BCQM III — Simulation Code

This repository contains the simulation code used for the numerical results in

Boundary-Condition Quantum Mechanics III (BCQM III):
stochastic event chains and emergent inertia

The code implements a minimal 1D event-chain model in which:

• A particle takes steps (s_n \in {-1,+1}) on a lattice of spacing (a).
• The coherence horizon (W_{\mathrm{coh}}) sets a persistence time (\tau = \tau_0 W_{\mathrm{coh}}) for the step direction.
• A small drive (b) (dimensionless) enters through a drift in the left/right choice probabilities, [ \Delta p = \kappa, b, S(W_{\mathrm{coh}}), ] where (S(W_{\mathrm{coh}})) is a geometric-series factor scaling as (S(W_{\mathrm{coh}}) \propto W_{\mathrm{coh}}^2) for large (W_{\mathrm{coh}}).
• The resulting trajectories are used to estimate:
  • ensemble trajectory clouds (Fig. 1),
  • mean displacement at zero drive (Fig. 2),
  • an effective inertial mass (m_{\mathrm{eff}}(W_{\mathrm{coh}})) from response to small (b) (Fig. 3),
  • velocity autocorrelation functions and their collapse when the lag is rescaled by (W_{\mathrm{coh}}) (Fig. 4).

All figures and CSV outputs in the BCQM III paper are reproducible from this code (up to Monte Carlo noise, with fixed seeds for reproducibility).

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Repository layout

Assuming the code lives in a folder called SIM/ inside the repo, you should see:

BCQM_III/
  SIM/
    bcqm3_sim.py        # core simulation model
    run_all.py          # main driver to regenerate all figures and CSVs
    run_all_2.py        # optional variant with LaTeX-style labels in plots
    figs/               # PDF figures (generated or pre-populated)
      fig1_trajectories.pdf
      fig2_mean_displacement.pdf
      fig3_meff_vs_Wcoh.pdf
      fig4_autocorr_collapse.pdf
    outputs/            # CSVs for reproducibility
      fig1_trajectories.csv
      fig2_mean_displacement.csv
      fig3_meff_values.csv

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TL;DR

bash git clone https://github.com/PMF57/BCQM_III.git cd BCQM_III/SIM pip install numpy matplotlib # or: pip install -r requirements.txt python run_all.py # regenerates all figures and CSVs