#!/usr/bin/env python3 """ Braided Field Simulation: Polaron-Polariton Topological Quantum Mechanics This script simulates the braided field concept combining: - Polaron: charge dragging physical distortion - Polariton: light coupled with matter - Anyon braiding in 2D with complex phase shifts """ import numpy as np import cmath import hashlib import json from dataclasses import dataclass from datetime import datetime, timezone from pathlib import Path from typing import List, Tuple import matplotlib.pyplot as plt ROOT = Path(__file__).resolve().parents[2] RECEIPT_PATH = ROOT / "4-Infrastructure" / "hardware" / "braided_field_sim_receipt.json" PLOT_PATH = ROOT / "4-Infrastructure" / "hardware" / "braiding_phase_space.png" @dataclass class Quasiparticle: """A quasiparticle in 2D space with position and phase.""" position: Tuple[float, float] phase: float particle_type: int # 0 = photon-like, 1 = electron-like, 2 = phonon-like @dataclass class Braiding: """A braiding operation that swaps two quasiparticles.""" i: int # index of first particle j: int # index of second particle phase_shift: float # complex phase shift e^(iθ) class Hamiltonian: """Multi-body Hamiltonian for polaron-polariton system.""" def __init__(self): self.photon_energy_coeff = 1.0 self.electron_energy_coeff = 0.5 self.phonon_energy_coeff = 0.3 self.interaction_coeff = 0.2 def photon_energy(self, psi: complex) -> float: return self.photon_energy_coeff * abs(psi)**2 def electron_energy(self, psi: complex) -> float: return self.electron_energy_coeff * abs(psi)**2 def phonon_energy(self, psi: complex) -> float: return self.phonon_energy_coeff * abs(psi)**2 def interaction_energy(self, psi: complex) -> float: return self.interaction_coeff * abs(psi)**4 def total_energy(self, psi: complex) -> float: return (self.photon_energy(psi) + self.electron_energy(psi) + self.phonon_energy(psi) + self.interaction_energy(psi)) class BraidedField: """A braided field state containing multiple quasiparticles.""" def __init__(self, particles: List[Quasiparticle], hamiltonian: Hamiltonian): self.particles = particles self.braiding_history: List[Braiding] = [] self.hamiltonian = hamiltonian self.magnetic_field = 0.0 def apply_braiding(self, i: int, j: int, phase_shift: float): """Apply a braiding operation to swap particles i and j.""" if i >= len(self.particles) or j >= len(self.particles): raise IndexError("Particle index out of range") # Swap particles and apply phase shift self.particles[i], self.particles[j] = self.particles[j], self.particles[i] # Apply phase shift to both particles self.particles[i].phase += phase_shift self.particles[j].phase += phase_shift # Record the braiding operation self.braiding_history.append(Braiding(i, j, phase_shift)) def topological_invariant(self) -> float: """Compute the topological invariant from braiding history.""" return sum(b.phase_shift for b in self.braiding_history) def total_wavefunction(self) -> complex: """Compute the total wavefunction of the field.""" psi = 0j for p in self.particles: psi += cmath.exp(1j * p.phase) return psi def total_energy(self) -> float: """Compute the total energy of the field.""" psi = self.total_wavefunction() return self.hamiltonian.total_energy(psi) def is_protection_candidate(self) -> bool: """Check the local candidate gate; this is not a proof of protection.""" invariant = self.topological_invariant() return invariant != 0 and self.magnetic_field > 0 class PolaronPolariton: """A topological polaron-polariton quasiparticle.""" def __init__(self, position: Tuple[float, float], statistics_param: float): self.photon_component = 1.0 + 0j self.electron_component = 1.0 + 0j self.phonon_component = 0.5 + 0j self.position = position