Dataset for: Jittery Quantum Boomerang Effect

Abstract

Dataset for: Jittery Quantum Boomerang Effect Authors: Pedro Dornelas, Gerson J. FerreiraAffiliation: Instituto de Física, Universidade Federal de Uberlândia, Uberlândia, Minas Gerais 38400-902, BrazilContact: pedrodornelas@ufu.br, gersonjferreira@ufu.brPreprint: arXiv:2606.10067 [cond-mat.dis-nn]Date: August 2026License: Creative Commons Attribution 4.0 International (CC-BY 4.0) 1. Overview This dataset contains the numerical simulation data for the manuscript "Jittery Quantum Boomerang Effect" (Pedro Dornelas & Gerson J. Ferreira). The simulations study the wave-packet dynamics of a spin-polarized electron packet in a disordered two-dimensional electron gas (2DEG) with Rashba spin-orbit coupling (modeling an InAs quantum well). The time evolution is computed using a Chebyshev polynomial expansion of the evolution operator combined with disorder ensemble averaging (NS samples). The dataset covers spatial densities, reciprocal space distributions (k-space), and time-dependent expectation values of position, momentum, and spin across clean and disordered regimes. Important Note on Normalization: All expectation values (position ⟨X⟩, squared position ⟨X²⟩, momentum ⟨p⟩, spin components ⟨σ⟩, and spin-momentum products ⟨ki sj⟩) as well as density distributions (dens, densk, spin_map, spin_map_k) are stored as raw sums accumulated across all disorder realizations. To obtain proper single-particle expectation values and normalized densities, each array must be divided by the number of disorder samples (NSamples). Note on Additional Data: Spatially- and momentum-resolved spin maps (spin_map, spin_map_k) and specific spin-momentum expectation values (⟨ki sj⟩) are included for completeness and exploratory research, although they were not directly plotted in the manuscript figures. 2. File Organization & Naming Convention All datasets are stored as compressed NumPy archives (.npz). The repository also includes zenodo_plots.ipynb, an interactive Jupyter Notebook that loads these datasets using relative paths to directly reproduce Figures 1–4 of the paper. data_clean_system.npz: Baseline simulation without impurity scattering (V0 = 0, τ → ∞). data_tau_[X.XX]ps.npz: Disordered simulations labeled by their Born-approximation scattering time τ (ranging from 0.25 ps to 14.35 ps). 3. Data Dictionary Each .npz file acts as a dictionary containing the following arrays and physical parameters: A. Constants & System Parameters hbar: Reduced Planck constant used in the simulation [meV ps]. mass: Effective mass of the particle [m0]. alpha: Spin-orbit coupling strength [meV nm]. V0: Impurity potential strength [meV]. tau: Calculated scattering time τ = 6ℏ² / (V0² m dx² π) [ps]. NSamples: Number of samples/impurities averaged over for disordered systems. B. Spatial & Momentum Grids Nx, Ny: Number of grid points in x and y directions. Lx, Ly: Physical length of the simulated box in x and y [nm]. dx, dy: Spatial step sizes [nm]. X, Y: 2D spatial coordinate meshes [nm]. x0, y0: Initial wavepacket center coordinates [nm]. KX, KY: 2D momentum/wavevector coordinate meshes [1/nm]. kx0, ky0: Initial wavevector of the wavepacket [1/nm]. C. Time Evolution (1D Arrays, length Nt) Nt: Total number of time steps. tmax: Maximum simulation time [ps]. t: Time array [ps]. dt: Time step size [ps]. Xav, Yav: Expectation values of position ⟨X⟩, ⟨Y⟩ [nm]. X2, Y2: Expectation values of squared position ⟨X²⟩, ⟨Y²⟩ [nm²]. expectation_px, expectation_py: Expectation values of momentum [1/nm]. sigmax, sigmay, sigmaz: Unnormalized sums of spin expectation values. D. Spin-Momentum Expectation Values (1D Arrays, length Nt) (Included in all datasets except data_tau_5.00ps.npz) kx_sx, kx_sy, kx_sz: Expectation values ⟨kx sx⟩, ⟨kx sy⟩, and ⟨kx sz⟩ [1/nm]. ky_sx, ky_sy, ky_sz: Expectation values ⟨ky sx⟩, ⟨ky sy⟩, and ⟨ky sz⟩ [1/nm]. E. Maps & Distributions (Multidimensional Arrays) (Spin maps are included only in data_tau_1.00ps.npz, data_tau_1.84ps.npz, data_tau_2.50ps.npz, and data_tau_10.00ps.npz) dens: Time-dependent spatial probability density |Ψ(x,y,t)|². densk: Time-dependent momentum probability density |Ψ(kx,ky,t)|². spin_map: Spatially resolved spin distribution. spin_map_k: Momentum-resolved spin distribution. 4. Usage Example (Python) import numpy as np import matplotlib.pyplot as plt # Load a dataset data = np.load('data_tau_1.00ps.npz') t = data['t'] N = data['NSamples'][()] tau = data['tau'][()] # 1. Normalized position expectation x_mean = (data['Xav'] / N) - data['x0'][()] # 2. Compute spatial variance on the fly: - ^2 x2_mean = data['X2'] / N var_x = x2_mean - (data['Xav'] / N)**2 plt.figure(figsize=(6, 4)) plt.plot(t, var_x, label=r'$\Delta x^2(t)$') plt.xlabel('Time [ps]') plt.ylabel(r'Variance [nm$^2$]') plt.title(f'Wavepacket Spreading (tau = {tau:.2f} ps)') plt.grid(True, linestyle='--', alpha=0.6) plt.legend() plt.tight_layout() plt.show()