Chaotic quantum systems show universal spectral patterns

A widely used approach to modeling complex quantum systems relies on a potentially unphysical simplification: assuming all interactions between particles are equally likely. Random-matrix ensembles, a long-standing theoretical tool, typically posit nonzero matrix elements across the Hamiltonian, a departure from conventional models where many interactions are absent. This framework also struggles to accurately represent systems where particle location matters, due to its inherent flexibility under basis rotations. Researchers are now engineering models that combine the benefits of random-matrix theory with spatial structure and local interactions to better represent chaotic many-body quantum systems with time-independent Hamiltonians. Spectral correlations within suitably chosen energy windows consistently align with calculations derived from random-matrix theory, revealing a surprising universality across diverse physical systems. This agreement extends to systems where the statistical properties of the Hamiltonian’s spectrum remain consistent despite variations in underlying physical details, a phenomenon previously observed and now further substantiated by detailed modeling. This approach retains the core principle of averaging physical properties over an ensemble of systems, a technique central to understanding complex quantum behavior. A key diagnostic for characterizing chaotic dynamics is…