A return to observability near exceptional points in a schematic PT-symmetric model

Conditional observability versus self-duality in a schematic model

In a simple PT-symmetric model we demonstrate that and how the violation of a reflection symmetry $E_j=-E_{N+1-j}$ of the spectrum (called "self-duality" by Dunne and Shifman) is connected with the loss of the simplicity of the shape of the boundary of the domain D of parameters where the Hamiltonian H is quasi-Hermitian, i.e., where all the bound-state energies are real.

Multiply Degenerate Exceptional Points and Quantum Phase Transitions

The realization of a genuine phase transition in quantum mechanics requires that at least one of the Kato's exceptional-point parameters becomes real. A new family of finite-dimensional and time-parametrized quantum-lattice models with such a property is proposed and studied. All of them exhibit, at a real exceptional-point time $t=0$, the Jordan-block spectral degeneracy structure of some of their observables sampled by Hamiltonian $H(t)$ and site-position $Q(t)$. The passes through the critical instant $t=0$ are interpreted as schematic simulations of non-equivalent versions of the Big-Bang-…

Anomalous mechanisms of the loss of observability in non-Hermitian quantum models

Quantum phase transitions in certain non-Hermitian systems controlled by non-tridiagonal Hamiltonian matrices are found anomalous. In contrast to the known models with tridiagonal-matrix structure in which the geometric multiplicity of the completely degenerate energy eigenvalue appears always equal to one, this multiplicity is found larger than one in the present models. The phenomenon is interpreted as a confluence of several decoupled Kato's exceptional points of equal or different orders.

无源系统中非厄米效应可观测性的基本约束

Fundamental constraints on the observability of non-Hermitian effects in passive systems

本研究利用散射理论，基于因果律要求通过内部时延算符量化无源系统中非厄米效应可见度的约束，对比不同对称类与效应发现非厄米趋肤效应的极端模式非正交性被有效掩盖。

Quasi-hermitian lattices with imaginary zero-range interactions

We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models as special cases. We provide numerical results regarding domains of observability and exceptional points, and discuss the possibility of explicit construction of general metric operators (which in turn determine all the physical Hilbert spaces). The condition of computational simplicity for the metrics motivates the introduction of certain one-parametric sp…

三费米子Swanson-like模型中的三重例外点及其幺正展开路径

Triple exceptional point with unitary paths of unfolding in a three-site fermionic Swanson-like model

研究费米子三站点Swanson模型的精确可解五参数量子力学幺正演化过程，揭示其最终导致可观测性丧失并落入三重例外点（EP3）的机制，给出了简并点的显式单参数形式及其幺正相容邻域（即访问EP3的通道）的闭式表达。