35 lines
3.4 KiB
Markdown
35 lines
3.4 KiB
Markdown
---
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title: "Butterfly effect"
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chunk: 4/4
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source: "https://en.wikipedia.org/wiki/Butterfly_effect"
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category: "reference"
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tags: "science, encyclopedia"
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date_saved: "2026-05-05T10:54:43.276736+00:00"
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instance: "kb-cron"
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---
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=== In quantum mechanics ===
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The potential for sensitive dependence on initial conditions (the butterfly effect) has been studied in a number of cases in semiclassical and quantum physics, including atoms in strong fields and the anisotropic Kepler problem. Some authors have argued that extreme (exponential) dependence on initial conditions is not expected in pure quantum treatments; however, the sensitive dependence on initial conditions demonstrated in classical motion is included in the semiclassical treatments developed by Martin Gutzwiller and John B. Delos and co-workers. The random matrix theory and simulations with quantum computers prove that some versions of the butterfly effect in quantum mechanics do not exist.
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Other authors suggest that the butterfly effect can be observed in quantum systems. Zbyszek P. Karkuszewski et al. consider the time evolution of quantum systems which have slightly different Hamiltonians. They investigate the level of sensitivity of quantum systems to small changes in their given Hamiltonians. David Poulin et al. presented a quantum algorithm to measure fidelity decay, which "measures the rate at which identical initial states diverge when subjected to slightly different dynamics". They consider fidelity decay to be "the closest quantum analog to the (purely classical) butterfly effect". Whereas the classical butterfly effect considers the effect of a small change in the position and/or velocity of an object in a given Hamiltonian system, the quantum butterfly effect considers the effect of a small change in the Hamiltonian system with a given initial position and velocity. This quantum butterfly effect has been demonstrated experimentally. Quantum and semiclassical treatments of system sensitivity to initial conditions are known as quantum chaos.
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== In popular culture ==
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The butterfly effect has appeared across media such as literature (for instance, A Sound of Thunder), films and television (such as The Simpsons), video games (such as Life Is Strange), webcomics (such as Homestuck), musical references (such as "Butterfly Effect" by Travis Scott), AI-driven expansive language models, and more.
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== See also ==
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== References ==
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== Further reading ==
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James Gleick, Chaos: Making a New Science, New York: Viking, 1987. 368 pp.
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Devaney, Robert L. (2003). Introduction to Chaotic Dynamical Systems. Westview Press. ISBN 0-670-81178-5.
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Hilborn, Robert C. (2004). "Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics". American Journal of Physics. 72 (4): 425–427. Bibcode:2004AmJPh..72..425H. doi:10.1119/1.1636492.
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Bradbury, Ray. "A Sound of Thunder." Collier's. 28 June 1952
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== External links ==
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Weather and Chaos: The Work of Edward N. Lorenz. A short documentary that explains the "butterfly effect" in context of Lorenz's work.
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The Chaos Hypertextbook. An introductory primer on chaos and fractals
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Dizikes, Peter (2008-06-08). "The meaning of the butterfly. Why pop culture loves the 'butterfly effect,' and gets it totally wrong". The Boston Globe. Boston, Massachusetts. Retrieved 2022-06-19.
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New England Complex Systems Institute - Concepts: Butterfly Effect
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ChaosBook.org. Advanced graduate textbook on chaos (no fractals)
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Weisstein, Eric W. "Butterfly Effect". MathWorld. |