EPSRC Reference: 
GR/L01084/01 
Title: 
CHAOS IN ATOMIC AND RELATED SYSTEMS: EXTENSIONS TO PERIODIC ORBIT THEORY 
Principal Investigator: 
Monteiro, Professor T 
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Department: 
Physics and Astronomy 
Organisation: 
UCL 
Scheme: 
Standard Research (PreFEC) 
Starts: 
01 March 1996 
Ends: 
30 April 1999 
Value (£): 
129,437

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Summary on Grant Application Form 
Periodic Orbit theory is the major tool of quantum chaology. Atomic provide sensitive tests of the theory. However the theory fails to reproduce observations in experimental spectra (e.g. diffractive effects) or near bifurcations (e.g. ghosts). We have developed a theory adequate for corescattering systems. It will be further developed in order to include the vicinity of bifurcations by using normal forms from catastrophe theory and solving the classical equations in the complex plane. We will extend our timeindependent work to a wavepacket treatment to cover recent shortpulse laser experiments. Standard periodic orbit theory is now a valuable toll in the analysis of mesoscopic systems in the chaotic regime which may form the basis for future electronic devices. The methods of atomic physics are readily adaptable to the problem of chaos in the resonant tunnelling diode in a magnetic field. We propose to transfer this technology and to develop a semi classical theory for the currentvoltage characteristics of the RTD analogous to that used for atomic photoabsorption spectra, to circumvent the need for prohibitive quantum calculations needed e.g. at large tilt angles. The system has been predicted to exhibit localisation (of dynamical origin but analogous to Anderson localisation). The interaction between this effect and periodicorbit scars remain an unanswered problem in quantum chaos. We will use our experience in quantum phasespace representations to investigate this effect and to identify observable effects.

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