Hi,
I'm reading the paper "String method for the study of rare event":
http://math.nyu.edu/%7Eweiqing/papers/stoch_string.pdf
However, as I lack a lot of background in Physics, I'd like to ask you
some questions.
For the following simple dynamics model (which is also mentioned in the
paper on pg. 2):
\dot{q} = -\nabla V{q} + \xi(t),
where \xi(t) is the whitenoise. Then
1. Mathematically, what are metastable states? As I guessed, they are
critical points of the potential function but from the paper, it's
seemed that I was wrong.
2. Also mathematically, how do you define the minimal energy path? I
guessed that a reasonable measure for the path energy is the L_1 norm of
the potential function along that path. Again, I think that I was
incorrect too.
3. Is this path the most likely transition pathway (i.e. highest
density)? If so, would you please give me a reference which proves this?
Thanks
.
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