Aubry-André Critical

random-matrix-quantum · 37 views
random-matrix-quantumquasiperiodic

What It Is

Almost-Mathieu operator at critical coupling λ=2 with golden-ratio incommensurate potential --- multifractal eigenstate intensity (deterministic multifractality, canonical exemplar from quasiperiodic origin)

Interpretation

Standard analysis sees: no strongly notable standard properties. The atlas additionally detects Higher-Order Statistics:c3_energy, Attractor Reconstruction:lyap_entropy. It sits beside Solar Flares Daily Peak in the atlas (standard-bank rank 39) — a neighbor conventional features miss.

What the atlas adds
Higher-Order Statistics:c3_energy+3.3z
third-cumulant burst energy (SOC irreducibility signature)
Attractor Reconstruction:lyap_entropy+2.9z
Kolmogorov-Sinai entropy production rate (sum of positive λ)
Atlas-extreme metrics the standard bank can’t predict for this source
2-adic:mean_distance-4.2zbank-miss 2.0σ
Zariski:nonsep_fraction+4.0zbank-miss 2.3σ
Klein Bottle:linear_complexity-3.9zbank-miss 1.2σ
Wasserstein:concentration+3.3zbank-miss 2.0σ
SL(2,ℝ) (Thurston):lyapunov_exponent+3.3zbank-miss 1.7σ
Symplectic:recurrence_rate+3.0zbank-miss 1.6σ
Möbius-S³:phase_profile_deviation+2.8zbank-miss 2.9σ
Piecewise-Linear:envelope_area-2.6zbank-miss 1.2σ

Composition

dtypefloat64
range[1.677e-14, 0.02408]
unique values16384 / 16384
mean ± std6.1e-05 ± 0.000385

Render Gallery

Native > phase_plot
Native > phase_plotraw
Native > timeseries
Native > timeseriesraw
Native > triple_lattice
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > lag_map
Boltzmann > spin_grid
Boltzmann > spin_grid
Cayley > default
Cayley > default
Chladni > free_plate_nodal
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_bottom
Chladni > plate_top
Chladni > plate_top
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > xy_path
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
Hodge–Laplacian > default
Inflation (Substitution) > barcode
Inflation (Substitution) > barcode
Inflation (Substitution) > d_curve
Inflation (Substitution) > d_curve
Information Theory > default
Information Theory > default
Julia Set > escape_histogram
Julia Set > escape_histogram
Klein Bottle > default
Klein Bottle > default
Laplacian > default
Laplacian > default
Logarithmic Spiral > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Möbius-S³ > s2_base_map
Ordinal Partition > default
Ordinal Partition > default
Penrose (Quasicrystal) > phi_spectrum
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > barcode
Persistent Homology > h1_diagram
Persistent Homology > h1_diagram
Predictability > default
Predictability > default
Recurrence Quantification > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Analysis > default
Spectral Graph > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > flux_grid
Symplectic > phase_space
Symplectic > phase_space
Ulam Spiral (Sacks) > default
Ulam Spiral (Sacks) > default
Ulam Spiral (Square) > default
Ulam Spiral (Square) > default
Visibility Graph > default
Visibility Graph > default
Wavelet Cascade > default
Wavelet Cascade > default

Atlas Position

Nearest neighborDistance
Solar Flares Daily Peak4.03cross-origin
Anderson 1D Localized4.41
Fibonacci Tight-Binding4.50

Open in Atlas →

Which Geometries Light Up

2-adic › 2-adic:distance_entropyrank 303/3070.7532
2-adic › 2-adic:mean_distancerank 304/3070.1079
Attractor Reconstruction › Attractor Reconstruction:embedding_divergence_sumrank 3/3073.5017
Attractor Reconstruction › Attractor Reconstruction:lyap_entropyrank 5/3073.5017
Catch24 › Catch24:DN_HistogramMode_10rank 1/3073.6296
Catch24 › Catch24:DN_HistogramMode_5rank 1/3077.3919
Catch24 › Catch24:CO_Embed2_Dist_tau_d_expfit_meandiffrank 303/3070.0142
Catch24 › Catch24:DN_Meanrank 307/3070.0018
Catch24 › Catch24:DN_Spread_Stdrank 307/3070.0133
Chladni › Chladni:temporal_burstinessrank 1/3070.7671
Continued Fraction › Continued Fraction:gauss_kuzmin_distancerank 1/3070.8724
D4 Triality › D4 Triality:triplet_temporalrank 5/3070.4016
Higher-Order Statistics › Higher-Order Statistics:kurt_maxrank 1/3077.7395
Higher-Order Statistics › Higher-Order Statistics:skew_meanrank 1/3073.2447
Hodge–Laplacian › Hodge–Laplacian:source_fractionrank 5/3070.6662
Klein Bottle › Klein Bottle:rank_deficitrank 2/3070.9919
Klein Bottle › Klein Bottle:rank_deficit_maxrank 3/3070.9996
Mostow Rigidity › Mostow Rigidity:distance_rigidityrank 305/3070.0361
Mostow Rigidity › Mostow Rigidity:laplacian_perturbation_stabilityrank 306/3070.5348
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_finerank 303/3070.0011
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_meanrank 304/3070.0011
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_stdrank 304/3070.0002
Predictability › Predictability:cond_entropy_k1rank 303/3070.0135
Projective ℙ² › Projective ℙ²:mean_distancerank 303/3070.0001
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):cocycle_growth_raterank 1/3071.9883
Spherical S² › Spherical S²:concentrationrank 2/3070.9992
Spherical S² › Spherical S²:hemisphere_balancerank 303/3070.0003
Spherical S² › Spherical S²:angular_spreadrank 305/3070.0453
Spirograph › Spirograph:rational_grid_proximityrank 304/3070.5052
Symplectic › Symplectic:phase_reflection_symmetryrank 1/3070.9999
Symplectic › Symplectic:recurrence_raterank 1/3070.9831
Symplectic › Symplectic:windowed_area_cvrank 2/3079.2084
S² × ℝ (Thurston) › S² × ℝ (Thurston):sphere_concentrationrank 2/3070.9994
S² × ℝ (Thurston) › S² × ℝ (Thurston):great_circle_dispersionrank 304/3070.0071
Ulam Spiral (Square) › Ulam Spiral (Square):polynomial_concentrationrank 303/3070.0204
Visibility Graph › Visibility Graph:degree_r_squaredrank 2/3070.9778
Wasserstein › Wasserstein:dist_from_uniformrank 1/3070.4837
Wasserstein › Wasserstein:concentrationrank 2/30731.7109
Wasserstein › Wasserstein:entropyrank 306/3070.0925
Wavelet Cascade › Wavelet Cascade:cascade_couplingrank 2/3070.9350
Zariski › Zariski:nonsep_fractionrank 2/3070.9767
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):gini_coefficientrank 2/3070.9744
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):gini_coefficientrank 3/3070.9629
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):hapax_ratiorank 5/3070.3175
in iterated-maps
alphabetical
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources

Structure Atlas — Open Atlas · GitHub