Justin Solomon
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 Sep 24 awarded Autobiographer Oct 28 comment Simulating quantum network of harmonic oscillators Unfortunately, this is our setup for better or for worse! Oct 27 comment Simulating quantum network of harmonic oscillators Ah yes, I am restricting them to be on a manifold. Since I'm doing simulation, the manifold is a triangulated surface, and I can write down its Laplacian operator if that's useful. Oct 26 comment Simulating quantum network of harmonic oscillators In the end I'll actually be doing this computation on a manifold rather than $\mathbb{R}^n$, so zero-length springs are alright. But, such factorizations won't be possible. Are there more generic tricks? Oct 25 asked Simulating quantum network of harmonic oscillators Oct 11 comment Similarity of probability amplitude functions Interesting -- I'll take a look, this seems like the type of physics I might be able to follow :-) Oct 11 awarded Commentator Oct 11 comment Diffusion of probability amplitudes I'll actually be taking $\Sigma$ to be a surface (consider a sphere, and writing $\psi$ in the basis of spherical harmonics). But as a math guy I can translate into this case -- an example with $\Sigma\subseteq\mathbb{R}^n$ is perfectly fine. I'm using $\Delta_\Sigma$ to denote the Laplacian associated with domain $\Sigma$ -- e.g. on $\mathbb{R}^n$ it would be $\Delta=\sum_i\frac{\partial^2}{\partial x_i^2}$. Oct 11 comment Diffusion of probability amplitudes Thanks -- I'll take a look in Liouville mechanics. In my application I'm actually working with objects that look like probability amplitudes $\psi$, so I'm hoping to find analogs from QM that can help me. In particular, I'm hoping rather than switching to doing all my math on $\rho$ to be able to do math on $\psi$ in a way that has the intended effect (in this case diffusion) on $\rho$. Does this make sense? Oct 10 comment Diffusion of probability amplitudes Yes, this property is of interest, although I'm hoping to find something closer to diffusion of probability values. Oct 9 asked Diffusion of probability amplitudes Oct 9 awarded Scholar Oct 9 comment Similarity of probability amplitude functions Ah, I think this is exactly what I need! BTW, this document appeals nicely to us math folks: physik.uni-leipzig.de/~uhlmann/PDF/UC07.pdf Oct 9 accepted Similarity of probability amplitude functions Oct 9 accepted Mathematical probabilistic interepretation of probability amplitude Oct 9 awarded Supporter Oct 7 comment Similarity of probability amplitude functions Both of the answers below provide useful metrics. Is there a metric that -- like the Wasserstein metric -- uses underlying distances on the space? Oct 6 asked Similarity of probability amplitude functions Oct 5 comment Mathematical probabilistic interepretation of probability amplitude Interesting! This makes it quite hard for us applied math types to evaluate whether it's useful for our own research :-) . I wonder if there's anyone who provides an introduction to quantum physics purely probablistically, sort of in the spirit of this document: scottaaronson.com/democritus/lec9.html Oct 4 comment Mathematical probabilistic interepretation of probability amplitude Thanks for posting the link to your book -- it looks closer to a language I might be able to speak, so I have downloaded it and will be taking a look on a flight later today!