Berry Random Wave
random-matrix-quantum · 37 views
random-matrix-quantumstochastic
What It Is
Berry's random plane wave --- superposition model for chaotic eigenstate statistics, Gaussian amplitude distribution
Interpretation
Standard analysis sees: smooth / autocorrelated; long-range memory (persistent); red spectrum (low-frequency / 1-over-f power); low-complexity (predictable, not noise-like); volatility-clustering (bursty). The atlas additionally detects Multifractal Spectrum:hurst_estimate.
What standard analysis sees
tail heaviness0.57
asymmetry0.60
occupancy0.65
short-range corr0.92
long-range memory0.87
spectral colour0.07
periodicity0.61
complexity0.09
time-irreversibility0.65
volatility clustering0.93
multifractality0.74
dimensionality0.29
nonstationarity0.70
What the atlas adds
Multifractal Spectrum:hurst_estimate+2.4z
self-affinity H = τ(2)/2 (alternate to Hölder hurst)
Atlas-extreme metrics the standard bank can’t predict for this source
Mostow Rigidity:spectral_rigidity | -2.1z | bank-miss 2.2σ |
Laplacian:curvature_autocorrelation | +2.0z | bank-miss 1.0σ |
Composition
dtypefloat64
range[-1.302, 1.591]
unique values16384 / 16384
mean ± std0.0255 ± 0.627
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Berry_Random_Wave.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Berry_Random_Wave.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Berry_Random_Wave.png)
Inflation (Substitution) > barcode
/d_curve/Berry_Random_Wave.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Berry_Random_Wave.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Berry_Random_Wave.png)
Ulam Spiral (Sacks) > default
/default/Berry_Random_Wave.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| FPUT N=16 | 2.60 | cross-origin |
| Lorenz-96 N=8 | 2.73 | cross-origin |
| Lorenz-96 N=36 | 2.76 | cross-origin |
Which Geometries Light Up
Laplacian › Laplacian:cross_scale_curvature_coherence | rank 4/307 | 0.9993 |
Laplacian › Laplacian:curvature_autocorrelation | rank 4/307 | 0.9993 |
Laplacian › Laplacian:biharmonic_ratio | rank 306/307 | 0.0000 |
Spectral Analysis › Spectral Analysis:spectral_peakedness | rank 5/307 | 0.9642 |
p-Variation › p-Variation:volatility_clustering | rank 4/307 | 0.9995 |
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