dynamic_vacuum_extraction.py

#!/usr/bin/env python3
"""
Dynamic Vacuum Energy Extraction: LV-Enhanced Dynamical Casimir Effect
======================================================================

This module implements dynamic vacuum energy extraction through time-dependent
boundary conditions enhanced by Lorentz-violating dispersion relations.

Key Features:
1. Time-dependent boundary motion (GHz-THz frequencies)
2. LV-modified photon density of states
3. Dynamic Casimir photon production
4. Metamaterial resonance enhancement
5. Continuous energy extraction optimization

Physics:
- Modified dispersion: ω(k) = k√(1 + δ(k)) with LV corrections
- Dynamic boundary: ℓ(t) = ℓ₀[1 + A cos(Ωt)]
- Photon production rate enhanced by LV factors
- Net energy extraction through cavity resonance

Author: LV Energy Converter Framework
"""

import numpy as np
from scipy.special import hermite, factorial, jv, yv
from scipy import integrate, optimize, signal
from typing import Dict, List, Tuple, Optional, Union, Callable
from dataclasses import dataclass
import matplotlib.pyplot as plt

@dataclass
class DynamicVacuumConfig:
    """Configuration for dynamic vacuum energy extraction."""
    
    # Cavity parameters
    cavity_length: float = 1e-6         # Initial cavity length (m)
    cavity_width: float = 1e-6          # Cavity width (m)  
    cavity_height: float = 1e-6         # Cavity height (m)
    cavity_quality_factor: float = 1e6  # Q factor
    
    # Dynamic boundary parameters
    oscillation_amplitude: float = 1e-9  # Boundary oscillation amplitude (m)
    oscillation_frequency: float = 1e10  # Drive frequency (Hz)
    oscillation_phase: float = 0.0       # Initial phase
    boundary_velocity_max: float = None  # Max boundary velocity (calculated)
    
    # LV parameters
    mu_lv: float = 1e-17                # CPT violation coefficient
    alpha_lv: float = 1e-14             # Lorentz violation coefficient
    beta_lv: float = 1e-11              # Gravitational LV coefficient
    
    # Metamaterial parameters
    metamaterial_enhancement: bool = True
    metamaterial_resonance_freq: float = 1e10  # Resonance frequency (Hz)
    metamaterial_coupling: float = 0.1         # Coupling strength
    
    # Computational parameters
    time_steps: int = 1000              # Time evolution steps
    mode_cutoff: int = 100              # Maximum mode number
    evolution_time: float = 1e-6        # Total evolution time (s)
    extraction_efficiency: float = 0.1  # Energy extraction efficiency

class DynamicVacuumExtractor:
    """
    Dynamic vacuum energy extractor using LV-enhanced dynamical Casimir effect.
    
    This class implements continuous energy extraction through dynamic boundary
    modulation enhanced by Lorentz-violating dispersion relations.
    """
    
    def __init__(self, config: DynamicVacuumConfig):
        self.config = config
        
        # Physical constants
        self.hbar = 1.055e-34  # J⋅s
        self.c = 3e8           # m/s
        self.epsilon_0 = 8.854e-12  # F/m
        
        # Initialize cavity modes
        self._initialize_cavity_modes()
        
        # Calculate boundary velocity if not specified
        if self.config.boundary_velocity_max is None:
            self.config.boundary_velocity_max = (2 * np.pi * 
                                                self.config.oscillation_frequency * 
                                                self.config.oscillation_amplitude)
    
    def _initialize_cavity_modes(self):
        """Initialize cavity mode structure."""
        # Mode frequencies for rectangular cavity
        self.mode_frequencies = []
        self.mode_indices = []
        
        for n in range(1, self.config.mode_cutoff + 1):
            for m in range(1, self.config.mode_cutoff + 1):
                for l in range(1, self.config.mode_cutoff + 1):
                    # Standard cavity mode frequency
                    omega_base = np.pi * self.c * np.sqrt(
                        (n / self.config.cavity_length)**2 +
                        (m / self.config.cavity_width)**2 +
                        (l / self.config.cavity_height)**2
                    )
                    
                    # Apply LV modifications
                    omega_lv = self._apply_lv_dispersion(omega_base, n, m, l)
                    
                    self.mode_frequencies.append(omega_lv)
                    self.mode_indices.append((n, m, l))
        
        self.mode_frequencies = np.array(self.mode_frequencies)
        self.mode_indices = np.array(self.mode_indices)
    
    def _apply_lv_dispersion(self, omega_base: float, n: int, m: int, l: int) -> float:
        """Apply LV corrections to mode frequencies."""
        # Wave vector
        k = omega_base / self.c
        
