Is it just me or it happens to you too: I have posted questions or answers here in the past, but now that I read them I have almost no idea what I was talking about!!
@0celo7 To get more background on what's happening in TW3? Probably TW2 has the highest density of relevant information. To learn how Geralt and Yen met, read the short stories, in particular The Last Wish. It's been a while since I've read the novels, but at least one of them should have more on Ciri
TW2 is also a very good game, just much shorter than TW3. Though one should play it twice, since the entire second act differs based on one decision :P
And I only care about the leading-order behavior, so a steepest-descent approximation is all I should need.
(the critical points can be determined in terms of the Lambert-W function, so numerically that's not a big deal)
Mostly I was trying to remember if the logic makes sense; it's been a while since I had to do steepest decent stuff beyond the trivial case ("everything with a narrow peak is Gaussian!")
I'm trying to understand how they work. Specifically, how can they have unidirectional edge modes while the whole structure seems to be reciprocal (no external magnetic field, etc.)
if you want to be able to handle $p<0$, your only hope is to relate it to a contour that comes in from $+\infty$ and then goes down through $\pm 2\pi i +\infty$
or actually
yeah, I know how to do it
come in from $+\infty$, then loop down and take the first valley on your left and go back to $-2\pi i +\infty$
so, that doesn't help you, but you can do it again
If $p$ is sufficiently negative, then all of the critical points are actually complex
The two on the real axis collide and move off axis.
So that complicates the picture a tad. But nothing major.
The main statement I wanted, though, was that if $p$ is negative, but small enough that there are two real critical points, then the contribution from that first saddle point is still the relevant one.
Which does seem to still be the case, so I'm happy with that.
@Semiclassical and actually, come to think of it, your integral isn't really that pathological, and it's actually, structurally, extremely close to the ones I use
@EmilioPisanty Just to give a sense of what I'm after: For $p>0$, it's enough to look at the original convergent integral along the real line and worry only about the real saddle.
(all three branches are purely real $x\in(-1/e,0)$, and the two branches have opposite imaginary parts for $x<-1/e$. So the green function is purely real.)
@0celo7 trying to figure out how to get it using University's subscription.
courtesy of scihub , I've never used it before as these APS supplemental materials are the only thing not supported by SciHub. (last time that I needed one, used my friend's account)
