# Category:Quantum Chaos

**Quantum Chaos** emerged as a new field of physics from the efforts to understand the properties of quantum systems which have chaotic deterministic dynamics in the classical limit. Such classical dynamics in a bounded phase space is characterized by a continuous spectrum of motion and exponential instability of trajectories
and belongs to the Category Chaos in Dynamical systems. In contrast the corresponding quantum systems have a discrete spectrum and are usually stable in respect to small perturbations. In spite of these differences the * correspondence principle of Niels Bohr* guaranties that the quantum evolution follows the classical chaotic dynamics during a certain time scale
which becomes larger and larger when the dimensionless

*goes to zero (see Figures). Also the*

**Planck constant***states that a narrow wave packet follows closely even a chaotic trajectory. However, due to the exponential instability of chaotic dynamics a wave packet spreading is exponentially fast and the*

**Ehrenfest theorem***on which the theorem is valid becomes logarithmically short. The problem of semiclassical quantization of such quantum systems had been pointed out by*

**Ehrenfest time***already in 1917 but it found its solution only at the end of the century.*

**Albert Einstein***What happens beyond the Ehrenfest time? What are the properties of quantum states in this regime?*The answers on these and other questions can be found in this Category.

**Quantum Chaos** finds applications in number theory, fractal and complex spectra, atomic and molecular physics, clusters and nuclei, quantum transport on small scales, mesoscopic solid-state systems, wave propagation, acoustics, quantum computers and other areas of physics. It has close links with the Random Matrix Theory, invented by * Wigner* for a description of spectra of complex atoms and nuclei, interacting quantum many-body systems, quantum systems with disorder, quantum complexity of large matrices.
A new research area of

**Quantum Chaos**focuses on the relationship between Classical Chaos and Quantum Entanglement.

Dima Shepelyansky Scholarpeadia Editor of Category:Quantum Chaos

## Pages in category "Quantum Chaos"

The following 36 pages are in this category, out of 36 total.