or
Continue with FacebookLooking to list your PhD opportunities? Log in here.
This project is no longer listed on FindAPhD.com and may not be available.
Click here to search FindAPhD.com for PhD studentship opportunities
Prof F Nijhoff
Applications accepted all year round
Competition Funded PhD Project (European/UK Students Only)
About the Project
The theory of integrable discrete systems also extends into the quantum domain, and it is here that the true richness of integrability is most visible (quantum mechanics being in essence a theory of discrete and algebraic objects). The current research concentrates on formulating a proper quantum theory for discrete mappings and integrable systems living on the space-time lattice. Exploiting the exactness of the models and integrable structures (R-matrices, quantum Lax pairs and determinants) the investigation is set to produce rigorous and analytic answers to questions which for other models are only accessible through numerical and perturbative methods. As such, quantum integrable discrete models form a paradigm for the development of new approaches in the quantum regime which have potential implications to areas such as string and conformal field theory, as well as in the theory of random matrices in mesoscopic physics, quantum computing and nanotechnology.
Integrable Systems
The Integrable Systems group in Leeds, one of the leading groups worldwide working on integrable systems, has been strengthened by three recent appointments, one at a senior level. Integrable Systems are systems that, albeit highly nontrivial and nonlinear, are amenable to exact and rigorous techniques for their solvability. They can take many shapes or forms: nonlinear evolution equations, partial and ordinary differential equations and difference equations, Hamiltonian many-body systems, quantum systems and spin models in statistical mechanics. A large number of mathematical techniques have been developed to unravel the rich structures behind these systems. The six permanent members of staff work with five postdocs and postgraduate students.
Leeds is a major centre for the theory of discrete and quantum integrable systems. This group represents a wide range of research activities into integrable nonlinear systems, their symmetries, solution techniques and the underlying mathematical structures, as well as more mathematical aspects of physical systems, for example quantum systems. The models comprise ordinary and partial differential and difference equations, dynamical mappings, discrete Painleve equations, Hamiltonian and many-particle systems and systems of hydrodynamic type. The theory and its specific models have wide-ranging applications, for example, in nonlinear optics, theory of water waves, integrable quantum field theory, statistical mechanics and combinatorics random matrix theory and nanotechnology.
Integrable Systems
The Integrable Systems group in Leeds, one of the leading groups worldwide working on integrable systems, has been strengthened by three recent appointments, one at a senior level. Integrable Systems are systems that, albeit highly nontrivial and nonlinear, are amenable to exact and rigorous techniques for their solvability. They can take many shapes or forms: nonlinear evolution equations, partial and ordinary differential equations and difference equations, Hamiltonian many-body systems, quantum systems and spin models in statistical mechanics. A large number of mathematical techniques have been developed to unravel the rich structures behind these systems. The six permanent members of staff work with five postdocs and postgraduate students.
Leeds is a major centre for the theory of discrete and quantum integrable systems. This group represents a wide range of research activities into integrable nonlinear systems, their symmetries, solution techniques and the underlying mathematical structures, as well as more mathematical aspects of physical systems, for example quantum systems. The models comprise ordinary and partial differential and difference equations, dynamical mappings, discrete Painleve equations, Hamiltonian and many-particle systems and systems of hydrodynamic type. The theory and its specific models have wide-ranging applications, for example, in nonlinear optics, theory of water waves, integrable quantum field theory, statistical mechanics and combinatorics random matrix theory and nanotechnology.
Project supervisors
Career overview
Professor Frank Nijhoff received a Doctoraat in Wiskunde en Natuurwetenschappen from Universiteit Leiden in 1984. He is an Emeritus Professor at the School of Mathematics at the University of Leeds. His research primarily focuses on the theory of continuous and discrete integrable systems, exploring their connections with various areas of pure and applied mathematics as well as physics. Professor Nijhoff has significantly contributed to the study of integrable lattice equations, which are partial difference equations that exhibit properties similar to well-known integrable partial differential equations, such as the Korteweg-de Vries (KdV) equation. His work has led to insights in soliton theory, algebraic geometry, Hamiltonian mechanics, and the theory of symmetries and conservation laws. He has also explored the quantisation of these systems, resulting in discrete versions of quantum mechanics, and has recently investigated the Lagrangian formalism of such systems, which has introduced new paradigms in variational calculus. Professor Nijhoff is a member of the Algebra, Geometry and Integrable Systems research group at the University of Leeds.
Research interests
Professor Nijhoff''s main research interests are directed towards the theory of continuous and discrete integrable systems and their connections with wider areas of pure and applied mathematics and physics. A significant starting point for many of his contributions has been the study of integrable lattice equations, which are partial difference equations on the space-time lattice that share many features with well-known integrable partial differential equations, such as the Korteweg-de Vries (KdV) equation. The exploration of solutions to these partial difference equations leads to connections with various areas of mathematics, including soliton theory, algebraic geometry, Hamiltonian mechanics, and the theory of symmetries and conservation laws. Notably, special solutions, or reductions, result in integrable dynamical mappings, discrete Painleve equations, and discrete systems of Calogero-Moser type. These systems can also be quantized, leading to corresponding systems in a discrete version of quantum mechanics. Additionally, the study of the Lagrangian formalism of these systems has recently introduced new paradigms in the theory of variational calculus. Professor Nijhoff is a member of the Algebra, geometry and integrable systems research group.
Mathematical Physics
Discrete Integrable Systems
Continuous Integrable Systems
Quantum Integrability
Painleve Equations
Lagrangian Multiform Theory
Integrable Lattice Equations
Soliton Theory
Algebraic Geometry
Hamiltonian Mechanics
Symmetries
Conservation Laws
Variational Calculus
Quantum Mechanics
Find a scholarship to fund your dream Masters
Sign in to view and filter all scholarship opportunities
or
Continue with Facebook