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Quantum chaos, a non-technical term, is scientific shorthand that refers to the use of chaos theory to explain quantum systems. Chaos theory can explain the irregularities that occur in all dynamical systems from the macro to the micro level. Those irregularities include a bobble in a satellite’s revolution around a planet or the unpredicted position of an electron on the atomic level. Quantum systems are those systems that operate on the molecular level. Taking those definitions together, quantum chaos attempts to account for irregularities in molecular systems.
For a long time, scientists were unsure if quantum chaos existed. Atoms tended to exhibit predictable wavelike patterns of energy. Objects at the molecular level did not seem to express extreme sensitivity to initial conditions, the traditional definition of physical chaos. Even some problems that did emerge could be explained through perturbation theory, which allows for minor deviations in a system that exhibits largely regular behavior that can be explained through classical physics.
As some physicists of the 20th century discovered, however, not all events occurring at the molecular level could be adequately explained or predicted through classical quantum models. According to those models, events such as particle movement from one site to the next one over, would require exponentially growing amounts of energy that would be impossible to generate. Because particles have been observed to move without producing those energy levels, though, scientists had to come up with a different way to explain the phenomenon.
One way scientists explained was through study of the Rydberg atom. Rydberg atoms are highly energized atoms that exhibit chaotic behaviors able to be explained through classical physics. Study of these atoms has shown that systems where quantum chaos is involved have highly correlated energy levels. The energy levels of the particles are not randomly distributed as in classical molecules. The events of one subsystem are inextricably related to the events of another subsystem. As a result, an energy spectrum can be used to at least partially explain the behaviors of these particles.
Another method was to look at situations in which classical physics was able to explain irregularities in large systems. The mechanics behind the wobble in the moon’s orbit around the earth because of the gravitational pull of the sun were used to create a statistical measurement that helped explain and predict the behaviors of low-energy particles. While classical models in physics cannot adequately explain the behaviors of these chaotic molecular systems, it is interesting that quantum chaos uses those models as a launching point to create new models to further understand these systems.