hidden_sector_portal.py

#!/usr/bin/env python3
"""
Hidden Sector Portal: Extra-Dimensional Energy Transfer with Lorentz Violation
==============================================================================

This module implements extra-dimensional energy transfer through hidden sector portals,
enhanced with Lorentz-violating modifications. The portal enables energy extraction
from higher-dimensional branes when LV parameters exceed experimental bounds.

Key Features:
1. Braneworld energy transfer through kinetic mixing
2. Extra-dimensional gravitational effects
3. LV-modified portal interactions
4. Dynamic dimensional coupling coefficients
5. Energy flux optimization across dimensional boundaries

Physics:
- Based on Randall-Sundrum and ADD extra-dimensional models
- Incorporates Lorentz violation through modified dispersion relations
- Portal fields mediate energy transfer between 4D brane and bulk
- LV enhances dimensional coupling when μ, α, β > experimental bounds

Author: Quantum Geometry Hidden Sector Framework
"""

import numpy as np
from scipy.special import kn, iv, hyp2f1, gamma
from scipy import integrate, optimize
from typing import Dict, List, Tuple, Optional, Union
from dataclasses import dataclass
import matplotlib.pyplot as plt

@dataclass
class HiddenSectorConfig:
    """Configuration for hidden sector portal calculations."""
    
    # Extra-dimensional parameters
    n_extra_dims: int = 2              # Number of extra dimensions
    compactification_radius: float = 1e-3  # Compactification radius (TeV^-1)
    brane_tension: float = 1.0         # Brane tension (normalized)
    
    # Portal parameters
    kinetic_mixing: float = 1e-3       # Portal-hidden sector kinetic mixing
    portal_mass: float = 0.1           # Portal field mass (GeV)
    coupling_strength: float = 1e-2    # Portal coupling strength
    
    # LV parameters
    mu_lv: float = 1e-18               # CPT-violating coefficient
    alpha_lv: float = 1e-15            # Lorentz violation in dispersion
    beta_lv: float = 1e-12             # Dimensional coupling LV
    
    # Computational parameters
    energy_range: Tuple[float, float] = (0.1, 10.0)  # Energy range (GeV)
    momentum_cutoff: float = 100.0     # Momentum cutoff (GeV)
    integration_points: int = 1000     # Integration points

class HiddenSectorPortal:
    """
    Hidden sector portal for extra-dimensional energy transfer.
    
    This class implements the calculation of energy transfer between our 4D brane
    and extra-dimensional hidden sectors through portal field interactions.
    """
    
    def __init__(self, config: HiddenSectorConfig):
        self.config = config
        self.experimental_bounds = {
            'mu_lv': 1e-19,      # Current CPT violation bounds
            'alpha_lv': 1e-16,   # Lorentz violation bounds
            'beta_lv': 1e-13     # Dimensional coupling bounds
        }
        
    def is_pathway_active(self) -> bool:
        """Check if LV parameters exceed experimental bounds to activate pathway."""
        return (self.config.mu_lv > self.experimental_bounds['mu_lv'] or
                self.config.alpha_lv > self.experimental_bounds['alpha_lv'] or
                self.config.beta_lv > self.experimental_bounds['beta_lv'])
    
    def lv_enhancement_factor(self, energy: float) -> float:
        """
        Calculate LV enhancement factor for dimensional coupling.
        
        Parameters:
        -----------
        energy : float
            Energy scale (GeV)
            
        Returns:
        --------
        float
            Enhancement factor from LV effects
        """
        # LV-modified dispersion relation enhancement
        mu_term = self.config.mu_lv * energy**2
        alpha_term = self.config.alpha_lv * energy
        beta_term = self.config.beta_lv * energy**(1 + self.config.n_extra_dims/2)
        
        return 1.0 + mu_term + alpha_term + beta_term
    
    def kaluza_klein_spectrum(self, n_mode: int, energy: float) -> float:
        """
        Calculate Kaluza-Klein mode energies with LV modifications.
        
