Mathematics Department Statistical Mechanics and Quantum Probability Group

Dr LJ Landau Department of Mathematics King's College London Strand, London WC2R 2LS United Kingdom Room 422, Strand Building Tel: +44-(0)20-7848 2219 (direct) Tel: +44-(0)20-7848 2217 (general office) Fax: +44-(0)20-7848 2017 E-mail: larry.landau@kcl.ac.uk

Member of the Statistical Mechanics and Quantum Probability Group

Contents:

Research Interests

• Quantum field theory
• Statistical mechanics

The non-classical nature of quantum systems may be explored by studying the violation of Bell's inequality, and a precise expression for the violation of Bell's inequality in relativistic quantum theory has been obtained. An improved understanding of the nature of quantum systems may be gained by considering large scale limits of these systems, where these quantum systems may become classical and/or irreversible. To study these limits for particles on a lattice, bounds on the magnitude of Bessel functions play an important role, and best possible uniform bounds on Bessel functions, considerably improving classical bounds, have been obtained.

Recent Publications

• Asymptotic Expansion of a Bessel Function Integral Using Hypergeometric Functions J. Comp. Appl. Math (with N.J.Luswili) (to appear around August 2001)
• Ratios of Bessel Functions and Roots of aJ_n (x)+xJ_n (x) = 0, J. Math. Anal. App. 240 (1999) 174-204
• Bessel Functions: Monotonicity and Bounds, J. London Math. Soc. (2) 61 (2000) 197-215
• Fermi Gas on a Lattice in the Van Hove Limit, J. Stat. Phys. 87 (1997) 821-845 (with T.G.Ho)
• Macroscopic Observation of a Quantum Particle in a Slowly Varying Potential, Annals of Physics 246 (1996) 190-227

Further Publications

• Penrose's Philosophical Error, in Concepts for Neural Networks (1997)
• Concepts for Neural Networks, edited by L.J.Landau and J.G.Taylor, Springer, ISBN 3-540-76163-2 (1997)
• Observation of Quantum Particles on a Large Space-Time Scale, Journal of Statistical Physics 77 (special volume in honour of O Penrose), 259-310 (1994)
• Weak coupling limit: Feynman Diagrams, in On Three Levels, NATO ASI series Vol. 324, eds. M.Fannes,C.Maes,A.Verbeure (Plenum Press, New York) (1994)
• The weak coupling limit for a Fermi gas in a random potential; in: Quantum and Non-Commutative Analysis, Mathematical Physics Studies 16, 167-178 (1993)
• On the weak coupling limit for a Fermi gas in a random potential, Reviews in Mathematical Physics 5, 209-298 (with T. Ho and A. Wilkins) (1993)

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