tonel, Ariel Prestes and Santos, Gilberto (2006) The two-site Bose-Hubbard model. Annales Henri Poincare, 7 7-8: 1591-1600. doi:10.1007/s00023-006-0295-3

  • Wagner, L., Links, J. and Isaac, P. (2005). Ribbon structure in symmetric pre-monoidal categories. In: G. S. Pogosyan, L. E. Vicent and K. B. Wolf, Group Theoretical Methods in Physics. XXV International Colloquium on Group Theoretical Methods in, Cocoyoc, Mexico, (557-562). 2-6 August, 2004.

  • Batchelor, M. T., Guan, X-W., Dunning, C. and Links, J. (2005). The 1D Bose Gas with Weakly Repulsive Delta Interaction. In: N. Hatano, N. Kawashima, S. Kiyashita, M. Oshikawa, T. Sakai, M. Shiroishi and S. Todo, Statistical Physics of Quantum Systems - novel orders and dynamics. Statistical Physics of Quantum Systems, Sendai, Japan, (53-56). 17 - 20 July 2004.

  • Hibberd, KE and Links, JR (2003) Integrability and exact solution of an electronic model with long range interactions. Institute of Physics Conference Series, 173 Supplement: 725-728.

  • Takizawa, M. C. and Links, J. (2003). Ladder operators for integrable one-dimensional lattice models. In: J. P. Gazeau, R. Kerner, J. P. Antoine, S. Metens and J. Y. Thibon, Group 24: Physical and Mathematical Aspects of Symmetries: Proceedings of the 24th International Colloquium on Group Theoretical Methods in Physics, Paris, 15-20 July 2002. 24th International Colloquium on Group Theoretical Methods in Physics (ICGTMP-2002), Paris, France, (417-420). 15-20 July 2002.

  • Guan, Xi-Wen, Foerster, Angela, Links, Jon and Zhou, Huan-Qiang (2002). Exact results for BCS systems. In: Workshop on Integrable Theories, Solitons and Duality, UNESP 2002. 2002 Workshop on Integrable Theories, Solitons and Duality, UNESP 2002, Sao Paulo, , (). July 1, 2002-July 6, 2002.

  • Hibberd, KE, Gould, MD and Links, JR (1998). U-q[gl(2 vertical bar 1)] and the anisotropic supersymmetric U model. In: Corney, SP, Delbourgo, R and Jarvis, PD, Group 22: Proceedings of the Xii International Colloquium On Group Theoretical Methods in Physics. 12th International Colloquium on Group Theoretical Methods in Physics (Group 22), Hobart Australia, (173-177). Jul 13-17, 1998.

  • Hibberd, KE, Links, JR and Gould, MD (1997). The supersymmetric U model and Bethe ansatz equations. In: Doebner, HD, Nattermann, P and Scherer, W, Group 21 - Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebra, Vols 1 and 2. XXI International Colloquium on Group Theoretical Methods in Physics - Group 21, Goslar Germany, (1042-1046). Jul 15-20, 1996.

Other Outputs

Grants (Administered at UQ)

PhD and MPhil Supervision

Current Supervision

Completed Supervision

Possible Research Projects

Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.

  • The study of few-body problems has a long history, and has offered up significant mathematical challenges arising from apparently simple physical systems. Recent progress in the manipulation of ultracold quantum systems, with a high degree of precision, has reignited interest in quantum few-body problems. In the case of integrable quantum systems, there is a wealth of mathematical machinery which has been developed to extract their exact solutions. This project will apply such integrablilty techniques to gain new insights into quantum few-body systems. Examples include bosonic multi-well tunneling models, multi-species fermionic tunneling models, and open fermionic systems.

  • Richardson-Gaudin equations arise in both the study of integrable quantum systems, and polynomial solutions of second-order differential equations. In the integrable systems setting, they have a close connection to the representation theory of certain infinite-dimensional Lie algebras. In the differential equation setting, the structure of the equations is invariant under Moebius transformations, and particular instances gives rise to symmetries. This project will investigate the consequences of these invariances and symmetries for the corresponding representation theory.

  • Quantum integrable systems are well-studied, through a variety of mathematical methods, due to the existence of exact solutions for their eigenvalue spectra. A perennial question is whether such solutions are complete. This project will extend some recent results on the topic to prove new completeness results for a particular class of integrable systems associated with the names of Richardson and Gaudin