Ssesolve/smesolve integration method

[Salvatore Di Lorenzo]

Hi everybody,

I'm a Master's student at Copenhagen University and I'm doing simulations of two particles on a Hubbard chain and with measurements on site occupation involved and I'm using ssesolve for that. I tried to simulate the same system but using a stochastic solver I built myself, and what I noticed is that, in order to reproduce the qutip results I need way bigger number of instants give a certain time. So if I put T=100, N_times=10000 with ssesolve, I need to do T=100, N_times = 500000 with my solver (otherwise I get weird stuff like the two particles getting on the same site despite a repulsive potential).

So I was wondering which numerical integration method does Qutip use to solve the Stocahstic Schrödinger/master equation. I've tried to read the documentation but it wasn't that easy and I found many references to other functions maybe defined elsewhere, that I don't know how to find.

[Éric Giguère]

Qutip has multiple SODE method available. 

They are listed at https://qutip.readthedocs.io/en/v5.1.1/apidoc/solver.html#stochastic-integrator

But most of them only support smesolve...

The default method for ssesolve is "platen",  "euler", "explicit1.5" and "rouchon" are also supported.

I am not sure what you mean by N_times, but if you created your tlist with `np.linspace(0, T, N_times)`, this N_times does not affect the step length of the solver.

The options `dt` controls it, the default is `0.001`. So you are probably using 100000 steps with qutip.

qutip.ssesolve(
    H, 

    psi_0, 

    tlist=np.linspace(0, 2, 11),
    sc_ops=sc_ops,

    e_ops=e_ops,
    options={"method": "rouchon", "dt": 0.0005},

    ntraj=1,
)

Hope this help