Finite-temperature and dynamical observables for quantum systems with NumPy/JAX compatibility.

Thermal Physics (thermal.py)

• Partition functions, Boltzmann weights, free energy
• Heat capacity, susceptibilities, temperature scans
• Numerically stable evaluations of $Z(\beta)$ and thermal averages

Spectral Functions (spectral/)

• Green's functions: greens_function_quadratic, greens_function_manybody, greens_function_lanczos
• Spectral functions from Green's functions or eigenvalues
• Momentum-resolved spectral functions $A(k,\omega)$
• Density of states with Lorentzian/Gaussian broadening

Response Functions (response/)

• Dynamic structure factors $S(q,\omega)$
• Generalized susceptibilities $\chi(q,\omega)$
• Unified interface for many-body and mean-field systems

Entanglement (density_matrix.py, entropy.py)

• Reduced density matrices, Schmidt decompositions
• Von Neumann, Rényi, and participation entropies
• JAX-accelerated versions available

Single-Particle (sp/)

• Correlation matrices for quadratic Hamiltonians
• Slater determinant and BdG quasiparticle support

Utilities

• eigenlevels.py: Level statistics (spacing ratios, unfolding)
• statistical.py: Windowed averaging, binning, jackknife estimators
• operators.py: Operator parsing and selection

# Thermal properties
from general_python.physics import thermal
Z = thermal.partition_function(energies, beta=1.0)
C_V = thermal.heat_capacity(energies, beta=1.0)

# Spectral functions
from general_python.physics.spectral import spectral_function
A = spectral_function.spectral_function(omega=0.5, eigenvalues=E, eigenvectors=U, eta=0.01)

# Green's functions
from general_python.physics.spectral.spectral_backend import greens_function_quadratic
G = greens_function_quadratic(omega, eigenvalues, eigenvectors, eta=0.01)

# Response functions
from general_python.physics.response import unified_response
chi, method = unified_response.compute_response(E, V, operator, omega_grid)

physics/
├── backend.py              # Unified interface to spectral & thermal
├── thermal.py              # Temperature-dependent properties
├── spectral/               # Green's functions & spectral functions
│   ├── spectral_backend.py # Core implementations
│   ├── greens_function.py  # Green's function wrappers
│   ├── spectral_function.py# Spectral function wrappers
│   └── dos.py              # Density of states
├── response/               # Dynamic response functions
│   ├── unified_response.py # Auto-selecting response calculator
│   ├── structure_factor.py # Structure factors
│   └── susceptibility.py   # Susceptibilities
├── sp/                     # Single-particle correlations
├── density_matrix.py       # Density matrices
├── entropy.py              # Entanglement entropies
└── statistical.py          # Data analysis utilities

Thermal averages: $\langle O \rangle_\beta = Z^{-1} \sum_n O_{nn} e^{-\beta E_n}$

Green's function: $G(\omega) = [(\omega + i\eta)I - H]^{-1}$ or Lehmann representation

Spectral function: $A(\omega) = -\frac{1}{\pi} \mathrm{Im}, G(\omega)$

Susceptibility: $\chi(\omega) = \sum_{m,n} \frac{(\rho_m - \rho_n)}{E_n - E_m - \omega - i\eta} |\langle m|O|n\rangle|^2$

Structure factor: $S(q,\omega) = \sum_{m,n} \rho_n |\langle m|S_q|n\rangle|^2 \delta(\omega - (E_m - E_n))$

Copyright © 2025 Maksymilian Kliczkowski. All rights reserved.