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 field of designs for and control of integrable quantum devices.

Research Interests

  • Quantum control designed from broken integrability
    This Australian Research Council funded project aims to open new avenues in quantum device engineering design. This will be achieved through the use of advanced mathematical methodologies developed around the notion of quantum integrability, and the breaking of that integrability. The expert team of Investigators will capitalise on their recent achievements in this field, which includes a first example of a quantum switch designed through broken integrability. The expected outcomes will encompass novel applications of abstract mathematical physics towards the concrete control of quantum mechanical architectures. These outcomes will promote new opportunities for the construction of atomtronic devices, which are rising as a foundation for next-generation quantum technologies.

Research Impacts

My current research aims to use the mathematical theory of quantum integrability to aid in the design of new quantum devices. Read about it some more at this blog on the Nature Research Device and Materials Engineering Community.

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

  • This project aims to open avenues in the mathematical design quantum devices based on cold atom systems. This will be achieved through the use of methodologies developed around the notion of quantum integrability, and the breaking of that integrability. The classic techniques of quantum integrability, centred around the Quantum Inverse Scattering Method and the Bethe Ansatz, will form the foundations for the theory. Potential applications will be developed for the field of atomtronics – analogues of electronic systems that are based on the transport of cold atoms.

    The successful applicant will be a member of an international collaboration that includes two institutes in Brazil. The applicant will enrol through the School of Mathematics and Physics.

View all Available Projects

Publications

Book Chapter

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

  • Bracken, Anthony R., Gould, Mark D., Links, Jon R. and Zhang, Yao-Zhong (1999). Integrable models of correlated electrons. Statistical Physics on the Eve of the 21st Century. (pp. 303-315) edited by Murry Batchelor and Luc Wille. River Ridge, New Jersey United States: World Scientific Publishing. doi: 10.1142/3964

Journal Article

Conference Publication

  • Links, Jon (2017). On completeness of Bethe Ansatz solutions for sl(2) Richardson–Gaudin systems. International Colloquium in Group Theoretical Methods in Physics, Rio de Janeiro, Brazil, 19-25 June 2016. Cham, Switzerland: Springer International Publishing. doi: 10.1007/978-3-319-69164-0_36

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

  • Birrell, A., Isaac, P. S. and Links, J. (2013). Exactly solvable BCS-BEC crossover Hamiltonians. The XXIX International Colloquium on Group-Theoretical Methods in Physics, Tianjin, China, 20-26 August 2012. Hackensack, NJ, United States: World Scientific. doi: 10.1142/9789814518550_0018

  • Moghaddam, Amir , Links, Jon and Zhang, Yao-Zhong (2013). Exactly solvable, non-Hermitian BCS Hamiltonian. XXIX International Colloquium on Group-Theoretical Methods in Physics, Tianjin, China, 20-26 August 2012. City of Singapore, Singapore: World Scientific Publishing.

  • Links, Jon, Foerster, Angela, Tonel, Ariel Prestes and Santos, Gilberto (2006). The two-site Bose-Hubbard model. Basel, Switzerland: Birkhauser Verlag Ag. doi: 10.1007/s00023-006-0295-3

  • Wagner, L., Links, J. and Isaac, P. (2005). Ribbon structure in symmetric pre-monoidal categories. XXV International Colloquium on Group Theoretical Methods in, Cocoyoc, Mexico, 2-6 August, 2004. Bristol, U.K.: Institute of Physics Publishing.

  • Batchelor, M. T., Guan, X-W., Dunning, C. and Links, J. (2005). The 1D Bose Gas with Weakly Repulsive Delta Interaction. Statistical Physics of Quantum Systems, Sendai, Japan, 17 - 20 July 2004. Japan: The Physical Society of Japan. doi: 10.1143/jpsjs.74s.53

  • Zhou, H. Q., Links, J. and McKenzie, R. H. (2003). Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate. Singapore: World Scientific Publishing Company. doi: 10.1142/S0217979203023203

  • Hibberd, KE and Links, JR (2003). Integrability and exact solution of an electronic model with long range interactions. Bristol: Iop Publishing Ltd.

  • Takizawa, M. C. and Links, J. (2003). Ladder operators for integrable one-dimensional lattice models. 24th International Colloquium on Group Theoretical Methods in Physics (ICGTMP-2002), Paris, France, 15-20 July 2002. Bristol, UK: Institute of Physics.

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

  • Hibberd, KE, Gould, MD and Links, JR (1998). U-q[gl(2 vertical bar 1)] and the anisotropic supersymmetric U model. 12th International Colloquium on Group Theoretical Methods in Physics (Group 22), Hobart Australia, Jul 13-17, 1998. CAMBRIDGE: INTERNATIONAL PRESS INC BOSTON.

  • Hibberd, KE, Links, JR and Gould, MD (1997). The supersymmetric U model and Bethe ansatz equations. XXI International Colloquium on Group Theoretical Methods in Physics - Group 21, Goslar Germany, Jul 15-20, 1996. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD.

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.

  • This project aims to open avenues in the mathematical design quantum devices based on cold atom systems. This will be achieved through the use of methodologies developed around the notion of quantum integrability, and the breaking of that integrability. The classic techniques of quantum integrability, centred around the Quantum Inverse Scattering Method and the Bethe Ansatz, will form the foundations for the theory. Potential applications will be developed for the field of atomtronics – analogues of electronic systems that are based on the transport of cold atoms.

    The successful applicant will be a member of an international collaboration that includes two institutes in Brazil. The applicant will enrol through the School of Mathematics and Physics.