        Parameters:
        -----------
        n_mode : int
            KK mode number
        energy : float
            Base energy scale (GeV)
            
        Returns:
        --------
        float
            Modified KK mode energy
        """
        # Standard KK tower
        kk_mass_squared = (n_mode / self.config.compactification_radius)**2
        
        # LV modifications to KK spectrum
        lv_correction = self.lv_enhancement_factor(energy)
        
        return np.sqrt(energy**2 + kk_mass_squared * lv_correction)
    
    def portal_propagator(self, momentum: float, energy: float) -> complex:
        """
        Calculate portal field propagator with LV corrections.
        
        Parameters:
        -----------
        momentum : float
            4-momentum (GeV)
        energy : float
            Energy (GeV)
            
        Returns:
        --------
        complex
            Portal propagator
        """
        # LV-modified momentum dispersion
        lv_factor = self.lv_enhancement_factor(energy)
        effective_mass_squared = self.config.portal_mass**2 * lv_factor
        
        # Portal propagator
        denominator = energy**2 - momentum**2 - effective_mass_squared + 1j * 1e-6
        return 1.0 / denominator
    
    def dimensional_coupling_strength(self, energy: float) -> float:
        """
        Calculate energy-dependent dimensional coupling strength.
        
        Parameters:
        -----------
        energy : float
            Energy scale (GeV)
            
        Returns:
        --------
        float
            Effective dimensional coupling
        """
        # Base coupling with dimensional suppression
        base_coupling = self.config.coupling_strength
        dimensional_suppression = (energy * self.config.compactification_radius)**(-self.config.n_extra_dims/2)
        
        # LV enhancement
        lv_enhancement = self.lv_enhancement_factor(energy)
        
        return base_coupling * dimensional_suppression * lv_enhancement
    
    def energy_transfer_amplitude(self, energy: float, kk_modes: int = 10) -> complex:
        """
        Calculate energy transfer amplitude through portal.
        
        Parameters:
        -----------
        energy : float
            Transfer energy (GeV)
        kk_modes : int
            Number of KK modes to include
            
        Returns:
        --------
        complex
            Transfer amplitude
        """
        amplitude = 0.0j
        
        # Sum over KK modes
        for n in range(kk_modes):
            kk_energy = self.kaluza_klein_spectrum(n, energy)
            coupling = self.dimensional_coupling_strength(energy)
            
            # Portal-mediated amplitude
            momentum = np.sqrt(max(0, kk_energy**2 - self.config.portal_mass**2))
            propagator = self.portal_propagator(momentum, energy)
            
            # KK mode contribution
            mode_weight = np.exp(-n * self.config.compactification_radius * energy)
            amplitude += coupling * propagator * mode_weight
        
        return amplitude
    
    def energy_transfer_rate(self, energy: float) -> float:
        """
        Calculate energy transfer rate per unit volume.
        
        Parameters:
        -----------
        energy : float
            Energy scale (GeV)
            
        Returns:
        --------
        float
            Energy transfer rate (GeV^4)
        """
        if not self.is_pathway_active():
            return 0.0
        
        amplitude = self.energy_transfer_amplitude(energy)
        
        # Phase space factors
        phase_space = energy**2 / (8 * np.pi**2)
        
        # Kinetic mixing suppression
        kinetic_factor = self.config.kinetic_mixing**2
        
        # Brane tension enhancement
        brane_factor = self.config.brane_tension
        
        return kinetic_factor * phase_space * abs(amplitude)**2 * brane_factor
    
    def total_power_extraction(self, volume: float = 1.0) -> float:
        """
        Calculate total power extraction from hidden sector.
        
        Parameters:
        -----------
        volume : float
            Extraction volume (m^3)
            
        Returns:
        --------
        float
            Total power (Watts)
        """
        if not self.is_pathway_active():
            return 0.0
        
        def integrand(energy):
            return self.energy_transfer_rate(energy)
        
        # Integrate over energy range
        power_density, _ = integrate.quad(
            integrand, 
            self.config.energy_range[0], 
            self.config.energy_range[1],
            limit=100
        )
        
        # Convert to Watts (GeV^4 to Watts conversion)
        # 1 GeV^4 ≈ 1.6e-3 J/m^3/s
        conversion_factor = 1.6e-3
        
        return power_density * volume * conversion_factor
    
    def optimize_portal_parameters(self, target_power: float = 1e-6) -> Dict[str, float]:
        """
        Optimize portal parameters for target power extraction.
        
