Anderson 1D Localized
quantum · 36 views
quantum
What It Is
1D tight-binding chain with random on-site disorder W=2 --- exponentially localized eigenstates from K independent disorder realizations, re-centered and concatenated
Interpretation
Standard analysis sees: heavy-tailed; right-skewed; multifractal; low-dimensional. The atlas finds no named structure, but the source is distinctively extreme on Attractor Reconstruction:lyap_entropy (+4.3z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.98
asymmetry0.98
occupancy0.15
short-range corr0.50
long-range memory0.60
spectral colour0.58
periodicity0.70
complexity0.65
time-irreversibility0.71
volatility clustering0.49
multifractality0.94
dimensionality0.02
nonstationarity0.60
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Attractor Reconstruction:lyap_entropy | +4.3z | bank-miss 2.3σ |
Spirograph:angular_order | +4.0z | bank-miss 1.3σ |
Wavelet Cascade:scale_gini_dispersion | +3.1z | bank-miss 1.9σ |
Möbius-S³:hopf_fiber_coherence | -2.1z | bank-miss 3.3σ |
Composition
dtypefloat64
range[4.506e-23, 0.2471]
unique values16384 / 16384
mean ± std0.00391 ± 0.0127
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Anderson_1D_Localized.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Anderson_1D_Localized.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Anderson_1D_Localized.png)
Inflation (Substitution) > barcode
/d_curve/Anderson_1D_Localized.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/Anderson_1D_Localized.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/Anderson_1D_Localized.png)
Ulam Spiral (Sacks) > default
/default/Anderson_1D_Localized.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Solar Flares Daily Peak | 4.60 | cross-domain |
| Aubry-André Critical | 4.66 | |
| Minkowski Question Mark | 4.99 | cross-domain |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:lyap_sum | rank 1/298 | 4.2021 |
Attractor Reconstruction › Attractor Reconstruction:lyap_entropy | rank 2/298 | 4.5984 |
AutoRegressive › AutoRegressive:ar_coef_2 | rank 3/298 | 0.6349 |
Catch24 › Catch24:DN_HistogramMode_5 | rank 4/298 | 1.8523 |
Catch24 › Catch24:DN_Mean | rank 294/298 | 0.0158 |
Continued Fraction › Continued Fraction:gauss_kuzmin_distance | rank 3/298 | 0.8217 |
G2 Root System › G2 Root System:kurtosis_differential | rank 4/298 | 2.4170 |
Hodge–Laplacian › Hodge–Laplacian:source_fraction | rank 2/298 | 0.6773 |
Mostow Rigidity › Mostow Rigidity:margulis_ratio | rank 296/298 | 0.0000 |
Möbius-S³ › Möbius-S³:hopf_fiber_coherence | rank 295/298 | 0.2193 |
Nonstationarity › Nonstationarity:trajectory_dim | rank 4/298 | 0.8173 |
Piecewise-Linear › Piecewise-Linear:envelope_area | rank 294/298 | 258.8600 |
Sol (Thurston) › Sol (Thurston):z_variance | rank 295/298 | 0.0177 |
Spectral Analysis › Spectral Analysis:spectral_bandwidth | rank 3/298 | 0.1881 |
Spirograph › Spirograph:angular_order | rank 4/298 | 11.4000 |
Wasserstein › Wasserstein:dist_from_uniform | rank 5/298 | 0.4725 |
in geophysicsAubry-André Critical →
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