Questions tagged [master-equation]

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QuTiP VS RK45: Which one gives the correct results for time-dependent systems?

I am writing a code for a quantum thermal machine which includes both coherent and dissipative time evolutions in its different stages of operation. However, evolving the system with "mesolve&...
3
votes
1answer
38 views

Show that if the Lindblad satisfy $\sum_\mu L_\mu L_\mu^\dagger=\sum_\mu L_\mu^\dagger L_\mu$ then $\rho\propto I$ is a fixed point of an evolution

How can we show that the Lindblad condition: $$\sum_{\mu}L_{\mu} L_{\mu}^{\dagger} = \sum_{\mu} L_{\mu}^{\dagger}L_{\mu},\tag{1}$$ implies that $\rho \propto I$ is the fixed point of the evolution ...
2
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1answer
35 views

How to solve non-"cross-damping off" Linblad equation in QuTiP?

As I understand from the official QuTiP guidlines, it is only capable of solving "cross-damping off" Master Equation in form: $\dot{\rho(t)} = -\dfrac{i}{\hbar}[H(t),\rho(t)] + \sum\limits_n\...
5
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1answer
64 views

What does "generator" mean in the master equation?

I seem to read a lot of times that some materials called this $\mathcal{L}$ in the equation(Lindblad master equation) below as the generator: $$ \mathcal{L} \rho=-i[H, \rho]+\sum_{\alpha}\left(V_{\...
3
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1answer
303 views

What is "Lindblad Superoperator" in Stochastic Master Equation

I was reading a paper titled "Using a Recurrent Neural Network to Reconstruct Quantum Dynamics of a Superconducting Qubit from Physical Observations" and was confused about a stochastic master ...
2
votes
1answer
110 views

How to formulate the master equation for three systems?

I have a three composite system of the form $H_{\text{tot}}=H_{ab}\otimes H_c$ where the system $C$ is behaving as the dissipator or the environment (I can model it as a thermal bath). And it is ...