On Tue, Jun 28, 2011 at 5:20 PM, Adam Byrd <span dir="ltr"><<a href="mailto:adam1.byrd@gmail.com">adam1.byrd@gmail.com</a>></span> wrote:<div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Jack,<br><br>I'm a summer intern just getting started with this project, so I don't know all the details yet (I can ask though). I know I need to find the Green's function which will involve the trace of the inverted Hamiltonian, as well as the rest of the matrix. I have inquired about avoiding the inversion altogether, but my instructor doesn't believe there is a way around it. Once I've worked through the math I want to explore other options though.<br>
<br>Respectfully,<br><font color="#888888">Adam</font><div><div></div><div class="h5"> </div></div></blockquote><div><br></div><div>Ah, it's not a discretized Hamiltonian, not a Hamiltonian matrix (<a href="http://en.wikipedia.org/wiki/Hamiltonian_matrix">http://en.wikipedia.org/wiki/Hamiltonian_matrix</a>). For 2d problems, there is a nice approach for efficiently computing the trace of the inverse here: <a href="http://www.ma.utexas.edu/users/lexing/publications/siscpar.pdf">http://www.ma.utexas.edu/users/lexing/publications/siscpar.pdf</a>. For 3d problems it is more difficult and I'm not sure what the best approach is.</div>
<div><br></div><div>Jack</div></div>