OTOC Growth

quantum · 36 views
quantum

What It Is

Out-of-time-order correlator d(log C)/dt for a chaotic mixed-field Ising chain (L=8, g=0.9, h=0.8, J=π/4) --- quantum Lyapunov scrambling rate; flat plateau at 2λ during exponential growth, decays toward zero at saturation

Interpretation

Standard analysis sees: heavy-tailed; right-skewed; smooth / autocorrelated; long-range memory (persistent); low-complexity (predictable, not noise-like); time-irreversible (sharp rises, slow decay); volatility-clustering (bursty); multifractal; low-dimensional; nonstationary / drifting. The atlas additionally detects critical slowing down.

What standard analysis sees
tail heaviness0.93
asymmetry0.97
occupancy0.17
short-range corr0.99
long-range memory1.00
spectral colour0.18
periodicity0.73
complexity0.04
time-irreversibility1.00
volatility clustering1.00
multifractality0.95
dimensionality0.10
nonstationarity0.99
What the atlas adds
critical slowing down+2.9z
lag-1 autocorrelation rises across the series — the early-warning signature of an approaching tipping point / regime shift (also fired by frequency chirps)
also fires on nonstationary arithmetic sequences whose autocorrelation drifts for non-dynamical reasons
Atlas-extreme metrics the standard bank can’t predict for this source
Wasserstein:self_similarity-7.9zbank-miss 2.7σ
Spirograph:angular_order+5.6zbank-miss 1.1σ
Moiré:moire_peak_alpha+5.4zbank-miss 1.5σ
Moiré:moire_integer_excess-4.0zbank-miss 2.2σ
Ulam Spiral (Square):polynomial_concentration+3.5zbank-miss 1.3σ
Ulam Spiral (Square):radial_periodicity+3.4zbank-miss 1.9σ
Wasserstein:transport_variability+3.2zbank-miss 1.8σ
Chladni:nodal_gap_ratio-3.0zbank-miss 2.0σ

Composition

dtypefloat64
range[-6.463e-05, 0.02807]
unique values16087 / 16384
mean ± std0.00171 ± 0.00492

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 > 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
PID Controller4.97cross-domain
SIR Epidemic5.42cross-domain
Magnetic Pendulum (3-Magnet)5.46cross-domain

