Conformal generation of an exotic rotationally invariant harmonic oscillator

Inzunza, Luis; Plyushchay, Mikhail S.

doi:10.1103/physrevd.103.106004

Cited by 9 publications

(46 citation statements)

References 55 publications

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“…The dynamics of test particles in rigidly rotating spacetime backgrounds is essentially affected by the appearance of gravitoelectromagnetic fields at the classical and quantum levels. For special values of the parameters of such and similar systems, classical dynamics of test particles can be completely integrable due to appearance of hidden symmetries, which also reveal themselves in peculiar properties of the corresponding quantum systems [5,6,10,11,12,17,39]. This section aims to investigate such effects for geodesic motion in a rotating conical background.…”

Section: Dynamics In Rigidly Rotating Spacetimesmentioning

confidence: 99%

“…Recently, in [39] we considered the exotic rotationally invariant harmonic oscillator generated from the planar free particle system by application of the conformal bridge transformation [28,29]. The model is described by the Hamiltonian 6…”

Section: Classical Eriho System In a Conical Spacementioning

confidence: 99%

“…(2.4). As a consequence, the model (3.1) admits two other physical interpretations [39]. First, it corresponds to a two-dimensional isotropic harmonic oscillator in a non-inertial reference frame rotating with angular velocity Ω. Alternatively, it can be considered as the Landau problem in the presence of an additional external harmonic potential…”

Section: Classical Eriho System In a Conical Spacementioning

confidence: 99%

“…For a given rational value (3.21) of γ, the true integrals L (ǫ),± α,s 1 ,s 2 and the dynamical quantities J (δ),± α,s 1 ,s 2 generate a non-linear algebra, which in the Euclidean isotropic case α = 1, γ = 0 reduces to the linear sp(4, R) algebra [17,39]. As in the Euclidean case, the transformation γ → 1/γ changes the system…”

Section: Classical Picturementioning

confidence: 99%

“…3, we supply the system with a harmonic trap potential with frequency ω and study its classical dynamics. As a result, we obtain an analog of the Euclidean exotic rotationally invariant harmonic oscillator (ERIHO) system [39], but now in the cosmic string background. This system has closed orbits and integrals of motion associated with a hidden symmetry only when both parameters |γ| = |Ω/ω| and α take rational values.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background

Inzunza,

Plyushchay

2021

Preprint

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Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the equations of motion are found by employing a local canonical transformation, that leads to their natural interpretation in terms of Riemann surfaces. The cone parameter α and the angular velocity Ω of the background determine the existence of hidden symmetries. Globally defined higher order integrals associated with perihelion of geodesic orbits appear at rational values of α. For the harmonic oscillator system with frequency ω, the integrals responsible for the trajectory closure arise only for rational values of α and |γ| = |Ω/ω|, with |γ| = 1 corresponding to the Landau problem. We face a quantum anomaly problem since the hidden symmetry operators can only be constructed when α is integer. Such operators are non-local in the case of the free particle. For the harmonic oscillator, the symmetry generators are obtained with the help of the conformal bridge transformation. We also study a multi-particle version of the harmonic oscillator system with |γ| = 1 using the mean-field theory and find that the emerging vortex structure respects a singular point of the background.

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Section: Dynamics In Rigidly Rotating Spacetimesmentioning

confidence: 99%

Section: Classical Eriho System In a Conical Spacementioning

confidence: 99%

Section: Classical Eriho System In a Conical Spacementioning

confidence: 99%

Section: Classical Picturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background

Inzunza,

Plyushchay

2021

Preprint

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Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background

Inzunza

Plyushchay

2022

J. High Energ. Phys.

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Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the equations of motion are found by employing a local canonical transformation, that leads to their natural interpretation in terms of Riemann surfaces. The cone parameter α and the angular velocity Ω of the background determine the existence of hidden symmetries. Globally defined higher order integrals associated with perihelion of geodesic orbits appear at rational values of α. For the harmonic oscillator system with frequency ω, the integrals responsible for the trajectory closure arise only for rational values of α and |γ| = |Ω/ω|, with |γ| = 1 corresponding to the Landau problem. We face a quantum anomaly problem since the hidden symmetry operators can only be constructed when α is integer. Such operators are non-local in the case of the free particle. For the harmonic oscillator, the symmetry generators are obtained with the help of the conformal bridge transformation. We also study a multi-particle version of the harmonic oscillator system with |γ| = 1 using the mean-field theory and find that the emerging vortex structure respects a singular point of the background.

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Conformal bridge transformation, $$ \mathcal{PT} $$- and supersymmetry

Inzunza

Plyushchay

2022

J. High Energ. Phys.

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Supersymmetric extensions of the 1D and 2D Swanson models are investigated by applying the conformal bridge transformation (CBT) to the first order Berry-Keating Hamiltonian multiplied by i and its conformally neutral enlargements. The CBT plays the role of the Dyson map that transforms the models into supersymmetric generalizations of the 1D and 2D harmonic oscillator systems, allowing us to define pseudo-Hermitian conjugation and a suitable inner product. In the 1D case, we construct a $$ \mathcal{PT} $$ PT -invariant supersymmetric model with N subsystems by using the conformal generators of supersymmetric free particle, and identify its complete set of the true bosonic and fermionic integrals of motion. We also investigate an exotic N = 2 supersymmetric generalization, in which the higher order supercharges generate nonlinear superalgebras. We generalize the construction for the 2D case to obtain the $$ \mathcal{PT} $$ PT -invariant supersymmetric systems that transform into the spin-1/2 Landau problem with and without an additional Aharonov-Bohm flux, where in the latter case, the well-defined integrals of motion appear only when the flux is quantized. We also build a 2D supersymmetric Hamiltonian related to the “exotic rotational invariant harmonic oscillator” system governed by a dynamical parameter γ. The bosonic and fermionic hidden symmetries for this model are shown to exist for rational values of γ.

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Conformal generation of an exotic rotationally invariant harmonic oscillator

Cited by 9 publications

References 55 publications

Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background

Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background

Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background

Conformal bridge transformation, $$ \mathcal{PT} $$- and supersymmetry

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