Read this response and predict the preceding dialog. The principal result of this development is an expression for the density of states which is the trace of the semiclassical Green's function and is given by the Gutzwiller trace formula: Recently there was a generalization of this formula for arbitrary matrix Hamiltonians that involves a Berry phase-like term stemming from spin or other internal degrees of freedom.

2-way dialog:
Person 1) What are the main types of quantum chaos?.
Person 2) One notable exception is diamagnetic lithium which, though exhibiting classical chaos, demonstrates Wigner (chaotic) statistics for the even-parity energy levels and nearly Poisson (regular) statistics for the odd-parity energy level distribution..
Person 1) What can you tell me about the types of quantum chaos?.
Person 2) Periodic-orbit theory gives a recipe for computing spectra from the periodic orbits of a system..
Person 1) Are there any other interesting aspects about this article?.
Person 2) In contrast to the Einstein–Brillouin–Keller method of action quantization, which applies only to integrable or near-integrable systems and computes individual eigenvalues from each trajectory, periodic-orbit theory is applicable to both integrable and non-integrable systems and asserts that each periodic orbit produces a sinusoidal fluctuation in the density of states..
Person 1) What happened after the development of the theory?.
Person 2) 