Quantum signatures of classical chaos, studied through the spectral statistics of bounded quantum systems whose classical counterparts are chaotic (stadium billiard, kicked rotor, hydrogen in a strong magnetic field, Sinai billiard). Core…
quantum-chaos
Wigner surmise + BGS conjecture: random-matrix universality of chaos
Wigner 1951 conjectured that the nearest-neighbor level-spacing distribution of unfolded eigenvalues of a large real-symmetric random…
Berry-Tabor 1977: integrable quantum systems show Poisson statistics
Berry-Tabor 1977 (Proc. R. Soc. A 356:375) argued that quantum counterparts of *integrable* classical systems have uncorrelated eigenvalues…
Maldacena-Shenker-Stanford 2016 universal chaos bound λ_L ≤ 2πk_BT/ℏ
Maldacena-Shenker-Stanford 2016 (JHEP 2016:106) proved a thermodynamic upper bound on the Lyapunov exponent extracted from the early-time…
Wigner GOE surmise moments: ⟨s⟩ = 1, ⟨s²⟩ = 4/π (exact)
Closed-form Gaussian-integral check of the Wigner GOE surmise P(s) = (π/2)·s·exp(-π·s²/4). Normalisation ∫₀^∞ P ds = 1 and unit mean ⟨s⟩ =…
Poisson level statistics: mean = variance = 1, P(0) = 1 (exact)
Closed-form check of the Berry-Tabor conjecture's Poisson spacing distribution. Normalisation: ∫₀^∞ exp(-s) ds = 1. First moment: ⟨s⟩ =…
MSS chaos bound saturation: λ_L/(2πT) = 1 at the SYK / black-hole point
Pinning statement of the Maldacena-Shenker-Stanford 2016 chaos bound at the saturation / reference point. In natural units ℏ = k_B = 1,…