self.statistics_parameter = statistics_param # θ in [0, 2π) def wavefunction(self) -> complex: """Combined wavefunction for polaron-polariton.""" return (self.photon_component + self.electron_component + self.phonon_component) def effective_mass(self) -> float: """Effective mass renormalized by phonon coupling.""" return 1.0 + abs(self.phonon_component) * 0.5 def braid(self, other: 'PolaronPolariton') -> Tuple['PolaronPolariton', 'PolaronPolariton']: """Braid two polaron-polaritons with phase shift.""" phase = cmath.exp(1j * self.statistics_parameter) pp1 = PolaronPolariton(self.position, self.statistics_parameter) pp1.photon_component = self.photon_component * phase pp1.electron_component = self.electron_component * phase pp1.phonon_component = self.phonon_component * phase pp2 = PolaronPolariton(other.position, other.statistics_parameter) pp2.photon_component = other.photon_component * phase pp2.electron_component = other.electron_component * phase pp2.phonon_component = other.phonon_component * phase return pp1, pp2 def simulate_braiding_sequence(): """Simulate a sequence of braiding operations.""" print("=== Braided Field Simulation ===\n") # Create quasiparticles particles = [ Quasiparticle((0.0, 0.0), 0.0, 0), # photon-like at origin Quasiparticle((1.0, 0.0), 0.0, 1), # electron-like at (1,0) Quasiparticle((0.5, 1.0), 0.0, 2), # phonon-like at (0.5,1) ] hamiltonian = Hamiltonian() field = BraidedField(particles, hamiltonian) print(f"Initial state: {len(particles)} quasiparticles") print(f"Initial wavefunction: {field.total_wavefunction():.4f}") print(f"Initial energy: {field.total_energy():.4f}") print(f"Topological invariant: {field.topological_invariant():.4f}\n") # Apply braiding operations print("Applying braiding operations:") # Braid 0 and 1 with phase shift π/2 field.apply_braiding(0, 1, np.pi/2) print(f" Braid (0,1) with phase π/2") print(f" Wavefunction: {field.total_wavefunction():.4f}") print(f" Energy: {field.total_energy():.4f}") print(f" Invariant: {field.topological_invariant():.4f}\n") # Braid 1 and 2 with phase shift π/3 field.apply_braiding(1, 2, np.pi/3) print(f" Braid (1,2) with phase π/3") print(f" Wavefunction: {field.total_wavefunction():.4f}") print(f" Energy: {field.total_energy():.4f}") print(f" Invariant: {field.topological_invariant():.4f}\n") # Braid 0 and 2 with phase shift π/4 field.apply_braiding(0, 2, np.pi/4) print(f" Braid (0,2) with phase π/4") print(f" Wavefunction: {field.total_wavefunction():.4f}") print(f" Energy: {field.total_energy():.4f}") print(f" Invariant: {field.topological_invariant():.4f}\n") # Apply magnetic field to enable topological protection field.magnetic_field = 1.0 print(f"Applied magnetic field: {field.magnetic_field}") print(f"Protection candidate: {field.is_protection_candidate()}\n") print(f"Final topological invariant: {field.topological_invariant():.4f}") print(f"Total braiding operations: {len(field.braiding_history)}") return { "initial_wavefunction": "3.0000+0.0000j", "final_wavefunction": f"{field.total_wavefunction():.4f}", "final_energy": field.total_energy(), "topological_invariant": field.topological_invariant(), "braiding_operations": len(field.braiding_history), "magnetic_field": field.magnetic_field, "protection_candidate": field.is_protection_candidate(), } def simulate_polaron_polariton_braiding(): """Simulate braiding of polaron-polaritons.""" print("\n=== Polaron-Polariton Braiding Simulation ===\n") # Create two polaron-polaritons pp1 = PolaronPolariton((0.0, 0.0), np.pi/4) # anyon with statistics parameter π/4 pp2 = PolaronPolariton((1.0, 0.0), np.pi/4) print(f"Initial polaron-polaritons:") print(f" PP1 wavefunction: {pp1.wavefunction():.4f}") print(f" PP1 effective mass: {pp1.effective_mass():.4f}") print(f" PP2 wavefunction: {pp2.wavefunction():.4f}") print(f" PP2 effective mass: {pp2.effective_mass():.4f}\n") # Braid them print("Braiding the two polaron-polaritons...") pp1_braided, pp2_braided = pp1.braid(pp2) print(f"After braiding:") print(f" PP1 wavefunction: {pp1_braided.wavefunction():.4f}") print(f" PP1 effective mass: {pp1_braided.effective_mass():.4f}") print(f" PP2 wavefunction: {pp2_braided.wavefunction():.4f}") print(f" PP2 effective mass: {pp2_braided.effective_mass():.4f}\n") # Compute the phase shift phase_shift = cmath.exp(1j * pp1.statistics_parameter) print(f"Braiding phase shift: {phase_shift:.4f}") print(f"Phase shift magnitude: {abs(phase_shift):.4f}") print(f"Phase shift angle: {cmath.phase(phase_shift):.4f} rad") return { "initial_wavefunction": f"{pp1.wavefunction():.4f}", "braided_wavefunction": f"{pp1_braided.wavefunction():.4f}", "effective_mass": pp1_braided.effective_mass(), "phase_shift": f"{phase_shift:.4f}", "phase_shift_magnitude": abs(phase_shift), "phase_shift_angle_rad": cmath.phase(phase_shift), } def plot_braiding_phase_space(): """Visualize the braiding phase space.""" print("\n=== Braiding Phase Space Visualization ===\n") # Generate phase shifts for different statistics parameters theta_values = np.linspace(0, 2*np.pi, 100) phase_shifts = [cmath.exp(1j * theta) for theta in theta_values] # Extract real and imaginary parts real_parts = [z.real for z in phase_shifts] imag_parts = [z.imag for z in phase_shifts] # Create plot plt.figure(figsize=(8, 8)) plt.plot(real_parts, imag_parts, 'b-', linewidth=2, label='Phase shift unit circle') plt.axhline(y=0, color='k', linestyle='-', alpha=0.3) plt.axvline(x=0, color='k', linestyle='-', alpha=0.3) plt.xlabel('Re(e^(iθ))') plt.ylabel('Im(e^(iθ))') plt.title('Braiding Phase Shifts in Complex Plane') plt.grid(True, alpha=0.3) plt.axis('equal') plt.legend() # Mark special cases special_cases = [ (0, 'Boson (θ=0)'), (np.pi, 'Fermion (θ=π)'), (np.pi/2, 'Semion (θ=π/2)'), (np.pi/4, 'θ=π/4'), ] for theta, label in special_cases: z = cmath.exp(1j * theta) plt.plot(z.real, z.imag, 'ro', markersize=8) plt.annotate(label, (z.real, z.imag), xytext=(10, 10), textcoords='offset points', fontsize=9) plt.tight_layout() plt.savefig(PLOT_PATH, dpi=150) print(f"Phase space plot saved to {PLOT_PATH}") return { "plot_path": str(PLOT_PATH), "phase_samples": len(theta_values), } if __name__ == "__main__": sequence_summary = simulate_braiding_sequence() polaron_polariton_summary = simulate_polaron_polariton_braiding() plot_summary = plot_braiding_phase_space() receipt = { "generated_utc": datetime.now(timezone.utc).isoformat(), "lawful": True, "mode": "virtual_only", "source_note": "No hardware programming, RF emission, JTAG, serial flashing, board access, or material claim. Python toy simulation only.", "sequence_summary": sequence_summary, "polaron_polariton_summary": polaron_polariton_summary, "plot_summary": plot_summary, "claim_boundary": "This simulation records a candidate braid-field control model. It does not prove topological protection, local-noise immunity, device feasibility, material existence, or compression advantage.", } encoded = json.dumps(receipt, indent=2, sort_keys=True).encode("utf-8") receipt["receipt_hash_preimage_sha256"] = hashlib.sha256(encoded).hexdigest() RECEIPT_PATH.write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n", encoding="utf-8") print("\n=== Simulation Complete ===") print("The braided field combines light, charge, and vibration") print("into a virtual candidate braid-field control model.") print("No topological protection, local-noise immunity, or device feasibility is proven.") print(f"Receipt written to {RECEIPT_PATH}")