8 problems

Calogero–Sutherland mapping conjecture. The spectral statistics of critical PLBRM with large $b$ can be mapped onto those of the Calogero–Sutherland model at low temperature

Let a critical power-law banded random matrix (PLBRM) have variance parameter $b$ in the regime of large $b$. The spectral statistics of the PLBRM are compared with those of fermio…

Consider the higher cumulants, of order greater than two, of the particle number in a macroscopic interval for interacting fermion models with general interaction parameter $\beta$…

Let $\beta$ be the interaction parameter, and let $c_\beta$ be a beta-dependent constant. The number variance is considered for interacting fermions in a harmonic potential, includ…

Let $|P\rangle_{\vec{\lambda}}$ be an AFLT basis state, where $\vec{\lambda}=(\lambda_1,\lambda_2)$, and let $\mathbf{H}_z$ be a generic quantum BO$_2$ Hamiltonian whose eigenvalue…

Let ${\mathcal F}$ be the Hilbert space of states, and let $\psi^{N,M}_{Q,\mathbf n}$ denote the states defined in the paper for $N,M\in\mathbb{N}_0$, $Q\in\mathbb{Z}$, and…

Let $\kappa=\beta/2$ be the parameter relating the quantum Calogero–Sutherland–Moser system to the Dyson index. The classical ILW governing system is the classical system discussed…

Let $N$ and $M$ be even, and let $\boldsymbol{\theta}$ and $\boldsymbol{\theta}'$ denote the two sets of conformal-block labels whose associated Calogero–Sutherland eigenstates are…