Defines temporal matrix scale invariance (tMSI) for correlation kernels, decouples dynamical exponent α from spectral exponent β via Mellin factorization, and classifies tipping points by the sign of an exact Landau quartic coefficient a4 derived from those exponents and a three-point structure cons
Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture
6 Pith papers cite this work, alongside 2,305 external citations. Polarity classification is still indexing.
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A source-extended Lie-group algorithm derives Ward identities for elastic Burgulence, showing viscoelastic turbulence has weaker symmetry constraints than Navier-Stokes turbulence.
A measurement-adapted coarse-graining method derives a fourth-order effective quantum master equation for open quantum systems, with analytical parameters, regularization for singularities, and demonstration on superconducting qubit readout dynamics.
Mellin spectral theory on the multiplicative half-line reveals decoupling of geometric exponent a from spectral exponent b, with a=b marking simple RG fixed points and a≠b indicating multicriticality.
Wavelet scaling α = 1/2 separates classically simulable area-law from volume-law phases for quantum kernels in world-model latents, with empirical VideoMAE latents and a Θ(d^{-2}) variance bound implying simulation hardness and quadratic measurement costs.
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.
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Temporal Matrix Scale Invariance and the Classification of Tipping Points
Defines temporal matrix scale invariance (tMSI) for correlation kernels, decouples dynamical exponent α from spectral exponent β via Mellin factorization, and classifies tipping points by the sign of an exact Landau quartic coefficient a4 derived from those exponents and a three-point structure cons
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Functional Renormalization for Elastic Burgulence
A source-extended Lie-group algorithm derives Ward identities for elastic Burgulence, showing viscoelastic turbulence has weaker symmetry constraints than Navier-Stokes turbulence.
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Model Order Reduction for Open Quantum Systems Based on Measurement-adapted Time-coarse Graining
A measurement-adapted coarse-graining method derives a fourth-order effective quantum master equation for open quantum systems, with analytical parameters, regularization for singularities, and demonstration on superconducting qubit readout dynamics.
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Multicriticality and Scaling: Mellin Spectral Theory, and the Decoupling of Geometric and Spectral Exponents
Mellin spectral theory on the multiplicative half-line reveals decoupling of geometric exponent a from spectral exponent b, with a=b marking simple RG fixed points and a≠b indicating multicriticality.
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Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability
Wavelet scaling α = 1/2 separates classically simulable area-law from volume-law phases for quantum kernels in world-model latents, with empirical VideoMAE latents and a Θ(d^{-2}) variance bound implying simulation hardness and quadratic measurement costs.
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Coherent and dissipative dynamics at quantum phase transitions
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.