Robin Lyth Hudson was a British mathematician notable for his contribution to
quantum probability.
Education and career
Robin Lyth Hudson received his Ph.D. from the
University of Oxford
The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the world's second-oldest university in contin ...
in 1966 under
John T. Lewis with a thesis entitled ''Generalised Translation-Invariant Mechanics''. He was appointed assistant lecturer
at the University of Nottingham in 1964, promoted to a chair in 1985 and served as Head of Department from 1987 to 1990. He spent sabbatical semesters in Heidelberg (1978), Austin Texas (1983) and Boulder Colorado (1996). After taking early retirement in 1997, he held part-time research posts at Nottingham Trent University (1997-2005), the Slovak Academy
of Sciences (1997-2000) and Loughborough University (2005–21), and a visiting professorship at the University of Łódź (2002) which awarded him an honorary doctorate in 2013.
Hudson was a mathematical physicist who was one of the pioneers of
quantum probability. An early result, now known as Hudson’s theorem in quantum optics, shows that the pure quantum states with positive
Wigner quasiprobability distribution
The Wigner quasiprobability distribution (also called the Wigner function or the Wigner–Ville distribution, after Eugene Wigner and Jean-André Ville) is a quasiprobability distribution. It was introduced by Eugene Wigner in 1932 to study qu ...
are the Gaussian ones. Together with PhD students, Robin established one of the first quantum central limit theorems, proved an early quantum de Finetti theorem, and introduced quantum Brownian motion as a non-commuting pair of families of unbounded operators, using the formalism of quantum field theory. He collaborated with
K. R. Parthasarathy first at the
University of Manchester
The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The university owns and operates majo ...
, and later at
University of Nottingham
The University of Nottingham is a public university, public research university in Nottingham, United Kingdom. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948. The University of Nottingham belongs t ...
and at
Loughborough University
Loughborough University (abbreviated as ''Lough'' or ''Lboro'' for post-nominals) is a public research university in the market town of Loughborough, Leicestershire, England. It has been a university since 1966, but it dates back to 1909, whe ...
, on their seminal work in
Quantum stochastic calculus Quantum stochastic calculus is a generalization of stochastic calculus to noncommuting variables. The tools provided by quantum stochastic calculus are of great use for modeling the random evolution of systems undergoing measurement, as in quantum ...
.
In later papers he developed a theory of quantum stochastic double product integrals and their application to the quantum
Yang-Baxter equation, the quantisation of
Lie bialgebra In mathematics, a Lie bialgebra is the Lie-theoretic case of a bialgebra: it is a set with a Lie algebra and a Lie coalgebra structure which are compatible.
It is a bialgebra where the multiplication is skew-symmetric and satisfies a dual Jacobi ...
s and quantum Lévy area.
[Hudson, Robin Lyth; Pulmannová, S. (2004). "Double product integrals and Enriquez quantisation of Lie bialgebras I: The quasitriangularity relations". Journal of Mathematical Physics. 45: 2090–2105.]
Selected works
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References
External links
Mathematical genealogy project page on Robin Lyth HudsonAncestry of Robin Lyth Hudson
1940 births
Living people
20th-century British mathematicians
21st-century British mathematicians
Probability theorists
Alumni of the University of Oxford
Academics of the University of Nottingham
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