OTOC Growth

random-matrix-quantum · 37 views
random-matrix-quantumspectral-RMT

What It Is

Out-of-time-order correlator d(log C)/dt for a non-integrable mixed-field Ising chain (L=8, transverse field h=0.8, longitudinal field g=0.9, coupling J=π/4) --- the commutator norm C(t) starts near zero (the opposite-end operators commute at t=0), grows as operators spread, then saturates; the emitted log-derivative peaks early and decays toward zero. At this size the onset is power-law in t with NO flat 2λ Lyapunov plateau (a clean exponential scrambling regime needs a semiclassical / large-N limit that spin-1/2 chains lack)

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 Higher-Order Statistics:c3_energy, Multifractal Spectrum:hurst_estimate.

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
Higher-Order Statistics:c3_energy+6.2z
third-cumulant burst energy (SOC irreducibility signature)
Multifractal Spectrum:hurst_estimate+2.8z
self-affinity H = τ(2)/2 (alternate to Hölder hurst)
Atlas-extreme metrics the standard bank can’t predict for this source
G2 Root System:pair_angle_kurtosis+9.2zbank-miss 1.4σ
Wasserstein:self_similarity-7.6zbank-miss 2.1σ
Spirograph:angular_order+5.4zbank-miss 1.4σ
Moiré:moire_peak_alpha+5.3zbank-miss 2.5σ
Navier-Stokes:cascade_asymmetry+4.2zbank-miss 1.1σ
Moiré:moire_integer_excess-3.9zbank-miss 1.5σ
Ulam Spiral (Square):radial_periodicity+3.5zbank-miss 1.4σ
Ulam Spiral (Square):polynomial_concentration+3.4zbank-miss 2.2σ

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 > 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
PID Controller4.90cross-origin
Magnetic Pendulum (3-Magnet)5.13cross-origin
Projectile with Drag5.43cross-origin

Open in Atlas →

Which Geometries Light Up

Ammann-Beenker (Octagonal) › Ammann-Beenker (Octagonal):convergent_resonancerank 2/3070.9928
AutoRegressive › AutoRegressive:ar_residual_fracrank 305/3070.0000
Cantor Set › Cantor Set:bit_plane_autocorrelationrank 4/3070.9973
Catch24 › Catch24:CO_FirstMin_acrank 1/30713359.0000
Catch24 › Catch24:SP_Summaries_welch_rect_area_5_1rank 1/3070.9999
Catch24 › Catch24:SB_BinaryStats_diff_longstretch0rank 2/3073549.0000
Catch24 › Catch24:DN_OutlierInclude_p_001_mdrmdrank 306/307-0.8563
Catch24 › Catch24:FC_LocalSimple_mean3_stderrrank 306/3070.0075
Catch24 › Catch24:PD_PeriodicityWang_th0_01rank 307/3070.0000
Cayley › Cayley:delta_hyp_normrank 303/3070.0000
Chladni › Chladni:captured_power_fractionrank 303/3070.0015
Chladni › Chladni:domain_ks_exponentialrank 307/3070.0000
Chladni › Chladni:nodal_gap_ratiorank 307/3070.0000
G2 Root System › G2 Root System:pair_angle_kurtosisrank 1/307326.5138
Higher-Order Statistics › Higher-Order Statistics:c3_energyrank 1/3073.4729
Hodge–Laplacian › Hodge–Laplacian:poisson_recovery_errorrank 304/3070.0210
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):temporal_variancerank 305/3070.0024
H² × ℝ (Thurston) › H² × ℝ (Thurston):radial_temporal_memoryrank 3/3074.9718
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_step_dispersionrank 306/3070.0057
Hölder Regularity › Hölder Regularity:holder_minrank 4/3070.9293
Klein Bottle › Klein Bottle:rank_deficit_maxrank 2/3071.0000
Klein Bottle › Klein Bottle:linear_complexityrank 307/3070.0000
Laplacian › Laplacian:cross_scale_curvature_coherencerank 1/3070.9996
Laplacian › Laplacian:curvature_autocorrelationrank 1/3070.9996
Laplacian › Laplacian:gradient_sign_persistencerank 4/3070.9962
Laplacian › Laplacian:biharmonic_ratiorank 304/3070.0000
Laplacian › Laplacian:poisson_recovery_errorrank 307/3070.0005
Moiré › Moiré:moire_peak_alpharank 1/3075.0000
Moiré › Moiré:moire_max_coherencerank 3/3070.9934
Moiré › Moiré:moire_phi_responserank 303/307-0.1145
Moiré › Moiré:moire_integer_excessrank 307/307-0.4471
Mostow Rigidity › Mostow Rigidity:mean_turn_anglerank 5/3070.9332
Mostow Rigidity › Mostow Rigidity:margulis_ratiorank 304/3070.0001
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_finerank 304/3070.0009
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_sloperank 307/307-0.6813
Möbius-S³ › Möbius-S³:hopf_fiber_coherencerank 2/3070.8101
Möbius-S³ › Möbius-S³:phase_profile_deviationrank 5/3070.6587
Navier-Stokes › Navier-Stokes:cascade_asymmetryrank 1/3071.0000
Nonstationarity › Nonstationarity:ac1_trendrank 4/3070.2093
Nonstationarity › Nonstationarity:variance_trendrank 304/307-0.2727
Predictability › Predictability:cond_entropy_k1rank 304/3070.0085
Predictability › Predictability:sample_entropyrank 307/3070.0025
Projective ℙ² › Projective ℙ²:distance_stdrank 304/3070.0000
Projective ℙ² › Projective ℙ²:mean_distancerank 305/3070.0000
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):trace_autocorrelationrank 2/3070.9998
Spectral Analysis › Spectral Analysis:spectral_bandwidthrank 305/3070.0005
Spectral Graph › Spectral Graph:weyl_exponentrank 1/3072.2334
Spirograph › Spirograph:angular_orderrank 1/30715.0000
Symplectic › Symplectic:windowed_area_cvrank 1/30710.3673
S² × ℝ (Thurston) › S² × ℝ (Thurston):great_circle_dispersionrank 306/3070.0020
Ulam Spiral (Square) › Ulam Spiral (Square):radial_dispersionrank 4/3070.6912
Ulam Spiral (Square) › Ulam Spiral (Square):polynomial_concentrationrank 5/3070.1239
Visibility Graph › Visibility Graph:nvg_hvg_reach_divergencerank 4/3070.9954
Visibility Graph › Visibility Graph:degree_exponent_gammarank 304/3070.3181
Visibility Graph › Visibility Graph:degree_r_squaredrank 306/3070.2269
Wasserstein › Wasserstein:distributional_stationarityrank 307/3070.5987
Wavelet Cascade › Wavelet Cascade:cascade_couplingrank 1/3070.9899
Wavelet Cascade › Wavelet Cascade:scale_gini_dispersionrank 305/3070.0074
p-Variation › p-Variation:volatility_clusteringrank 2/3070.9997
p-Variation › p-Variation:variation_indexrank 306/3071.0003
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Structure Atlas — Open Atlas · GitHub