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bio website stanford.edu/~justso1
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visits member for 1 year, 11 months
seen Oct 28 '12 at 23:31

I am a PhD student at Stanford University studying geometry processing and computer graphics.


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!
Oct
4
comment Mathematical probabilistic interepretation of probability amplitude
So the function $\psi$ somehow encodes position and velocity/momentum? I understand that they are different states, but am unclear on how to "read" the different states. What do we know about the particle at $x$ relative to the particle at $y$ if $\psi(x)=1$ and $\psi(y)=\frac{\sqrt{2}}{2}(1+i)$? Is there any mathematical explanation for what's going on?