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

• PauliLindbladOpenSystem
• BosonLindbladOpenSystem
• FermionLindbladOpenSystem
• MixedLindbladOpenSystem

For examples showing how to use PauliLindbladOpenSystems, please see the the spins section. For examples showing how to use FermionLindbladOpenSystems, please see the the fermions section. For examples showing how to use BosonLindbladOpenSystems, please see the the bosons section. For examples showing how to use MixedLindbladOpenSystems, please see the the mixed system section.