Asymptotic non-Hermitian degeneracy phenomenon and its exactly solvable simulation

• URL: http://arxiv.org/abs/2603.13141v1
• Date: Fri, 13 Mar 2026 16:30:09 GMT
• Title: Asymptotic non-Hermitian degeneracy phenomenon and its exactly solvable simulation
• Abstract summary: We explain why there is no reasonable small-perturbation-based regularization of the similar unacceptable quantum models.<n>The explanation is based on a partial formal analogy of the IEP singularity with the conventional exceptional point (EP)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Up to these days, the popular PT-symmetric imaginary cubic oscillator did not find any consistent probabilistic quantum-mechanical interpretation because its Hamiltonian has been shown, by mathematicians, intrinsic-exceptional-point (IEP) singular. In the paper we explain why there is even no reasonable small-perturbation-based regularization of the similar unacceptable (i.e., IEP-singular) quantum models. The explanation is based on a partial formal analogy of the IEP singularity with the conventional exceptional point (EP). What is important is that we are able to construct a simplified $N$ by $N$-matrix (and exactly solvable) toy-model Hamiltonian admitting the asymptotic (i.e., high-excitation) EP-related wave-function degeneracy which, in some sense (i.e., in the limit of large $N$) mimics several aspects of its IEP analogue. In this comparison, the difference is that the regularization of the EP singularities is possible (using an ad hoc perturbation of size ${\cal O}(1/N)$) while an analogous regularization of the IEP singularity is not (we have to consider $N \to \infty$).

Related papers

• Typical entanglement in anyon chains: Page curves beyond Lie group symmetries [41.99844472131922]
  We study bipartite entanglement statistics in one-dimensional anyon chains constrained by fusion rules of unitary pre-modular categories.<n>Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(sqrtL)$ or $O(1)$ symmetry-type corrections.<n> Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions.
  arXiv  Detail & Related papers  (2026-03-26T18:00:03Z)
• Theory for the spectral splitting exponent of exceptional points [0.2578242050187029]
  We develop a theory to directly predict the scaling exponent from the matrix positions of the perturbation.<n>Our framework provides a useful design principle for engineering perturbations to achieve a desired spectral response.
  arXiv  Detail & Related papers  (2025-09-02T10:32:07Z)
• Unveiling the Self-Orthogonality at Exceptional Points in Driven $\mathcal{PT}$-Symmetric Systems [79.16635054977068]
  We explore the effect of self-orthogonality at exceptional points (EPs) in non-Hermitian Parity-Time-symmetric systems.<n>Using a driven three-band lattice model, we show that the Rabi frequency diverges as the system approaches an EP due to the coalescence of eigenstates.
  arXiv  Detail & Related papers  (2025-07-14T12:53:10Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• Intrinsic exceptional point -- a challenge in quantum theory [0.0]
  In spite of its unbroken $cal PT-$symmetry, the popular imaginary cubic oscillator Hamiltonian $H(IC)=p2+rm ix3$ does not satisfy all of the necessary postulates of quantum mechanics.<n>The failure is due to the intrinsic exceptional point'' (IEP) features of $H(IC)$ and, in particular, to the phenomenon of a high-energy parallelization of its bound-state-mimicking eigenvectors.
  arXiv  Detail & Related papers  (2024-11-19T13:40:30Z)
• Quantifying non-Hermiticity using single- and many-particle quantum properties [20.37811669228711]
  The non-Hermitian paradigm of quantum systems displays salient features drastically different from Hermitian counterparts.<n>We propose a formalism that quantifies the (dis-)similarity of these right and left ensembles, for single- as well as many-particle quantum properties.<n>Our findings can be instrumental in unveiling new exotic quantum phases of non-Hermitian quantum many-body systems.
  arXiv  Detail & Related papers  (2024-06-19T13:04:47Z)
• Geometric relative entropies and barycentric Rényi divergences [16.385815610837167]
  monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure. We show that monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
  arXiv  Detail & Related papers  (2022-07-28T17:58:59Z)
• Confluences of exceptional points and a systematic classification of quantum catastrophes [0.0]
  Specific quantum phase transitions of our interest are assumed associated with the fall of a closed, unitary quantum system into its exceptional-point (EP) singularity. The physical realization of such a "quantum catastrophe" (connected, typically, with an instantaneous loss of the diagonalizability of the corresponding parameter-dependent Hamiltonian $H(g)$) depends, naturally, on the formal mathematical characteristics of the EP. We illustrate and discuss, using several solvable toy models, some of the most elementary mechanisms of the EP-merger realization of the process of the transition $g to g(EP)$
  arXiv  Detail & Related papers  (2022-02-05T13:41:08Z)
• On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation [62.997667081978825]
  Incompatibility (AI) is a measure which quantifies the difference between the Holevo and the SLD scalar bounds. We show that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than $mu_sf min = 1/(d-1)$.
  arXiv  Detail & Related papers  (2021-07-28T15:16:37Z)
• $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
  Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
  arXiv  Detail & Related papers  (2021-03-27T09:46:36Z)
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies [0.0]
  A family of phase transitions in closed and open quantum systems is known to be mediated by a non-Hermitian degeneracy. In our paper the EP-mediated quantum phase transitions with $K>1$ are called "clustered" For the sake of maximal simplicity our attention is restricted to the real-harmonic-oscillator-type N by N matrix Hamiltonians.
  arXiv  Detail & Related papers  (2021-02-24T13:17:55Z)
• Perturbation theory near degenerate exceptional points [0.0]
  The Hamiltonians $H=H_0+lambda V$ are non-Hermitian and lie close to their unobservable exceptional-point (EP) degeneracy limit. The method of construction of the bound states is described. The emergence of a counterintuitive connection between the value of $L$, the structure of the matrix elements of perturbations, and the possible loss of the stability and unitarity of the processes of the unfolding of the EP is given a detailed explanation.
  arXiv  Detail & Related papers  (2020-08-02T13:28:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.