Berlin 2001 – scientific programme

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AMPD: EPS AMPD

AMPD 7: Sitzung 7

AMPD 7.1: Talk

Thursday, April 5, 2001, 09:55–10:30, H105

Complex dynamics in simple atoms — •Andreas Buchleitner — Max–Planck–Institut for Physics of Complex Systems, Dresden

Presumably the best candidates to establish the correspondence between classical and quantum dynamics are simple atomic systems with few degrees of freedom. If we consider atoms with one or two highly excited valence electrons, we deal with the direct microscopic edition of the classical two– or three–body Coulomb problem, i.e. essentially with point particles interacting through a Coulomb field. For the hydrogen atom, this immediately leads to Bohr’s and Sommerfeld’s semiclassical interpretation of experimentally observed spectra, which pictures the Rydberg electron localized along classical Kepler trajectories. However, as soon as we excite both electrons of the helium atom to comparable energy levels, the old quantization scheme as well as our intuition gets into trouble, due to the nonlinear coupling of the atomic degrees of freedom through the electron–electron interaction. Chaos is born out from the apparently simple classical equations of motion, and quantum excitation spectra close to the double ionization threshold exhibit a dramatic complexity. A similar situation arises for single electron Rydberg states exposed to a static magnetic (or crossed electric and magnetic) field(s), close (or above) the ionization threshold, and classically chaotic dynamics induce the efficient ionization of periodically driven atomic systems, at tiny photon energies much below the limit set by the familiar photo effect.

Only during the past 25 years did we learn to decipher this complexity of strongly perturbed Rydberg systems, thanks to novel statistical and semiclassical methods which have been unified and elaborated under the label "quantum chaos". A large part of this activity has been devoted to simple model systems (chaotic billiards or kicked tops and rotors) with purely discrete spectra, where the essential quantum fingerprints of chaos could be elaborated with moderate computational effort. However, with the latest advances in computational methods and resources, we can nowadays refocus on realistic atomic systems, with all their additional complications like, e.g., quantum scattering of the Rydberg electron off a non–Coulombic multielectron core, finite decay rates to the atomic continuum, or incoherent relaxation processes induced through the coupling to an incoherent environment. It turns out that atoms are perfect, low-dimensional micro–laboratories which display fundamental phenomena of coherent quantum transport in disordered media – such as Anderson localization and conductance fluctuations – together with typical quantum manifestations of the mixed regular chaotic structure of the classical dynamics, such as chaos assisted tunneling and/or ionization. Furthermore, classical chaos allows – contrary to its reputation – for the emergence of perfectly stable, nondispersive wave–packets, which extend Schrödinger’s example of the harmonic oscillator to (periodically driven) Coulomb systems.

After a brief introduction to the fundamental concepts of quantum chaos, the talk will illustrate their crucial relevance to understand, characterize and control complex dynamics of simple atoms.