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15 votes
1 answer
1k views

Borel-Écalle re-summation and resurgence: criteria and results

This is about the theory of Borel-Écalle re-summation and resurgence, see Refs below. This states that the perturbative series (say of the vacuum expectation value of an operator $\mathcal{O}$ in ...
wonderich's user avatar
  • 10.5k
12 votes
1 answer
735 views

Parametrisations for null temperature functions: nonuniqueness of solutions to the heat equation

Disclaimer. I expect this is a highly open problem, but maybe I'm wrong and someone has come up with some answers besides those given here. In any case, all information appreciated, thanks! Definition....
Zen Harper's user avatar
  • 1,990
4 votes
3 answers
464 views

What classes of functions are closed under all rescalings?

Let us denote by the symbol $\mathcal{G}$, a group of functions $f: \mathbb{R} \rightarrow \mathbb{R}$ (with the composition operation) that is additionally closed under all affine change of variables ...
Euplio M.'s user avatar
3 votes
1 answer
226 views

Analytic continuation of instantaneous eigenstates of a time-dependent hamiltonian

We are considering the instantaneous eigenstates of an analytically time-dependent hamiltonian and I would like to know how legitimate it is to extend them to the complex plane. Specifically, our ...
Emilio Pisanty's user avatar
3 votes
0 answers
235 views

Chern number of projection-Topological magic in physics

I enclosed a computation from a well-known paper in the field of mathematical physics where the Chern number of the first Landau level is computed (the result claimed is $-1$) and the full paper can ...
Ben Curnow's user avatar
1 vote
1 answer
195 views

System of quadratic complex equations

I want to solve this system of N non-linear equations without using a numerical method: $x_{k}^{2}= \alpha_{k }+ \sum\limits_{m=1}^{N} (\beta_{km} x_{m} + \psi_{km} x_{m}^{*})$ With $\left| x_{k}-...
A13j0's user avatar
  • 13