Beyond Relativity: How Planck-Scale Effects Warp the Quantum Oscillator
![The energy spectrum of the Klein-Gordon oscillator bifurcates into positive and negative branches-[latex]E_{N}^{(+)}[/latex] and [latex]E_{N}^{(-)}[/latex]-and its deformation via different DSR implementations-including standard AC/MS and generalized forms in first-order expansions-demonstrates how foundational energy relationships, such as [latex]E_{N}^{(0)}=\pm\sqrt{m^{2}c^{4}+2mc^{2}\hbar\omega\,N}[/latex], are not absolute but rather malleable properties contingent on the underlying systemic structure, where [latex]N\in\mathbb{N}_{0}[/latex] represents a non-negative integer defining the oscillator’s state.](https://arxiv.org/html/2602.22444v1/2602.22444v1/Fig_energy_levels.png)
New research explores how the fundamental limits of spacetime, as predicted by Doubly Special Relativity, alter the energy levels of a quantum harmonic oscillator in three dimensions.

![The study’s determination of [latex]K^{-}d[/latex] scattering lengths-achieved through a Lednický-Lyuboshits fit-aligns with existing theoretical calculations derived from SIDDHARTA and KEK experimental data, as evidenced by the correspondence between the ALICE measurement’s systematic and statistical uncertainties, represented by full and empty ellipses respectively.](https://arxiv.org/html/2602.22833v1/2602.22833v1/x2.png)
![A four-dimensional Markov Chain Monte Carlo analysis constrained the mass and orbital radius of quasi-periodic oscillations for stellar-mass black holes - XTE J1550-564, GRO J1655-40, GRS 1915+105, and M82 X-1 - revealing the inherent uncertainty in these parameters as defined by [latex]1\sigma[/latex] and [latex]2\sigma[/latex] confidence intervals, and highlighting the probabilistic nature of astrophysical modeling.](https://arxiv.org/html/2602.22264v1/2602.22264v1/M82_X-1_in.png)

![In heavy-ion collisions of lead nuclei at [latex]\sqrt{s_{NN}} = 5.02 \text{TeV}[/latex], the centrality dependence of the correlated two-particle flow coefficient, [latex]f_{CME}[/latex],-extracted via correlations relative to the spectator and participant planes as defined by Eq. 7-reveals a consistent trend across varying degrees of collision centrality, as indicated by the statistical and systematic uncertainties represented by vertical bars and boxes, respectively, and further validated by a constant fit within a 95% confidence level band.](https://arxiv.org/html/2602.22900v1/2602.22900v1/x6.png)
![The study demonstrates a correlation between the strength parameter α and the dimensionless decay constant [latex]\tilde{\beta}[/latex], with observed minor dependencies on the [latex]M\_B[/latex] mass and a relationship to both the inverse of the initial time [latex]1/\sqrt{t\_0}[/latex] and the Hubble parameter [latex]H[/latex], further influenced by temperature [latex]T[/latex] within the Standard Model’s effective degrees of freedom [latex]g\_{\rm eff,SM}(T)[/latex].](https://arxiv.org/html/2602.23002v1/2602.23002v1/x15.png)
![The study demonstrates a decomposition and weighting of spin-[latex]\frac{1}{2}[/latex] U(1) gauge links interacting with a matter Hamiltonian, revealing the intricate relationships within the system described by the inequality [latex]\tilde{1}[/latex].](https://arxiv.org/html/2602.22332v1/2602.22332v1/x4.png)
![This work establishes upper limits on the kinetic-mixing parameter ε as a function of dark-photon mass [latex]m_{A^{\prime}}[/latex], derived from [latex]B_{x}B_{y}[/latex] and [latex]B_{y}B_{x}[/latex] channels and enhanced through noise subtraction utilizing [latex]B_{z}[/latex] as a coherent reference, demonstrating a sensitivity reaching over [latex]10^{7}[/latex] scanned masses and providing constraints complementary to those from astrophysical observations and existing bounds such as the Coulomb-law limit and projections for future implementations with sensitivities of [latex]0.1\,\mathrm{fT}/\sqrt{\mathrm{Hz}}[/latex].](https://arxiv.org/html/2602.22308v1/2602.22308v1/x2.png)