qutip solver issues

[Mohamed Ahmed Eltohfa]

I thought about this for a while and I cannot find where things go wrong. I am simulating the evolution one atom decaying with a collapse operator destroy(2), and the Hamiltonian is 0. The initial density operator is |e><g| which is, I think, a state that should decay with rate 1/2. However, when I simulate using mesolve, I get the same state at each time step. I feel this is wrong, but I cannot find the buy in my thinking or in qutip!

[Paul Menczel]

Hello,

I suspect the problem is that |e><g| is not a density operator. A density operator must always have trace one.

Perhaps you mean either the mixed state `(|e><e| + |g><g|) / 2` or the superposition state `(|e> + |g>)(<e| + <g|) / 2`?

Best regards,

Paul

[Mohamed Ahmed Eltohfa]

Thank you for you answer, Paul. I know that my state is not a valid density operator. But if QuTiP treats the master equation as a matrix differential equation with no constraints on the trace or positivity, then the state |e><g| is an eigenstate with eigenvalue -1/2 meaning it should decay to the zero matrix after a while. 

The reason I was evolving this density operator (which is not a strictly valid one) is related to calculating the time autocorrelation function of the electric field emitted during the decay of |e><e| state. In this case, I learned that I  should act by the sigma + on the right of the excited state, evolve the system, and then evaluate the expectation value of sigma - at each time step. This expectation value should be the time autocorrelation function.

[nwla...@gmail.com]

hi mohamed,

this sounds like an issue that has come up a few times in v5 with mesolve doing automatic normalization, see https://github.com/qutip/qutip/pull/2427

Try either mesolve(..., options={"normalize_output": False}), or use the latest version of qutip from github that includes the above PR, and see if it resolves the problem

[Mohamed Ahmed Eltohfa]

Thank you so much. I was about to write my own solver code to bypass this issue. That will save me a lot of time.