Add support for time-dependent Hamiltonians

SciML / DifferentialEquations.jl

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.

https://docs.sciml.ai/DiffEqDocs/stable/

Other

2.84k stars 224 forks source link

Add support for time-dependent Hamiltonians #384

Open homocomputeris opened 5 years ago

homocomputeris commented 5 years ago

Follows from #380.

If split and 2nd-order time-dependent problems can be solved, then problems with corresponding time-dependent Hamiltoninans can be solved too.

Some useful references:

The general approach is described in Time-Average on the Numerical Integration of Nonautonomous Differential Equations (preprint).
An example of Splitting methods for non-autonomous linear systems

ChrisRackauckas commented 5 years ago

This could make a good GSoC project.

joeyli99 commented 5 years ago

I meet a same question. I was wondering if there is any progress?

ChrisRackauckas commented 5 years ago

For second order methods, our current state is the form

http://docs.juliadiffeq.org/latest/types/dynamical_types.html http://docs.juliadiffeq.org/latest/solvers/dynamical_solve.html

The solvers technically let you give it a t argument, so you can define a partitioned ODE from a time-dependent Hamtiltonian. We also have https://github.com/JuliaDiffEq/ExponentialUtilities.jl for doing fast matrix exponentials. So we are just about there.