18 problems

A $CPT$-symmetric field theory is a field theory invariant under the combined action of charge conjugation, parity, and time reversal. A field theory is non-Hermitian when its Hami…

A Hamiltonian is assumed to possess ${\cal PCT}$ symmetry, and this symmetry is said to be spontaneously broken when the Hamiltonian's eigenstates do not respect it. Reality-and-po…

For a single-band one-dimensional model, let the generalized Brillouin zone (GBZ) be the collection of complex numbers $z_p(E)$ and $z_{p+1}(E)$ satisfying $|z_p(E)|=|z_{p+1}(E)|$,…

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

Continuity conjecture. The Clifford linear gap function is pointwise continuous.

Let an open quantum system, particularly one governed by a non-Hermitian Hamiltonian, be considered in a regime analogous to a non-chaotic or integrable regime. Conjecture on non-c…

Critical-skin-effect Amoeba-limit conjecture.

Union conjecture. The Amoeba spectrum represents the union of the non-Bloch spectra for all possible lattice geometries.

Amoeba spectral conjecture. The energy spectra for any lattice geometry in the TDL should be given by the spectra from the Amoeba formulation.

Universality conjecture. These observed features occur universally in the spontaneously broken ${\cal PT}$-regimes of non-Hermitian systems: the signs of the heat supply or removal…

Prosen's conjecture. The total number of proper eigenstates of $\hat{\mathcal{M}}_{\ell,m}$ is equal to the dimension of $\mathcal{V}_{\ell,m}^r$.

Superintegrable models are obtained from reductions of free particles in higher-dimensional spaces. Reduction conjecture. This reduction principle also holds for non-Hermitian Hami…

A non-Hermitian system is purely dissipative when all eigenvalues of its Bloch Hamiltonian lie in the lower complex plane. Purely dissipative-system conjecture. Purely dissipative…

Exponent-pattern conjecture. The powers $\gamma^{K_n}$ entering $\Theta^{(N)}_{i,j}(\gamma)$ should obey the empirical rules

For given $L$ and $M$, let $P$, with $P\leq M$, be the number of $\alpha$-independent roots within a set of $M$ roots, and let $n(L,M,P)$ denote the number of non-spurious solution…

The Lieb–Liniger model is considered with a complexified coupling parameter $g$. Encircling an exceptional point can permute eigenenergies and eigenspaces, producing anholonomy in…

In a quantum model, let $H$ be a non-Hermitian ${\cal PT}$-symmetric Hamiltonian, where ${\cal P}$ denotes parity and ${\cal T}$ denotes complex conjugation, mimicking time reversa…

Let $\mathcal{L}_{\varepsilon,q}$ denote the newly proposed affine Toda field theory Lagrangians obtained by taking the simple roots $\alpha_i$ in the antilinearly invariant root s…