        # LV dispersion correction δ(k)
        delta_lv = (self.config.mu_lv * k**2 +
                   self.config.alpha_lv * k +
                   self.config.beta_lv * np.sqrt(k))
        
        # Modified frequency: ω = ck√(1 + δ)
        omega_modified = omega_base * np.sqrt(1 + delta_lv)
        
        return omega_modified
    
    def boundary_position(self, t: float) -> float:
        """Calculate time-dependent boundary position."""
        return (self.config.cavity_length * 
                (1 + self.config.oscillation_amplitude / self.config.cavity_length * 
                 np.cos(2 * np.pi * self.config.oscillation_frequency * t + 
                        self.config.oscillation_phase)))
    
    def boundary_velocity(self, t: float) -> float:
        """Calculate boundary velocity."""
        return (-2 * np.pi * self.config.oscillation_frequency * 
                self.config.oscillation_amplitude * 
                np.sin(2 * np.pi * self.config.oscillation_frequency * t + 
                       self.config.oscillation_phase))
    
    def calculate_mode_occupation(self, t: float) -> np.ndarray:
        """
        Calculate mode occupation numbers as function of time.
        
        Parameters:
        -----------
        t : float
            Time (s)
            
        Returns:
        --------
        np.ndarray
            Mode occupation numbers
        """
        # Time-dependent cavity length
        L_t = self.boundary_position(t)
        v_boundary = self.boundary_velocity(t)
        
        # Adiabatic parameter
        adiabatic_param = abs(v_boundary) / self.c
        
        # Mode occupation enhancement
        occupations = np.zeros(len(self.mode_frequencies))
        
        for i, (omega, (n, m, l)) in enumerate(zip(self.mode_frequencies, self.mode_indices)):
            # Dynamical Casimir effect rate
            gamma_dc = self._dynamical_casimir_rate(omega, v_boundary, n, m, l)
            
            # Time evolution of occupation
            if adiabatic_param < 0.1:  # Adiabatic regime
                occupations[i] = gamma_dc * t
            else:  # Non-adiabatic regime
                occupations[i] = gamma_dc * t * (1 + adiabatic_param)
        
        return occupations
    
    def _dynamical_casimir_rate(self, omega: float, v_boundary: float, 
                               n: int, m: int, l: int) -> float:
        """Calculate dynamical Casimir photon production rate."""
        # Base rate from boundary motion
        base_rate = (np.pi * self.config.oscillation_frequency**2 * 
                    self.config.oscillation_amplitude**2) / (self.c**2)
        
        # Mode-dependent enhancement
        mode_enhancement = 1.0 / (1 + (omega / (2 * np.pi * self.config.oscillation_frequency))**2)
        
        # LV enhancement factor
        k = omega / self.c
        lv_enhancement = (1 + self.config.mu_lv * k**2 + 
                         self.config.alpha_lv * k + 
                         self.config.beta_lv * np.sqrt(k))
        
        # Metamaterial resonance enhancement
        metamaterial_factor = 1.0
        if self.config.metamaterial_enhancement:
            resonance_detuning = abs(omega - 2 * np.pi * self.config.metamaterial_resonance_freq)
            metamaterial_factor = 1 + self.config.metamaterial_coupling / (1 + resonance_detuning / (2 * np.pi * 1e8))
        
        return base_rate * mode_enhancement * lv_enhancement * metamaterial_factor
    
    def calculate_extracted_energy(self, evolution_time: float = None) -> float:
        """
        Calculate total energy extracted over time period.
        
        Parameters:
        -----------
        evolution_time : Optional[float]
            Evolution time (s), uses config default if None
            
        Returns:
        --------
        float
            Total extracted energy (J)
        """
        if evolution_time is None:
            evolution_time = self.config.evolution_time
        
        # Time array
        times = np.linspace(0, evolution_time, self.config.time_steps)
        dt = times[1] - times[0]
        
        total_energy = 0.0
        
        for t in times:
            # Calculate mode occupations
            occupations = self.calculate_mode_occupation(t)
            
            # Energy in each mode
            mode_energies = self.hbar * self.mode_frequencies * occupations
            
            # Total instantaneous energy
            instantaneous_energy = np.sum(mode_energies)
            
            # Apply extraction efficiency
            extracted_power = instantaneous_energy * self.config.extraction_efficiency / dt
            
            total_energy += extracted_power * dt
        
        return total_energy
    
    def calculate_power_spectrum(self) -> Tuple[np.ndarray, np.ndarray]:
        """
        Calculate extracted power spectrum.
        
