Perturbation theory near degenerate exceptional points

• URL: http://arxiv.org/abs/2008.00479v1
• Date: Sun, 2 Aug 2020 13:28:00 GMT
• Title: Perturbation theory near degenerate exceptional points
• Authors: Miloslav Znojil
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed. What is assumed is, firstly, that the perturbed Hamiltonians $H=H_0+\lambda V$ are non-Hermitian and lie close to their unobservable exceptional-point (EP) degeneracy limit $H_0$. Secondly, in this EP limit, the geometric multiplicity $L$ of the degenerate unperturbed eigenvalue $E_0$ is assumed, in contrast to the majority of existing studies, larger than one. Under these assumptions the method of construction of the bound states is described. Its specific subtleties are illustrated via the leading-order recipe. 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 singularity is given a detailed explanation.

Related papers

• Sample-Efficient Constrained Reinforcement Learning with General Parameterization [35.22742439337603]
  We consider a constrained Markov Decision Problem (CMDP) where the goal of an agent is to maximize the expected discounted sum of rewards over an infinite horizon. We develop the Primal-Dual Accelerated Natural Policy Gradient (PD-ANPG) algorithm that ensures an $epsilon$ global optimality gap and $epsilon$ constraint violation.
  arXiv  Detail & Related papers  (2024-05-17T08:39:05Z)
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors [7.371841894852217]
  Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena. We introduce an interesting quantity (denoted as $eta$) as a new variant of the Petermann factor to measure non-unitarity.
  arXiv  Detail & Related papers  (2022-08-31T16:24:03Z)
• Realizing exceptional points of any order in the presence of symmetry [0.0]
  Exceptional points(EPs) appear as degeneracies in the spectrum of non-Hermitian matrices. In general, an EP of order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed. For two-, three- and four-band systems, we explicitly present the constraints needed for the occurrence of EPs in terms of system parameters.
  arXiv  Detail & Related papers  (2022-02-14T19:55:34Z)
• 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)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• $\PT$ 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)
• Scattering data and bound states of a squeezed double-layer structure [77.34726150561087]
  A structure composed of two parallel homogeneous layers is studied in the limit as their widths $l_j$ and $l_j$, and the distance between them $r$ shrinks to zero simultaneously. The existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac's delta function. The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.
  arXiv  Detail & Related papers  (2020-11-23T14:40:27Z)
• Non-Hermitian N-state degeneracies: unitary realizations via antisymmetric anharmonicities [0.0]
  degeneracy of an $N-$plet of bound states is studied in the framework of quantum theory of closed (i.e., unitary) systems. For an underlying Hamiltonian $H=H(lambda)$ the degeneracy occurs at a Kato's exceptional point.
  arXiv  Detail & Related papers  (2020-10-28T14:41:52Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)

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.