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[Docs] Update documentation for time evolution (qutip#241)
* update documentation for time evolution * separate `sesolve` and `mesolve` in docs
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# [Time Evolution and Quantum System Dynamics](@id doc:Time-Evolution-and-Quantum-System-Dynamics) | ||
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This page is still under construction, please visit [API](@ref doc-API) first. | ||
**Table of contents** | ||
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```@contents | ||
Pages = [ | ||
"intro.md", | ||
"solution.md", | ||
"sesolve.md", | ||
"mesolve.md", | ||
"mcsolve.md", | ||
"stochastic.md", | ||
"time_dependent.md", | ||
] | ||
Depth = 2:3 | ||
``` | ||
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## [Introduction](@id doc-TE:Introduction) | ||
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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. `QuantumToolbox` provides many ways to model dynamics. | ||
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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. | ||
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The following table lists the solvers provided by `QuantumToolbox` for dynamic quantum systems and the corresponding type of solution returned by the solver: | ||
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| **Equation** | **Function Call** | **Returned Solution** | | ||
|:-------------|:------------------|:----------------------| | ||
| Unitary evolution, Schrödinger equation | [`sesolve`](@ref) | [`TimeEvolutionSol`](@ref) | | ||
| Lindblad master eqn. or Von Neuman eqn. | [`mesolve`](@ref) | [`TimeEvolutionSol`](@ref) | | ||
| Monte Carlo evolution | [`mcsolve`](@ref) | [`TimeEvolutionMCSol`](@ref) | | ||
| Stochastic Schrödinger equation | [`ssesolve`](@ref) | [`TimeEvolutionSSESol`](@ref) | |
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# Time Evolution and Quantum System Dynamics | ||
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## [Monte-Carlo Solver](@id doc-TE:Monte-Carlo-Solver) | ||
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This page is still under construction, please visit [API](@ref doc-API) first. |
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# Time Evolution and Quantum System Dynamics | ||
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## [Lindblad Master Equation Solver](@id doc-TE:Lindblad-Master-Equation-Solver) | ||
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This page is still under construction, please visit [API](@ref doc-API) first. | ||
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### Von Neumann equation | ||
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### The Lindblad master equation |
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# Time Evolution and Quantum System Dynamics | ||
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## [Schrödinger Equation Solver](@id doc-TE:Schrödinger-Equation-Solver) | ||
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This page is still under construction, please visit [API](@ref doc-API) first. |
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# Time Evolution and Quantum System Dynamics | ||
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## [Time Evolution Solutions](@id doc-TE:Time-Evolution-Solutions) | ||
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This page is still under construction, please visit [API](@ref doc-API) first. | ||
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### Solution | ||
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### Multiple trajectories solution |
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# Time Evolution and Quantum System Dynamics | ||
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## [Stochastic Solver](@id doc-TE:Stochastic-Solver) | ||
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This page is still under construction, please visit [API](@ref doc-API) first. | ||
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### Stochastic Schrodinger equation |
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# Time Evolution and Quantum System Dynamics | ||
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## [Solving Problems with Time-dependent Hamiltonians](@id doc-TE:Solving-Problems-with-Time-dependent-Hamiltonians) | ||
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This page is still under construction, please visit [API](@ref doc-API) first. |