Robin Lyth Hudson was a British mathematician notable for his contribution to

quantum probability The Born rule (also called Born's rule) is a key postulate of quantum mechanics which gives the probability that a measurement of a quantum system will yield a given result. In its simplest form, it states that the probability density of findin ...

Education and career

Robin Lyth Hudson received his Ph.D. from the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

in 1966 under

John T. Lewis John Trevor Lewis (15 April 1932 – 21 January 2004) was a Welsh mathematical physicist who made contributions to areas including quantum measurement, Bose–Einstein condensation and large deviations theory. He was a senior professor at the ...

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

. 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 quan ...

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 , mottoeng = Knowledge, Wisdom, Humanity , established = 2004 – University of Manchester Predecessor institutions: 1956 – UMIST (as university college; university 1994) 1904 – Victoria University of Manchester 1880 – Victoria Univer ...

, 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, when L ...

, 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 {{UK-mathematician-stub