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