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- W3136750825 abstract "An exotic rotationally invariant anisotropic harmonic oscillator (RI-AHO) is constructed by applying a non-unitary isotropic conformal bridge transformation (CBT) to a free planar particle. It is described by the isotropic harmonic oscillator Hamiltonian supplemented by a Zeeman type term with a real coupling constant $g$. The model reveals the Euclidean ($|g| 1$) phases separated by the phases $g=+1$ and $g=-1$ of the Landau problem in the symmetric gauge with opposite orientation of the magnetic field. A hidden symmetry emerges in the system at rational values of $g$. Its generators, together with the Hamiltonian and angular momentum produce non-linearly deformed $mathfrak{u}(2)$ and $mathfrak{gl}(2,{mathbb R})$ algebras in the cases of $0 |g|>1$, which transmute one into another under the inversion $grightarrow -1/g$. Similarly, the true, $mathfrak{u}(2)$, and extended conformal, $mathfrak{gl}(2,{mathbb R})$, symmetries of the isotropic Euclidean oscillator ($g=0$) interchange their roles in the isotropic Minkowskian oscillator ($|g|=infty$), while two copies of the $mathfrak{gl}(2,{mathbb R})$ algebra of analogous symmetries mutually transmute in Landau phases. We show that the RI-AHO is transformed by a peculiar unitary transformation into a usual, rotationally non-invariant AHO generated, in turn, by anisotropic CBT. The relationship of the RI-AHO with subcritical phases of the harmonically extended Landau problem is established." @default.
- W3136750825 created "2021-03-29" @default.
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- W3136750825 date "2021-03-13" @default.
- W3136750825 modified "2023-09-27" @default.
- W3136750825 title "Conformal generation of an exotic rotationally invariant anisotropic oscillator" @default.
- W3136750825 hasPublicationYear "2021" @default.
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