Quantum Walk
random-matrix-quantum · 37 views
random-matrix-quantumquasiperiodic
What It Is
Hadamard walk on a 257-site ring --- coin polarization ⟨σ_z(t)⟩ with ongoing wraparound dynamics and quantum recurrences
Interpretation
Standard analysis sees: anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power). The atlas additionally detects Nonstationarity:adf_pvalue. It sits beside Hofstadter Q in the atlas (standard-bank rank 20) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.65
asymmetry0.35
occupancy0.41
short-range corr0.12
long-range memory0.05
spectral colour0.95
periodicity0.42
complexity0.76
time-irreversibility0.73
volatility clustering0.41
multifractality0.38
dimensionality0.81
nonstationarity0.39
What the atlas adds
Nonstationarity:adf_pvalue+3.1z
unit-root nonstationarity (ADF cannot reject random-walk null)
Atlas-extreme metrics the standard bank can’t predict for this source
Gottwald-Melbourne:k_variance | +4.0z | bank-miss 1.7σ |
AutoRegressive:ar_coef_1 | -2.6z | bank-miss 1.7σ |
Bispectrum:coupling_frequency_centroid | -2.5z | bank-miss 1.5σ |
Composition
dtypefloat64
range[-0.1362, 0]
unique values16384 / 16384
mean ± std-0.0798 ± 0.00718
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/Quantum_Walk.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Quantum_Walk.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Quantum_Walk.png)
Inflation (Substitution) > barcode
/d_curve/Quantum_Walk.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/Quantum_Walk.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/Quantum_Walk.png)
Ulam Spiral (Sacks) > default
/default/Quantum_Walk.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| IMS Bearing Degraded | 4.44 | cross-origin |
| Hofstadter Q | 4.44 | cross-origin |
| Riemann Zeta Zeros | 4.56 | cross-origin |
Which Geometries Light Up
AutoRegressive › AutoRegressive:ar_coef_1 | rank 305/306 | -1.6779 |
Chladni › Chladni:modal_nodal_cascade | rank 1/306 | 2.1584 |
Laplacian › Laplacian:poisson_recovery_error | rank 1/306 | 15.6729 |
Möbius-S³ › Möbius-S³:phase_profile_deviation | rank 306/306 | 0.1079 |
Navier-Stokes › Navier-Stokes:ess_rescaling_gain | rank 4/306 | 0.9900 |
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