Open Systems
Open systems represent a full system and environment. Mathematically, this means that a LindbladOpenSystem represents the entire Lindblad equation. The Lindblad equation is a master equation determining the time evolution of the density matrix: \[ \dot{\rho} = \mathcal{L}(\rho) =-i [\hat{H}, \rho] + \sum_{j,k} \Gamma_{j,k} \left( L_{j}\rho L_{k}^{\dagger} - \frac{1}{2} \{ L_k^{\dagger} L_j, \rho \} \right) \] with the Hamiltonian of the system \(\hat{H}\), the rate matrix \(\Gamma_{j,k}\), and the Lindblad operator \(L_{j}\).
Each LindbladOpenSystem is therefore composed of a HamiltonianSystem: \[ -i [\hat{H}, \rho] \]
and a LindbladNoiseSystem: \[ \sum_{j,k} \Gamma_{j,k} \left( L_{j} \rho L_{k}^{\dagger} - \frac{1}{2} \{ L_k^{\dagger} L_j, \rho\} \right) \]
The open systems in struqture are
SpinLindbladOpenSystemBosonLindbladOpenSystemFermionLindbladOpenSystemMixedLindbladOpenSystem