Generalized classical and quantum Zernike Hamiltonians

• URL: http://arxiv.org/abs/2511.09541v1
• Date: Thu, 13 Nov 2025 02:01:20 GMT
• Title: Generalized classical and quantum Zernike Hamiltonians
• Authors: Francisco J. Herranz, Alfonso Blasco, Rutwig Campoamor-Stursberg, Ivan Gutierrez-Sagredo, Danilo Latini, Ian Marquette,
• Abstract summary: A superintegrable generalization of the classical and quantum Zernike systems is reviewed.<n>The corresponding Hamiltonians are endowed with higher-order integrals.<n>For the quantum system, the symmetry algebra and the spectra are provided for a representative case.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A superintegrable generalization of the classical and quantum Zernike systems is reviewed. The corresponding Hamiltonians are endowed with higher-order integrals and can be interpreted as higher-order superintegrable perturbations of the 2D spherical (Higgs), hyperbolic, and Euclidean harmonic oscillators. As a new result, the complete polynomial Higgs-type symmetry algebra of the generalized classical system is presented. For the generalized quantum system, the symmetry algebra and the spectra are provided for a representative case.

Related papers

• Spectrum-generating algebra and intertwiners of the resonant Pais-Uhlenbeck oscillator [0.0]
  We study the quantum Pais-Uhlenbeck oscillator at the resonant (equal-frequency) point.<n>We show that quantising a classically equivalent Hamiltonian yields a radically different quantum theory.
  arXiv  Detail & Related papers  (2026-01-28T16:33:29Z)
• The deep Hilbert space of all-to-all interacting SU(3) atoms: from quantum to classical [45.94400632660844]
  We study the emergence of chaos in multilevel atoms with all-to-all interactions, inspired by cavity QED.<n>Our work contributes to the study of the quantum-classical correspondence in chaotic systems, and uncovers a rich structure in multilevel all-to-all interacting models.
  arXiv  Detail & Related papers  (2025-12-04T19:00:01Z)
• Path integral approach to quantum thermalization [39.25860941747971]
  We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems.<n>We show that it is capable of describing a wide range of system classes and disorder models.<n>We present our formalism in a self-contained and pedagogical manner, aiming to provide a transferable toolbox for the first-principles description of many-body chaotic quantum systems.
  arXiv  Detail & Related papers  (2025-09-07T12:10:48Z)
• Isospectrality and non-locality of generalized Dirac combs [41.94295877935867]
  We consider a generalization of Dirac's comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions.<n>We classify a large class of isospectral relations, determining which Hamiltonians are spectrally unique, and which are instead related by a unitary or anti-unitary transformation.
  arXiv  Detail & Related papers  (2025-05-23T13:58:50Z)
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos [44.99833362998488]
  We develop an analytical approach to the spectral form factor and out-of-time ordered correlators in zero-dimensional Brownian models of quantum chaos.
  arXiv  Detail & Related papers  (2024-10-21T10:56:49Z)
• Quantum Chaos on Edge [36.136619420474766]
  We identify two different classes: the near edge physics of sparse'' and the near edge of dense'' chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension. While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different.
  arXiv  Detail & Related papers  (2024-03-20T11:31:51Z)
• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders [9.617349193925188]
  Entanglement constitutes one of the key concepts in quantum mechanics and serves as an indispensable tool in the understanding of quantum many-body systems. We perform extensive numerical investigations of extensive entanglement properties of coupled quantum spin chains.
  arXiv  Detail & Related papers  (2023-11-03T04:06:20Z)
• Canonical typicality under general quantum channels [39.58317527488534]
  In the present work we employ quantum channels to define generalized subsystems. We show that generalized subsystems also display the phenomena of canonical typicality. In particular we demonstrate that the property regulating the emergence of the canonical typicality behavior is the entropy of the channel used to define the generalized subsystem.
  arXiv  Detail & Related papers  (2023-08-30T21:29:45Z)
• Hybrid quantum-classical systems: Quasi-free Markovian dynamics [0.0]
  In the case of a quantum-classical hybrid system, the problem of characterizing the most general dynamical semigroup is solved under the restriction of being quasi-free. We show how to extract multi-time probabilities and how to connect them to the quantum notions of positive operator valued measure and instrument. A concrete example is given, showing how a classical component can input noise into a quantum one and how the classical system can extract information on the behaviour of the quantum one.
  arXiv  Detail & Related papers  (2023-07-05T19:26:09Z)
• Motivating semiclassical gravity: a classical-quantum approximation for bipartite quantum systems [0.0]
  We derive a "classical-quantum" approximation scheme for a broad class of bipartite quantum systems. In this approximation, one subsystem evolves via classical equations of motion with quantum corrections, and the other subsystem evolves quantum mechanically.
  arXiv  Detail & Related papers  (2023-06-01T18:05:33Z)
• Hybrid quantum-classical dynamics of pure-dephasing systems [0.0]
  We consider the interaction dynamics of a classical oscillator and a quantum two-level system for different pure-dephasing Hamiltonians of the type $widehatH(q,p)=H_C(q,p)boldsymbol1+H_I(q,p)widehatsigma_z$.
  arXiv  Detail & Related papers  (2023-03-08T12:22:00Z)
• Symmetry classification of typical quantum entanglement [10.698681396351494]
  Entanglement entropy of typical quantum states, also known as the Page curve, plays an important role in quantum many-body systems and quantum gravity. Our work elucidates the interplay of symmetry and entanglement in quantum physics and provides characterization of symmetry-enriched quantum chaos.
  arXiv  Detail & Related papers  (2023-01-18T20:41:32Z)
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states [11.04121146441257]
  We prove that the entanglement entropy of any pure initial state of a bosonic quantum system grows linearly in time. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems.
  arXiv  Detail & Related papers  (2021-07-23T07:55:38Z)
• The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems [5.524804393257921]
  We prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. We apply our result to prove new entropic uncertainty relations with quantum memory, a generalization of the quantum Entropy Power Inequality, and the linear time scaling of the entanglement entropy produced by quadratic Hamiltonians.
  arXiv  Detail & Related papers  (2021-05-12T12:52:40Z)
• On the classical and quantum dynamics of a class of nonpolynomial oscillators [0.0]
  We consider two one dimensional nonlinear oscillators, namely (i) Higgs oscillator and (ii) a $k$-dependent nonpolynomial rational potential. We observe that the quantum version of the Higgs oscillator is exactly solvable under appropriate restrictions of the ordering parameters. The three dimensional generalization of the quantum counterpart of the $k$-dependent nonpolynomial potential is found out to be quasi exactly solvable.
  arXiv  Detail & Related papers  (2020-08-17T07:52:37Z)

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.