Home page for D Richards

Email Address: D.Richards@open.ac.uk

Books

• Introduction to Dynamics I C Percival and D Richards (Cambridge University Press, 1982)

  An errata list is given here

• Advanced Mathematical Methods with Maple (Cambridge University Press, published, November 2001).

  There are over 1000 exercises in this book many solutions of which may be obtained by going here .

  A list of errata is here .

Courses

• M820 The Calculus of Variations and Advanced Calculus

  This course comprises twelve chapters and, in order to limit the size of the PDF files, is split into three components. The first component, containing the contents and chapters 1-4, may be viewed from here ; the second, chapters 5-8, from here and the third, containing the index and chapters 9-12, from here . These version were last corrected February 2008.

• M821 Nonlinear Differential Equations

  There is no errata list at present.

Research interests

• Nonlinear classical systems and their corresponding quantal analogue.

Topics of current interest

Excerpt from current research degree prospectus ...

• Studying the manner in which the chaotic phenomena observed in the motion of most classical nonlinear systems are manifest in the equivalent quantal systems. The research concentrates on systems accessible to experiments, particularly strong time-dependent electric fields on excited atoms, and there is a fruitful collaboration with Professor P M Koch's experimental group at Stony Brook. The main aims of the work are to understand the general features of the classical and quantal motion of systems perturbed by strong time-dependent forces; and to understand the circumstances in which classical and quantum observables behave similarly and when they differ.

Recent publications and preprints

• Core-induced chaos in intra-shell transitions. With D Fregenal, M Forre and E Hrsdal. Submitted to Phys Rev A. Reprint
• The effect of parallel static and microwave electric fields on excited hydrogen atoms. Published in New J Phys. 7 (2005) 138. Reprint
• Intensity-dependent dispersion under conditions of electromagnetically induced transparency in coherently prepared multistate atoms. Phys Rev A 67 023818-1:5 (2003)
• A Scaling law for the energy levels of a non-linear schrodinger equation. J.Phys. B34, 1805-1813 (2001) Preprint
• Appearing and Disappearing Strong-Field Resonances in H atoms. Phys. Rev A61, 060101-1 (2000)
• Stochastic wave functions diagrams for electromagnetically induced transparency, inversionless gain and shelving. J Mod Opt 54, 315-333 (1998).
• Stochastic Schrodinger equations for optical fields based on atom detection, Phys Rev A58, 2690-2698 (1998).
• Stark-state resonances induced by low-frequency elliptically polarised fields. J. Phys B30 4019-4047 (1997) Preprint
• Resonant, elliptical-polarisation control of microwave ionisation of hydrogen atoms. Phys. Rev Lett 78, 3840-3843 (1997).
• The Periodically Driven Excited Hydrogen Atom . A review article in Classical, Semiclassical and Quantum Dynamics in Atoms 1997, (Springer, Lecture notes in Physics) Preprint
• Polarisation independence of microwave ionisation thresholds of excited hydrogen atoms near the principle resonance. Phys Rev Lett 76, 892-895 (1996).
• The effects of classical resonance islands in time-dependent quantum mechanics. J. Phys. B29, 5237-5271, (1996). Preprint
• The dynamics of high harmonic generation. J Phys. B29, 2935-2949 (1996). Preprint
• One-dimensional excited hydrogen atoms in short-pulsed high frequency fields. J. Phys B28 L413-L421 (1995).
• Robust scarred states. J Phys B27 2169-2189 (1994).

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