        Parameters:
        -----------
        target_power : float
            Target power extraction (Watts)
            
        Returns:
        --------
        Dict[str, float]
            Optimized parameters
        """
        def objective(params):
            coupling, mixing, radius = params
            
            # Update configuration
            old_coupling = self.config.coupling_strength
            old_mixing = self.config.kinetic_mixing
            old_radius = self.config.compactification_radius
            
            self.config.coupling_strength = coupling
            self.config.kinetic_mixing = mixing
            self.config.compactification_radius = radius
            
            # Calculate power
            power = self.total_power_extraction()
            
            # Restore configuration
            self.config.coupling_strength = old_coupling
            self.config.kinetic_mixing = old_mixing
            self.config.compactification_radius = old_radius
            
            return abs(power - target_power)
        
        # Optimization bounds
        bounds = [
            (1e-4, 1e-1),   # coupling_strength
            (1e-5, 1e-2),   # kinetic_mixing
            (1e-4, 1e-2)    # compactification_radius
        ]
        
        # Initial guess
        x0 = [self.config.coupling_strength, self.config.kinetic_mixing, 
              self.config.compactification_radius]
        
        # Optimize
        result = optimize.minimize(objective, x0, bounds=bounds, method='L-BFGS-B')
        
        return {
            'coupling_strength': result.x[0],
            'kinetic_mixing': result.x[1],
            'compactification_radius': result.x[2],
            'optimized_power': target_power,
            'success': result.success
        }
    
    def parameter_sensitivity_analysis(self) -> Dict[str, np.ndarray]:
        """
        Analyze sensitivity to LV parameters.
        
        Returns:
        --------
        Dict[str, np.ndarray]
            Sensitivity analysis results
        """
        # Parameter ranges
        mu_range = np.logspace(-20, -16, 20)
        alpha_range = np.logspace(-17, -13, 20)
        beta_range = np.logspace(-14, -10, 20)
        
        # Base power
        base_power = self.total_power_extraction()
        
        results = {
            'mu_range': mu_range,
            'alpha_range': alpha_range,
            'beta_range': beta_range,
            'mu_sensitivity': [],
            'alpha_sensitivity': [],
            'beta_sensitivity': []
        }
        
        # Mu sensitivity
        original_mu = self.config.mu_lv
        for mu in mu_range:
            self.config.mu_lv = mu
            power = self.total_power_extraction()
            results['mu_sensitivity'].append(power / base_power if base_power > 0 else power)
        self.config.mu_lv = original_mu
        
        # Alpha sensitivity
        original_alpha = self.config.alpha_lv
        for alpha in alpha_range:
            self.config.alpha_lv = alpha
            power = self.total_power_extraction()
            results['alpha_sensitivity'].append(power / base_power if base_power > 0 else power)
        self.config.alpha_lv = original_alpha
        
        # Beta sensitivity
        original_beta = self.config.beta_lv
        for beta in beta_range:
            self.config.beta_lv = beta
            power = self.total_power_extraction()
            results['beta_sensitivity'].append(power / base_power if base_power > 0 else power)
        self.config.beta_lv = original_beta
        
        return results
    
    def visualize_energy_spectrum(self, save_path: Optional[str] = None):
        """
        Visualize energy transfer spectrum and KK modes.
        
        Parameters:
        -----------
        save_path : Optional[str]
            Path to save the plot
        """
        fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(12, 10))
        
        # Energy transfer rate spectrum
        energies = np.linspace(self.config.energy_range[0], self.config.energy_range[1], 100)
        transfer_rates = [self.energy_transfer_rate(e) for e in energies]
        
        ax1.semilogy(energies, transfer_rates, 'b-', linewidth=2)
        ax1.set_xlabel('Energy (GeV)')
        ax1.set_ylabel('Transfer Rate (GeV⁴)')
        ax1.set_title('Energy Transfer Rate Spectrum')
        ax1.grid(True, alpha=0.3)
        
        # KK mode spectrum
        kk_modes = range(10)
        energy_test = 1.0
        kk_energies = [self.kaluza_klein_spectrum(n, energy_test) for n in kk_modes]
        
        ax2.plot(kk_modes, kk_energies, 'ro-', linewidth=2, markersize=6)
        ax2.set_xlabel('KK Mode Number')
        ax2.set_ylabel('Mode Energy (GeV)')
        ax2.set_title('Kaluza-Klein Spectrum')
        ax2.grid(True, alpha=0.3)
        
