Quantum Many

# Quantum Many-Body Theory Calculation Application

A comprehensive iOS application for physicists, materials scientists, and researchers working with quantum many-body theory calculations.

## Features

### 1. Keldysh Closed Time Path (CTP) Analysis
- Calculate evolution operators for non-equilibrium quantum systems
- Compute two-point correlation functions
- Analyze time-ordered, retarded, and advanced correlation functions
- Support for custom Hamiltonian and operator inputs

### 2. Non-Equilibrium Green's Functions
- Calculate lesser, greater, retarded, and advanced Green's functions
- Compute Keldysh Green's functions
- Fourier transform between time and frequency domains
- Visualize Green's functions in both time and frequency representations

### 3. Quantum Master Equation Solver
- Solve Lindblad master equation for open quantum systems
- Numerical integration using Runge-Kutta 4th order method
- Calculate density matrix evolution
- Compute purity and von Neumann entropy
- Support for multiple Lindblad operators

### 4. Fluctuation-Dissipation Theorem Verification
- Verify quantum fluctuation-dissipation relations
- Calculate response functions (susceptibility)
- Compute correlation function spectra
- Compare response and correlation functions according to FDT

### 5. Open Quantum System Analysis
- Study system-environment coupling effects
- Calculate decoherence time (T2)
- Calculate relaxation time (T1)
- Analyze quantum fidelity decay
- Compute entanglement evolution using concurrence