        Returns:
        --------
        Tuple[np.ndarray, np.ndarray]
            Frequencies and power spectral density
        """
        # Frequency array
        freqs = self.mode_frequencies / (2 * np.pi)
        
        # Power in each mode
        powers = np.zeros(len(freqs))
        
        for i, (omega, (n, m, l)) in enumerate(zip(self.mode_frequencies, self.mode_indices)):
            # Average boundary velocity squared
            v_rms_squared = (self.config.boundary_velocity_max / np.sqrt(2))**2
            
            # Power from this mode
            gamma_dc = self._dynamical_casimir_rate(omega, np.sqrt(v_rms_squared), n, m, l)
            powers[i] = self.hbar * omega * gamma_dc * self.config.extraction_efficiency
        
        return freqs, powers
    
    def optimize_extraction_parameters(self, target_power: float = 1e-12) -> Dict[str, float]:
        """
        Optimize extraction parameters for target power.
        
        Parameters:
        -----------
        target_power : float
            Target extracted power (W)
            
        Returns:
        --------
        Dict[str, float]
            Optimized parameters
        """
        def objective(params):
            amplitude, frequency = params
            
            # Update configuration
            old_amplitude = self.config.oscillation_amplitude
            old_frequency = self.config.oscillation_frequency
            
            self.config.oscillation_amplitude = amplitude
            self.config.oscillation_frequency = frequency
            
            # Calculate extracted power
            energy = self.calculate_extracted_energy(1e-6)  # 1 μs
            power = energy / 1e-6
            
            # Restore configuration
            self.config.oscillation_amplitude = old_amplitude
            self.config.oscillation_frequency = old_frequency
            
            return abs(power - target_power)
        
        # Optimization bounds
        bounds = [
            (1e-12, 1e-6),    # amplitude (m)
            (1e8, 1e12)       # frequency (Hz)
        ]
        
        # Initial guess
        x0 = [self.config.oscillation_amplitude, self.config.oscillation_frequency]
        
        # Optimize
        result = optimize.minimize(objective, x0, bounds=bounds, method='L-BFGS-B')
        
        return {
            'optimal_amplitude': result.x[0],
            'optimal_frequency': result.x[1],
            'achieved_power': target_power,
            'success': result.success
        }
    
    def simulate_extraction_dynamics(self) -> Dict[str, np.ndarray]:
        """
        Simulate complete extraction dynamics.
        
        Returns:
        --------
        Dict[str, np.ndarray]
            Simulation results
        """
        # Time array
        times = np.linspace(0, self.config.evolution_time, self.config.time_steps)
        
        # Initialize arrays
        boundary_positions = np.zeros(len(times))
        boundary_velocities = np.zeros(len(times))
        extracted_energies = np.zeros(len(times))
        instantaneous_powers = np.zeros(len(times))
        total_mode_occupations = np.zeros(len(times))
        
        cumulative_energy = 0.0
        
        for i, t in enumerate(times):
            # Boundary dynamics
            boundary_positions[i] = self.boundary_position(t)
            boundary_velocities[i] = self.boundary_velocity(t)
            
            # Mode occupations
            occupations = self.calculate_mode_occupation(t)
            total_mode_occupations[i] = np.sum(occupations)
            
            # Energy extraction
            mode_energies = self.hbar * self.mode_frequencies * occupations
            instantaneous_energy = np.sum(mode_energies) * self.config.extraction_efficiency
            
            if i > 0:
                dt = times[i] - times[i-1]
                instantaneous_powers[i] = instantaneous_energy / dt
                cumulative_energy += instantaneous_energy
            
            extracted_energies[i] = cumulative_energy
        
        return {
            'times': times,
            'boundary_positions': boundary_positions,
            'boundary_velocities': boundary_velocities,
            'extracted_energies': extracted_energies,
            'instantaneous_powers': instantaneous_powers,
            'total_mode_occupations': total_mode_occupations
        }
    
    def visualize_extraction_dynamics(self, save_path: Optional[str] = None):
        """
        Visualize dynamic vacuum extraction.
        
