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Ordered Motion and Crystals

When classical motion of particles is not chaotic it can be confined to the surface of donut-shaped objects or "tori" which live in four or more dimensions. The images in this category are attempts to represent these higher dimensional objects in two and three dimensions.

Quantum Random Waves

Quantum Random Waves (random additions of plane waves going every which way) are the quantum analog to classical chaos. Their intriguing patterns and structures may be seen also in standing waves inside cavities which are classically chaotic.

Classical Electron Flow

The images in this category are based on the flow patterns for electrons riding over bumpy landscape in very small devices about the size of a bacterium. The electrons have more than enough energy to ride over any bump in the landscape, and the concentrations of electron flow are newly discovered indirect effects of that bumpy ride.

Quantum Modes and Classical Analogs

Waves confined to an region bounded by walls exhibit "modes" or standing wave patterns that oscillate at a fixed frequency. This is true of matter waves too. The wave patterns are strongly related to classical trajectories bouncing inside the same walls.

Quasi Classical Correspondence, Quantum Scars

Quantum scars are accumulation of wavefunction amplitude for standing waves along special classical trajectories called periodic orbits. Periodic orbits defy chaos by closing exactly on themselves, thus repeating forever the same motion. Such orbits constitute 0% of all orbits in a chaotic system (i.e. they are quite rare!) but they seem to have a grip on some finite fraction of the quantum standing waves.

Quantum Resonances

Resonances are very common in nature and affect almost all aspects of motion and energy transfer. When one object or region is oscillating at a frequency that is also natural for another object or region, the two can readily exchange energy. Large amoounts of energy can even squeeze through small holes, so efficient is the resonant energy transfer.

Classical Collisions

Collisions are ubiquitous in the microscopic world. The also tend to be chaotic, in the sense that small changes in the approach of two colliding partners result in huge differences later in time. This chaos is the "engine of entropy", the tendency toward disorder in nature.

Quantum Quasi Crystal

Quasicrystals show some aspects of crystalline order, but are missing the long range order we expect of a crystal. That is, with an ordinary crystal we can always move around by multiples of the repeating distances ("lattice constants") and come to an repeated atom or structure; not so in quasicrystals. Quasicrystals of small quasi-repeat distances like a crystal at first glance, but then stubbornly refuses to yield to our human tendency to search for a pattern. There is no repeating pattern, not ever!


Maps are surrogates for "real" dynamical systems. They consist of simple rules for jumping form place to place on a plane. When iterated many times, such simple rules can give rise to tremendous complexity, including full blow chaos. Quantum versions of such maps exist too, and we can mimick their behavior by coloring the points according to their wavelike phase (crest = red, trough = green, etc.)


Caustics are seen in abundance in the Transport series, but here we focus on the origin of caustics as projections of three dimensional transparent sheets onto two dimensions. The sheets consist of colored panels; the color combine with eachother (by color subtraction for example) in unexpected ways.

Rogue Waves

Rogue waves are singular, steep, and often breaking waves dangerous to even the largest ships. The flow of ocean waves through large eddies in the open sea may produce rogue or "freak" waves and turns out to be quite similar to the flow of quantum waves in semiconductor electron gasses, on a scale some 10,000,000 smaller. There are differences, though, including the need to average over wave propagation direction and speed. This resulted in new visual effects which I have highlighted and exploited in the Rogue Wave series.

Screen Savers

You may download screen savers, including some of Eric's images, from the National Science Foundation Website: www.nsf.gov/news/overviews/nano/screensaver.jsp (Copy and paste address into your browser).


Sound waves and analysis shares many common elements with other wave phenomena, including quantum waves. We have become interested in harmonic analysis and sound perception, which inspired these images


Ordered Motion and Crystals || Quantum Random Waves || Classical Electron Flow || Quantum Modes and Classical Analogs || Quasi Classical Correspondence, Quantum Scars || Quantum Resonances || Classical Collisions || Quantum Quasi Crystal || Maps || Caustics || Rogue Waves || Screen Savers || Sound

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