[Trilinos-Users] Anasazi: Matrix exponential for time evolution ?

[David Hochstuhl]

Hello,

 

I have not only a single question but rather need a whole algorithm...lets start:

 

I am trying to propagate the Schrödinger equation in time,

i d/dt C = H(t) C

where H is a sparse matrix.

 

The initial state to this propagation was found by solving the time-independent Schrödinger equation

H C = E C

with Anasazi.

 

 

Ok, for the time evolution, I basically need to perform the following steps (or a combination of the two):

 

(i) Add a time-dependent pertubation D(t) to H,

     i.e. H(t) = H + D(t)

    (D is for instance the action of an electromagnetic field

 

(ii) For a given state C(t), apply the matrix exponential of -I*H(t) to obtain C(t+dt)

      C(t+dt) = exp(-I*H(t)*dt) C(t)

 

 

This can be done for instance with a simple implementation of the Lanczos algorithm, that people

usually call "short iterative Lanczos". However, the Anasazi solvers are of course much better than my

hand-written Lanczos agorithm. So, is there any way to perform the above procedure in an efficient way.

 

I thought about it yet, but I didn't find an efficient solution, and

before I start coding I wanted to hear what the trilinos cracks mean.

so, thanks in advance,

 

David

 

 

 
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