**Quantum chaos** is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is, "What is the relationship between quantum mechanics and classical chaos?" The correspondence principle states that classical mechanics is the classical limit of quantum mechanics. If this is true, then there must be quantum mechanisms underlying classical chaos; although this may not be a fruitful way of examining classical chaos. If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, how can exponential sensitivity to initial conditions arise in classical chaos, which must be the correspondence principle limit of quantum mechanics? In seeking to address the basic question of quantum chaos, several approaches have been employed:

- Development of methods for solving quantum problems where the perturbation cannot be considered small in perturbation theory and where quantum numbers are large.
- Correlating statistical descriptions of eigenvalues (energy levels) with the classical behavior of the same Hamiltonian (system).
- Semiclassical methods such as periodic-orbit theory connecting the classical trajectories of the dynamical system with quantum features.
- Direct application of the correspondence principle.

Read more about Quantum Chaos: History, Approaches, Quantum Mechanics in Non-perturbative Regimes, Correlating Statistical Descriptions of Quantum Mechanics With Classical Behavior, Recent Directions in Quantum Chaos, Berry–Tabor Conjecture

### Famous quotes containing the words quantum and/or chaos:

“A personality is an indefinite *quantum* of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite *quantum* of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.”

—Hubert C. Heffner (1901–1985)

“I have great belief in the fact that whenever there is *chaos*, it creates wonderful thinking. I consider *chaos* a gift.”

—Septima Clark (1898–1987)