Open in Atlas →

Which Geometries Light Up

Ammann-Beenker (Octagonal) › Ammann-Beenker (Octagonal):convergent_resonancerank 2/2980.9928
AutoRegressive › AutoRegressive:ar_residual_fracrank 297/2980.0000
Cantor Set › Cantor Set:bit_plane_autocorrelationrank 3/2980.9973
Catch24 › Catch24:CO_FirstMin_acrank 1/29813359.0000
Catch24 › Catch24:SP_Summaries_welch_rect_area_5_1rank 1/2980.9999
Catch24 › Catch24:SB_BinaryStats_diff_longstretch0rank 2/2983549.0000
Catch24 › Catch24:DN_OutlierInclude_p_001_mdrmdrank 297/298-0.8563
Catch24 › Catch24:FC_LocalSimple_mean3_stderrrank 297/2980.0075
Catch24 › Catch24:PD_PeriodicityWang_th0_01rank 297/2980.0000
Cayley › Cayley:delta_hyp_normrank 294/2980.0000
Chladni › Chladni:captured_power_fractionrank 295/2980.0015
Chladni › Chladni:domain_ks_exponentialrank 298/2980.0000
Chladni › Chladni:nodal_gap_ratiorank 298/2980.0000
Fractal (Mandelbrot) › Fractal (Mandelbrot):potential_roughnessrank 297/2980.0032
Gottwald-Melbourne › Gottwald-Melbourne:radial_spectral_structurerank 3/2980.9996
Gottwald-Melbourne › Gottwald-Melbourne:angular_spectral_structurerank 5/2980.9846
Higher-Order Statistics › Higher-Order Statistics:c3_energyrank 1/2983.4729
Hodge–Laplacian › Hodge–Laplacian:poisson_recovery_errorrank 295/2980.0210
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):temporal_variancerank 296/2980.0024
H² × ℝ (Thurston) › H² × ℝ (Thurston):radial_temporal_memoryrank 3/2984.9718
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_step_dispersionrank 297/2980.0057
Hölder Regularity › Hölder Regularity:increment_autocorrelationrank 1/2980.9999
Hölder Regularity › Hölder Regularity:hurst_exponentrank 2/2980.9538
Hölder Regularity › Hölder Regularity:holder_minrank 4/2980.9293
Klein Bottle › Klein Bottle:rank_deficit_maxrank 2/2981.0000
Klein Bottle › Klein Bottle:orientation_coherencerank 3/2980.9972
Klein Bottle › Klein Bottle:linear_complexityrank 297/2980.0000
Laplacian › Laplacian:cross_scale_curvature_coherencerank 1/2980.9996
Laplacian › Laplacian:curvature_autocorrelationrank 1/2980.9996
Laplacian › Laplacian:laplacian_spectral_ratiorank 1/2981.0000
Laplacian › Laplacian:gradient_sign_persistencerank 4/2980.9962
Laplacian › Laplacian:biharmonic_ratiorank 295/2980.0000
Laplacian › Laplacian:poisson_recovery_errorrank 298/2980.0005
Moiré › Moiré:moire_peak_alpharank 1/2985.0000
Moiré › Moiré:moire_max_coherencerank 3/2980.9934
Moiré › Moiré:moire_phi_responserank 296/298-0.1145
Moiré › Moiré:moire_integer_excessrank 298/298-0.4471
Mostow Rigidity › Mostow Rigidity:mean_turn_anglerank 5/2980.9332
Mostow Rigidity › Mostow Rigidity:margulis_ratiorank 295/2980.0001
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_finerank 295/2980.0009
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_sloperank 298/298-0.6813
Multifractal Spectrum › Multifractal Spectrum:hurst_estimaterank 2/2980.9419
Möbius-S³ › Möbius-S³:hopf_fiber_coherencerank 3/2980.8101
Möbius-S³ › Möbius-S³:phase_profile_deviationrank 5/2980.6587
Navier-Stokes › Navier-Stokes:cascade_asymmetryrank 1/2981.0000
Navier-Stokes › Navier-Stokes:intermittency_autocorrrank 1/2980.9999
Nonstationarity › Nonstationarity:ac1_trendrank 4/2980.2093
Nonstationarity › Nonstationarity:variance_trendrank 297/298-0.2727
Persistent Homology › Persistent Homology:total_persistencerank 295/2981.0000
Persistent Homology › Persistent Homology:persistence_entropyrank 297/2980.0000
Predictability › Predictability:cond_entropy_k1rank 295/2980.0085
Predictability › Predictability:sample_entropyrank 298/2980.0025
Projective ℙ² › Projective ℙ²:distance_stdrank 295/2980.0000
Projective ℙ² › Projective ℙ²:mean_distancerank 296/2980.0000
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):trace_autocorrelationrank 2/2980.9998
Spectral Analysis › Spectral Analysis:spectral_flatnessrank 294/2980.0000
Spectral Analysis › Spectral Analysis:spectral_bandwidthrank 296/2980.0005
Spectral Graph › Spectral Graph:weyl_exponentrank 1/2982.2334
Spirograph › Spirograph:angular_orderrank 1/29815.0000
Symplectic › Symplectic:windowed_area_cvrank 1/29810.3673
Symplectic › Symplectic:phase_reflection_symmetryrank 5/2980.9959
S² × ℝ (Thurston) › S² × ℝ (Thurston):great_circle_dispersionrank 297/2980.0020
Ulam Spiral (Square) › Ulam Spiral (Square):radial_periodicityrank 4/2980.6912
Ulam Spiral (Square) › Ulam Spiral (Square):polynomial_concentrationrank 5/2980.1239
Visibility Graph › Visibility Graph:nvg_hvg_reach_divergencerank 3/2980.9954
Visibility Graph › Visibility Graph:degree_exponent_gammarank 295/2980.3181
Visibility Graph › Visibility Graph:degree_r_squaredrank 297/2980.2269
Wasserstein › Wasserstein:transport_variabilityrank 5/2980.1305
Wasserstein › Wasserstein:self_similarityrank 298/2980.5987
Wavelet Cascade › Wavelet Cascade:cascade_couplingrank 1/2980.9899
Wavelet Cascade › Wavelet Cascade:scale_gini_dispersionrank 296/2980.0074
p-Variation › p-Variation:volatility_clusteringrank 2/2980.9997
p-Variation › p-Variation:increment_persistencerank 3/2980.9999
p-Variation › p-Variation:var_p2rank 297/2980.0000
p-Variation › p-Variation:variation_indexrank 297/2981.0003
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Structure Atlas — Open Atlas · GitHub