Propagators of singular anharmonic oscillators with quasi-equidistant spectra
- URL: http://arxiv.org/abs/2512.16695v1
- Date: Thu, 18 Dec 2025 16:00:00 GMT
- Title: Propagators of singular anharmonic oscillators with quasi-equidistant spectra
- Authors: Andrey M. Pupasov-Maksimov, Marcelo Silva Oliveira,
- Abstract summary: Two-well and three-well families of potentials and the corresponding propagators are presented.<n>Axially symmetric magnetic field configurations corresponding to these potentials have been identified.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Darboux transformations of the singular harmonic oscillator are considered. Analytical expressions for the propagators are obtained, using the image method applied to formal singular propagators. Two-well and three-well families of potentials and the corresponding propagators are presented. Axially symmetric magnetic field configurations corresponding to these potentials have been identified.
Related papers
- Direct derivation of the modified Langevin noise formalism from the canonical quantization of macroscopic electromagnetism [51.56484100374058]
We derive the exact analytical expressions for the polariton operators in terms of the canonical CQME field operators.<n>We provide a direct and rigorous derivation of the Langevin noise formalism from the canonical theory in the Schrdinger picture.
arXiv Detail & Related papers (2026-03-04T17:53:31Z) - Affine Symmetry and the Group-Theoretic Basis of the Unruh Effect [0.0]
We derive the thermal spectrum of Rindler particles observed by an accelerated observer.<n>We show that analogous phenomena may arise in any quantum system admitting realizations of translation and dilation eigenstates.
arXiv Detail & Related papers (2025-12-27T16:58:50Z) - Pseudo-Hermitian extensions of the harmonic and isotonic oscillators [9.944647907864256]
We describe certain pseudo-Hermitian extensions of the harmonic and isotonic oscillators.<n>We explicitly solve for the wavefunctions in the position representation and also explore their intertwining relations.
arXiv Detail & Related papers (2024-08-02T17:15:17Z) - Generalized Gouy Rotation of Electron Vortex beams in uniform magnetic fields [54.010858975226945]
The intrinsic rotation of electron vortex beams has been experimentally observed in magnetic fields by breaking the beam's cylindrical symmetry.<n>We introduce and derive the generalized Gouy rotation angle, which links the Gouy phase of an extended Landau state to the experimentally observed angular variation.<n>Our results are, in principle, applicable to any system involving electron vortex beams in uniform magnetic fields.
arXiv Detail & Related papers (2024-07-03T03:29:56Z) - Rational extensions of the Dunkl oscillator in the plane and exceptional
orthogonal polynomials [0.0]
It is shown that rational extensions of the isotropic Dunkl oscillator in the plane can be obtained by adding some terms.
In the latter, it becomes an anisotropic potential, whose explicit form has been found in the simplest case.
arXiv Detail & Related papers (2023-05-09T14:23:14Z) - Resonant Parametric Photon Generation in Waveguide-coupled Quantum Emitter Arrays [83.88591755871734]
We have developed a theory of parametric photon generation in the waveguides coupled to arrays of quantum emitters with temporally modulated resonance frequencies.
Such generation can be interpreted as a dynamical Casimir effect.
We demonstrate numerically and analytically how the emission directionality and photon-photon correlations can be controlled by the phases of the modulation.
arXiv Detail & Related papers (2023-02-24T18:07:49Z) - Intrinsic decoherence dynamics in the three-coupled harmonic oscillators
interaction [77.34726150561087]
We give an explicit solution for the complete equation, i.e., beyond the usual second order approximation used to arrive to the Lindblad form.
arXiv Detail & Related papers (2021-08-01T02:36:23Z) - Localized vibrational modes in waveguide quantum optomechanics with
spontaneously broken PT symmetry [117.44028458220427]
We study theoretically two vibrating quantum emitters trapped near a one-dimensional waveguide and interacting with propagating photons.
In the regime of strong optomechanical interaction the light-induced coupling of emitter vibrations can lead to formation of spatially localized vibration modes, exhibiting parity-time symmetry breaking.
arXiv Detail & Related papers (2021-06-29T12:45:44Z) - Fano interference in quantum resonances from angle-resolved elastic
scattering [62.997667081978825]
We show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles in a single channel shape resonance.
We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules.
arXiv Detail & Related papers (2021-05-12T20:41:25Z) - The rotating harmonic oscillator revisited [0.0]
We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method.
A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients.
Truncation of the series yields some particular eigenvalues and eigenfunctions in exact analytical form.
arXiv Detail & Related papers (2020-07-22T21:42:02Z) - Generic example of algebraic bosonisation [0.0]
Rotational invariance is taken into account within the scheme for the first time.
A connection to the formalism of the fractional quantum Hall effect is pointed out.
arXiv Detail & Related papers (2020-01-21T16:26:31Z)
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.