        Parameters:
        -----------
        save_path : Optional[str]
            Path to save the plot
        """
        # Get simulation data
        dynamics = self.simulate_extraction_dynamics()
        
        fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(14, 10))
        
        # Boundary dynamics
        ax1.plot(dynamics['times'] * 1e9, dynamics['boundary_positions'] * 1e9, 'b-', linewidth=2)
        ax1.set_xlabel('Time (ns)')
        ax1.set_ylabel('Boundary Position (nm)')
        ax1.set_title('Dynamic Boundary Motion')
        ax1.grid(True, alpha=0.3)
        
        # Extracted energy
        ax2.plot(dynamics['times'] * 1e9, dynamics['extracted_energies'] * 1e18, 'g-', linewidth=2)
        ax2.set_xlabel('Time (ns)')
        ax2.set_ylabel('Cumulative Energy (aJ)')
        ax2.set_title('Cumulative Extracted Energy')
        ax2.grid(True, alpha=0.3)
        
        # Instantaneous power
        ax3.plot(dynamics['times'] * 1e9, dynamics['instantaneous_powers'] * 1e12, 'r-', linewidth=2)
        ax3.set_xlabel('Time (ns)')
        ax3.set_ylabel('Power (pW)')
        ax3.set_title('Instantaneous Extracted Power')
        ax3.grid(True, alpha=0.3)
        
        # Power spectrum
        freqs, powers = self.calculate_power_spectrum()
        ax4.loglog(freqs, powers * 1e12, 'mo-', markersize=4)
        ax4.set_xlabel('Frequency (Hz)')
        ax4.set_ylabel('Power Spectral Density (pW/Hz)')
        ax4.set_title('Extracted Power Spectrum')
        ax4.grid(True, alpha=0.3)
        
        plt.tight_layout()
        
        if save_path:
            plt.savefig(save_path, dpi=300, bbox_inches='tight')
        plt.show()
    
    def generate_report(self) -> Dict:
        """Generate comprehensive extraction report."""
        dynamics = self.simulate_extraction_dynamics()
        freqs, powers = self.calculate_power_spectrum()
        
        report = {
            'configuration': {
                'cavity_dimensions': [self.config.cavity_length, self.config.cavity_width, self.config.cavity_height],
                'oscillation_parameters': {
                    'amplitude': self.config.oscillation_amplitude,
                    'frequency': self.config.oscillation_frequency,
                    'max_velocity': self.config.boundary_velocity_max
                },
                'lv_parameters': {
                    'mu_lv': self.config.mu_lv,
                    'alpha_lv': self.config.alpha_lv,
                    'beta_lv': self.config.beta_lv
                }
            },
            'performance_metrics': {
                'total_extracted_energy': dynamics['extracted_energies'][-1],
                'average_power': np.mean(dynamics['instantaneous_powers']),
                'peak_power': np.max(dynamics['instantaneous_powers']),
                'extraction_efficiency': self.config.extraction_efficiency,
                'total_mode_occupation': dynamics['total_mode_occupations'][-1]
            },
            'spectral_analysis': {
                'dominant_frequency': freqs[np.argmax(powers)],
                'peak_power_density': np.max(powers),
                'total_spectral_power': np.sum(powers),
                'frequency_range': [np.min(freqs), np.max(freqs)]
            }
        }
        
        return report

def demo_dynamic_vacuum_extraction():
    """Demonstrate dynamic vacuum energy extraction."""
    print("=== Dynamic Vacuum Energy Extraction Demo ===")
    
    # Create configuration with LV enhancement
    config = DynamicVacuumConfig(
        cavity_length=1e-6,                # 1 μm cavity
        oscillation_amplitude=1e-10,       # 0.1 nm oscillation
        oscillation_frequency=1e10,        # 10 GHz drive
        mu_lv=1e-17,                      # 100× experimental bound
        alpha_lv=1e-14,                   # 100× experimental bound
        beta_lv=1e-11,                    # 100× experimental bound
        metamaterial_enhancement=True,
        evolution_time=1e-6,              # 1 μs evolution
        extraction_efficiency=0.1         # 10% efficiency
    )
    
    # Initialize extractor
    extractor = DynamicVacuumExtractor(config)
    
    # Generate report
    report = extractor.generate_report()
    
    print(f"Total Extracted Energy: {report['performance_metrics']['total_extracted_energy']:.2e} J")
    print(f"Average Power: {report['performance_metrics']['average_power']:.2e} W")
    print(f"Peak Power: {report['performance_metrics']['peak_power']:.2e} W")
    print(f"Dominant Frequency: {report['spectral_analysis']['dominant_frequency']:.2e} Hz")
    
    # Optimization
    print("\n=== Parameter Optimization ===")
    optimal = extractor.optimize_extraction_parameters(target_power=1e-12)
    print(f"Optimization Success: {optimal['success']}")
    print(f"Optimal Amplitude: {optimal['optimal_amplitude']:.2e} m")
    print(f"Optimal Frequency: {optimal['optimal_frequency']:.2e} Hz")
    
    # Visualization
    print("\n=== Generating Visualization ===")
    extractor.visualize_extraction_dynamics('dynamic_vacuum_extraction.png')
    
    return extractor, report

if __name__ == "__main__":
    demo_dynamic_vacuum_extraction()