Approaches
Questions related to the correspondence principle arise in many different branches of physics, ranging from nuclear to atomic, molecular and solid-state physics, and even to acoustics, microwaves and optics. Important observations often associated with classically chaotic quantum systems are spectral level repulsion, dynamical localization in time evolution (e.g. ionization rates of atoms), and enhanced stationary wave intensities in regions of space where classical dynamics exhibits only unstable trajectories (as in scattering).
In the semiclassical approach of quantum chaos, phenomena are identified in spectroscopy by analyzing the statistical distribution of spectral lines and by connecting spectral periodicities with classical orbits. Other phenomena show up in the time evolution of a quantum system, or in its response to various types of external forces. In some contexts, such as acoustics or microwaves, wave patterns are directly observable and exhibit irregular amplitude distributions.
Quantum chaos typically deals with systems whose properties need to be calculated using either numerical techniques or approximation schemes (see e.g. Dyson series). Simple and exact solutions are precluded by the fact that the system's constituents either influence each other in a complex way, or depend on temporally varying external forces.
Read more about this topic: Quantum Chaos
Famous quotes containing the word approaches:
“The Oriental philosophy approaches easily loftier themes than the modern aspires to; and no wonder if it sometimes prattle about them. It only assigns their due rank respectively to Action and Contemplation, or rather does full justice to the latter. Western philosophers have not conceived of the significance of Contemplation in their sense.”
—Henry David Thoreau (1817–1862)
“No one ever approaches perfection except by stealth, and unknown to themselves.”
—William Hazlitt (1778–1830)
“You should approach Joyce’s Ulysses as the illiterate Baptist preacher approaches the Old Testament: with faith.”
—William Faulkner (1897–1962)