4 problems

Approximate joint-eigenstate conjecture. If $(\bm{\lambda},\nu)\in\bar{\Lambda}_{\epsilon}^{\mathrm{C}}(\bm{A},B)$, then there is a unit state $\bm{\psi}$ such that

Let $n$ be the matrix size and let $m\leq n$ be the model parameter, with fixed parameters $\delta$ and $a$. Spectral scaling conjecture. For both model 1 and model 2, when $n$ and…

Let $n$ be the matrix size, let $m\geq 1$ be fixed, and let $S_{\delta J}^{(1)}(m)$ denote model 1. Let $\lambda_0$ be the distinguished point included in the pseudospectrum, and l…

Let $S_{\delta J}^{(2)}(m)$ denote the model 2 matrix, with matrix size $n$, parameters $\delta$ and $a$, and let $\lambda_0$ be the distinguished eigenvalue of the original system…