Anderson localisation on spatially structured random graphs shows a transition shifting to stronger disorder with increasing hopping range, vanishing beyond a critical range with direct delocalised-localised transition and Kosterlitz-Thouless-like scaling, without an intervening multifractal phase.
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GOE-like spectral chaos is neither necessary nor sufficient for quantum Mpemba crossings in a clean U(1)-conserving XXZ chain; the crossing is controlled by local charge-sector coherence structure instead.
A flow equation for the resonance density exponent θ(w) derived in the SJA predicts resonance proliferation driving delocalization, with θ(w)>0 for localized phases and instability signaling thermalization, matching numerics in Anderson and MBL models.
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Anderson localisation in spatially structured random graphs
Anderson localisation on spatially structured random graphs shows a transition shifting to stronger disorder with increasing hopping range, vanishing beyond a critical range with direct delocalised-localised transition and Kosterlitz-Thouless-like scaling, without an intervening multifractal phase.
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Spectral Chaos Does Not Determine Quantum Mpemba Crossings
GOE-like spectral chaos is neither necessary nor sufficient for quantum Mpemba crossings in a clean U(1)-conserving XXZ chain; the crossing is controlled by local charge-sector coherence structure instead.
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Resonance Proliferation Across Localization Transitions
A flow equation for the resonance density exponent θ(w) derived in the SJA predicts resonance proliferation driving delocalization, with θ(w)>0 for localized phases and instability signaling thermalization, matching numerics in Anderson and MBL models.