OBSERVATION OF SCARRED WAVE-FUNCTIONS IN A QUANTUM-WELL WITH CHAOTIC ELECTRON DYNAMICS

Qualitative insight into the properties of a quantum-mechanical system can be gained from the study of the relationship between the system's classical newtonian dynamics, and its quantum dynamics as described b y the Schrodinger equation. The Bohr-Sommerfeld quantization scheme--w hich underlies the historically important Bohr model for hydrogen-like atoms--describes the relationship between the classical and quantum-m echanical regimes, but only for systems with stable, periodic or quasi periodic orbits'. Only recently has progress been made in understandin g the quantization of systems that exhibit non-periodic, chaotic motio n. The spectra of quantized energy levels for such systems are irregul ar, and show fluctuations associated with unstable periodic orbits of the corresponding classical system(1-3). These orbits appear as 'scars '-concentrations of probability amplitude--in the wavefunction of the system(4). Although wavefunction scarring has been the subject of exte nsive theoretical investigation(5-10), it has not hitherto been observ ed experimentally in a quantum system. Here we use tunnel-current spec troscopy to map the quantum-mechanical energy levels of an electron co nfined in a semiconductor quantum well in a high magnetic held(10-13). We find clear experimental evidence for wavefunction scarring, in ful l agreement with theoretical predictions(10).