Permanent Chaos: How Disorder Emerges in Static Quantum Systems express
In the mid-20th century, physicists noticed something odd: the energy levels of complex atomic nuclei behaved like lottery balls — completely unpredictable. Since then, the search for such hidden chaos in the microworld has never stopped. Until recently, it was thought that chaos only appeared in systems that are constantly pushed, like a blender. But now scientists have managed to prove its existence in a completely static quantum system — they used a trick proposed long ago by Feynman and Kitaev: a quantum clock mechanism. It's like sewing an internal metronome into a static structure — the system itself doesn't change, but its energy pattern bears the imprint of chaos. This same pattern, reminiscent of the echo of a distant explosion, has long been known in black hole physics, hinting at a deep connection between gravity and quantum mechanics. This discovery helps explain why heat spreads so quickly even in insulators, and why the spectra of complex atoms remain stable despite internal disorder.
Original abstract
as written by the authors arXiv:2606.30635
Quantum chaos is commonly associated with the emergence of random-matrix statistics in the spectra of quantum systems. A useful diagnostic is provided by the spectral form factor (SFF), which for random matrix ensembles displays a universal linear-growth regime (`ramp'). In the last decade, a landmark result by Bertini, Kos and Prosen (BKP) identified for the first time a class of geometrically local quantum dynamics of finite-dimensional particles where the SFF provably exhibits a random-matrix ramp: periodically driven (Floquet) qudit chains whose evolution is described by `dual-unitary' circuits. Here, building on the BKP result and on a recently proposed variant of the Feynman-Kitaev clock construction, we obtain a spectral ramp in a class of static, geometrically local Hamiltonians. Our strategy is to embed the Floquet quasienergy spectrum of a dual-unitary circuit into the energy spectrum of a static local Hamiltonian, and to prove that the latter's connected SFF inherits the BKP ramp within a symmetry sector. This is to our knowledge the first proof of a spectral ramp in a time-independent, geometrically local many-body system with finite local Hilbert space dimension.
Energy levels of atomic nuclei behave like winning lottery numbers — completely random. This opened physicists' eyes to quantum chaos.