The Physics Society of Iran Iranian Journal of Physics Research 1682-6957 25 4 2026 02 20 The spectral form factor in Bosonic integrable systems with local random interactions The spectral form factor in Bosonic integrable systems with local random interactions 423 429 3748 10.47176/ijpr.25.4.82162 FA Ali Mollabashi School of Quantum Physics and Matter, Institute for Research in Fundamental Sciences (IPM) 0000-0002-8192-1260 Saleh Rahimi-Keshari School of Quantum Physics and Matter, Institute for Research in Fundamental Sciences (IPM) 0000-0003-2108-7486 Journal Article 2025 08 05 The spectral form factor (SFF) is a widely used tool for diagnosing quantum chaos and information scrambling. Recent studies have shown that the SFF can also indicate scrambling behavior in integrable systems when non-local random couplings are present. In this work, we investigate integrable bosonic systems governed by quadratic Hamiltonians with local random interactions. Through numerical analysis, we demonstrate that the SFF exhibits a ramp at intermediate times, a feature absent in integrable systems without randomness. The presence of this ramp provides evidence supporting the notion of quantum information scrambling in locally coupled, yet integrable, systems. The spectral form factor (SFF) is a widely used tool for diagnosing quantum chaos and information scrambling. Recent studies have shown that the SFF can also indicate scrambling behavior in integrable systems when non-local random couplings are present. In this work, we investigate integrable bosonic systems governed by quadratic Hamiltonians with local random interactions. Through numerical analysis, we demonstrate that the SFF exhibits a ramp at intermediate times, a feature absent in integrable systems without randomness. The presence of this ramp provides evidence supporting the notion of quantum information scrambling in locally coupled, yet integrable, systems. https://ijpr.iut.ac.ir/article_3748_aaaccd2766ec67aecbe26459bb828d81.pdf