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Paper 1
Floquet Codes from Derived Semi-Regular Hyperbolic Tessellations on Orientable and Non-Orientable Surfaces
Douglas F. Copatti, Giuliano G. La Guardia, Waldir S. Soares, Edson D. Carvalho, Eduardo B. Silva
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.29811
- arXiv
- 2603.29811
In this paper, we construct several new quantum Floquet codes on compact, orientable, as well as non-orientable surfaces. In order to obtain such codes, we identify these surfaces with hyperbolic polygons and examine hyperbolic semi-regular tessellations on such surfaces. The method of construction presented here generalizes similar constructions concerning hyperbolic Floquet codes on connected and compact surfaces with genus $g \geq 2$. A performance analysis and an investigation of the asymptotic behavior of these codes are also presented.
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Klein--Gordon oscillator with linear--fractional deformed Casimirs in doubly special relativity
Abdelmalek Boumali, Nosratollah Jafari
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.06637
- arXiv
- 2603.06637
We study the Klein--Gordon (KG) oscillator in a doubly special relativity (DSR) framework, where the mass-shell condition is deformed through a linear--fractional (Möbius-type) modification of the Casimir invariant. This is induced by a nonlinear map from physical momenta $p^μ$ to auxiliary Lorentz-covariant variables $π^μ$. In $(1+1)$ dimensions, the deformation is controlled by a constant covector $a_μ$, yielding inequivalent realizations depending on whether $a_μ$ is timelike, spacelike, or lightlike. Implementing the KG oscillator via a reverted-product nonminimal coupling, we obtain exact closed-form spectra and explicit eigensolutions for both particle and antiparticle branches across all three geometries. Timelike and lightlike deformations produce identical spectra characterized by a Planck-suppressed additive displacement. This breaks the exact $E\leftrightarrow -E$ symmetry via a term linear in $E$, interpretable as a branch-independent reparametrization of the energy origin. Conversely, the spacelike deformation is strictly isospectral to the undeformed oscillator but generates complex-shifted wavefunctions and a non-Hermitian spatial operator. We provide a compact $\mathcal{PT}$-symmetric and pseudo-Hermitian formulation by constructing an explicit similarity map $\mathcal{S}$ to a Hermitian oscillator, deriving the metric operator $η=\mathcal{S}^\dagger \mathcal{S}$, and establishing biorthonormal relations. Finally, we compare quantitatively with the Magueijo--Smolin (DSR2) model: the squared-denominator invariant leads to a larger Planck-suppressed displacement at fixed $m/E_{Pl}$, highlighting the denominator power's role in controlling spectral shifts. Representative plots illustrate the dependence on deformation ratio, oscillator strength, and excitation level.
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