        # Dimensional coupling vs energy
        coupling_strengths = [self.dimensional_coupling_strength(e) for e in energies]
        
        ax3.loglog(energies, coupling_strengths, 'g-', linewidth=2)
        ax3.set_xlabel('Energy (GeV)')
        ax3.set_ylabel('Coupling Strength')
        ax3.set_title('Dimensional Coupling vs Energy')
        ax3.grid(True, alpha=0.3)
        
        # LV enhancement factor
        lv_factors = [self.lv_enhancement_factor(e) for e in energies]
        
        ax4.plot(energies, lv_factors, 'm-', linewidth=2)
        ax4.set_xlabel('Energy (GeV)')
        ax4.set_ylabel('LV Enhancement Factor')
        ax4.set_title('Lorentz Violation Enhancement')
        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[str, Union[float, bool, str]]:
        """
        Generate comprehensive analysis report.
        
        Returns:
        --------
        Dict[str, Union[float, bool, str]]
            Analysis report
        """
        report = {
            'pathway_active': self.is_pathway_active(),
            'total_power_extraction': self.total_power_extraction(),
            'lv_parameters': {
                'mu_lv': self.config.mu_lv,
                'alpha_lv': self.config.alpha_lv,
                'beta_lv': self.config.beta_lv
            },
            'experimental_bounds': self.experimental_bounds,
            'portal_configuration': {
                'n_extra_dims': self.config.n_extra_dims,
                'compactification_radius': self.config.compactification_radius,
                'kinetic_mixing': self.config.kinetic_mixing,
                'coupling_strength': self.config.coupling_strength
            },
            'enhancement_factor_1GeV': self.lv_enhancement_factor(1.0),
            'transfer_rate_1GeV': self.energy_transfer_rate(1.0),
            'dimensional_coupling_1GeV': self.dimensional_coupling_strength(1.0)
        }
        
        return report

def demo_hidden_sector_portal():
    """Demonstrate hidden sector portal functionality."""
    print("=== Hidden Sector Portal Demo ===")
    
    # Create configuration with LV parameters above bounds
    config = HiddenSectorConfig(
        mu_lv=1e-18,     # Above experimental bound
        alpha_lv=1e-15,  # Above experimental bound
        beta_lv=1e-12,   # Above experimental bound
        n_extra_dims=2,
        compactification_radius=1e-3,
        kinetic_mixing=1e-3,
        coupling_strength=1e-2
    )
    
    # Initialize portal
    portal = HiddenSectorPortal(config)
    
    # Generate report
    report = portal.generate_report()
    
    print(f"Pathway Active: {report['pathway_active']}")
    print(f"Total Power Extraction: {report['total_power_extraction']:.2e} W")
    print(f"LV Enhancement (1 GeV): {report['enhancement_factor_1GeV']:.3f}")
    print(f"Transfer Rate (1 GeV): {report['transfer_rate_1GeV']:.2e} GeV⁴")
    
    # Optimization
    print("\n=== Parameter Optimization ===")
    optimal = portal.optimize_portal_parameters(target_power=1e-6)
    print(f"Optimization Success: {optimal['success']}")
    print(f"Optimal Coupling: {optimal['coupling_strength']:.2e}")
    print(f"Optimal Mixing: {optimal['kinetic_mixing']:.2e}")
    print(f"Optimal Radius: {optimal['compactification_radius']:.2e}")
    
    # Sensitivity analysis
    print("\n=== Sensitivity Analysis ===")
    sensitivity = portal.parameter_sensitivity_analysis()
    print(f"Max μ sensitivity: {max(sensitivity['mu_sensitivity']):.3f}")
    print(f"Max α sensitivity: {max(sensitivity['alpha_sensitivity']):.3f}")
    print(f"Max β sensitivity: {max(sensitivity['beta_sensitivity']):.3f}")
    
    # Visualization
    print("\n=== Generating Visualization ===")
    portal.visualize_energy_spectrum('hidden_sector_portal_analysis.png')
    
    return portal, report

if __name__ == "__main__":
    demo_hidden_sector_portal()