Specific numerical method for time evolution of density matrices/wave vectors

[melkani...@gmail.com]

Hi,

I have been working on a problem involving the evolution of a density matrix using the Liouville-von Neumann equation and I recently realized that one cannot use conventional Euler's method or Runge-Kutta methods since they do not preserve the total probability amplitude. (Is that correct?). For example, see my question HERE at stack-exchange and the answer following. I have been told that what one needs to use are something called symplectic methods.

In that context, I wished to ask what specific numerical method does Qutip use for the time evolution of density matrices/wave vectors? So that I may use the same method for my problem. (The matrix I use is very large so that I cannot use Qutip directly).

I did try to find the answer in the references but I could not.

Thank you for your help.

[Paul Nation]

The norm is preserved up to numerical precision just from the form of the operators.  Explicit preservation does require symplectic methods.  You would need a dissipative integrator though.  We use an Adams-Bashforth.

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