Introduction

Although in some cases, we want to find the stationary states of a quantum system, often we are interested in the dynamics: how the state of a system or an ensemble of systems evolves with time. QuTiP provides many ways to model dynamics.

There are two kinds of quantum systems: open systems that interact with a larger environment and closed systems that do not. In a closed system, the state can be described by a state vector. When we are modeling an open system, or an ensemble of systems, the use of the density matrix is mandatory.

The following table lists of the solvers QuTiP provides for dynamic quantum systems and indicates the type of object returned by the solver:

QuTiP Solvers

Equation	Function	Class	Returns
Unitary evolution, Schrödinger equation.	sesolve	SESolver	Result
Periodic Schrödinger equation.	fsesolve	None	Result
Schrödinger equation using Krylov method	krylovsolve	None	Result
Lindblad master eqn. or Von Neuman eqn.	mesolve	MESolver	Result
Monte Carlo evolution	mcsolve	MCSolver	McResult
Non-Markovian Monte Carlo	nm_mcsolve	NonMarkovianMCSolver	NmmcResult
Bloch-Redfield master equation	brmesolve	BRSolver	Result
Floquet-Markov master equation	fmmesolve	FMESolver	FloquetResult
Stochastic Schrödinger equation	ssesolve	SSESolver	MultiTrajResult
Stochastic master equation	smesolve	SMESolver	MultiTrajResult
Transfer Tensor Method time-evolution	ttmsolve	None	Result
Hierarchical Equations of Motion evolution	heomsolve	HEOMSolver	HEOMResult