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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Superconducting qubit experiments reveal a non-ergodic glassy regime in a 2D disordered spin model, with power-law Hilbert-space dynamics, frozen degrees of freedom, and vanishing spin diffusion above a disorder threshold.
Pedagogical lecture notes derive standard RMT laws with the cavity method, illustrate applications, and catalogue advanced analytical techniques for disordered systems.
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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.
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Hilbert space signatures of non-ergodic glassy dynamics
Superconducting qubit experiments reveal a non-ergodic glassy regime in a 2D disordered spin model, with power-law Hilbert-space dynamics, frozen degrees of freedom, and vanishing spin diffusion above a disorder threshold.
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Lecture notes on random matrix theory: the results, the applications, and the analytical tools
Pedagogical lecture notes derive standard RMT laws with the cavity method, illustrate applications, and catalogue advanced analytical techniques for disordered systems.