BGS conjecture
The '''Bohigas–Giannoni–Schmit for simple quantum mechanical systems few degrees of freedom holds that spectra of time reversal-invariant systems whose classical analogues are K-systems show the same fluctuation properties as predicted by the GOE.
Alternatively, the spectral fluctuation measures of a classically chaotic quantum system coincide with those of the canonical random-matrix ensemble in the same symmetry class.
That is, the Hamiltonian of a microscopic analogue of a classical chaotic system can be modeled by a random matrix from a Gaussian ensemble as the distance of a few spacings between eigenvalues of a chaotic Hamiltonian operator generically statistically correlates with the spacing laws for eigenvalues of large random matrices.
A simple example of the unfolded quantum energy levels in a classically chaotic system correlating like that would be Sinai billiards:
- Energy levels:
- Spectral density:
- Average spectral density:
- Correlation:
- Unfolding:
- Unfolded correlation:
- BGS conjecture:
Links
- in Scholarpedia.