Jeff Goldblum's character (the lovable bachelor in distress) in Jurassic Park brought about public awareness to the general concept of chaos theory. This strange branch of mathematics deals with highly-sensitive systems, able to change dramatically with only the slightest change in circumstance. And, while enigmatic in many ways, researchers have just recently succeeded in developing an equation that answers the question: "How does chaos behave?"
To accomplish this ambitious task, researchers, partly from Lund University, studied chaotic states at the atomic level. In this "quantum environment," subatomic particles do not behave in regards to the "normal" rules of nature. However, despite this, they still retain chaos states that appear to be universal. Quantum chaos, as opposed to its macro counterpart, has been described as an explanation of the irregular motion of electrons, nuclei, rays of light, or even sound waves. In addition to exploring these phenomena, the researchers looked at statistical properties that exist at different energy states in a chaotic, quantum environment.
Theoretical but Practical
According to Vladimir Osipov, a researcher at Lund University's Faculty of Science and one of the study authors, "In chaotic quantum systems, the energy levels repel each other, and they affect each other even if they are far apart."
Scientists can now represent the chaotic behavior described by the math in a quantum system with perfect accuracy: "Yes, we now have an exact equation. Personally, I am actually surprised that it was possible at all," said Osipov.
And, while the theoretical understanding of these actions and interactions will only continue to grow, an understanding of chaos has practical applications in the development of financial tools, brain surgery, and even the study of string theory. Previously it was impossible to pinpoint specific quantum chaos states because any number entered in a calculation could lead to dramatic changes and fluctuations, but this new equation bypasses such difficulties, allowing scientists to accurately identify chaos characteristics. Despite, even, the potential for practical application, this development drastically improves our understanding of quantum mechanics in general, and more specifically within a quantum system.