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Register a new userA relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry
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We consider a background of the violation of the Lorentz symmetry determined by the tensor $left( K_{F}right)_{mu ualphabeta}$ which governs the Lorentz symmetry violation out of the Standard Model Extension, where this background gives rise to a Coulomb-type potential, and then, we analyse its effects on a relativistic quantum oscillator. Furthermore, we analyse the behaviour of the relativistic quantum oscillator under the influence of a linear scalar potential and this background of the Lorentz symmetry violation. We show in both cases that analytical solutions to the Klein-Gordon equation can be achieved.
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Based on models of confinement of quarks, we analyse a relativistic scalar particle subject to a scalar potential proportional to the inverse of the radial distance and under the effects of the violation of the Lorentz symmetry. We show that the effects of the Lorentz symmetry breaking can induced a harmonic-type potential. Then, we solve the Klein-Gordon equation analytically and discuss the influence of the background of the violation of the Lorentz symmetry on the relativistic energy levels.
The relativistic bound-state energy spectrum and the wavefunctions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein-Gordon and Dirac equations are solved analytically to obtain the results. The electron energies of hydrogen-like atoms are studied numerically.
The quintessence-like potential of vacuum energy can meet the requirement from both quantum gravity and the accelerating expansion of the universe. The anti-de Sitter vacuum in string theory has to be lifted to the meta-stable de Sitter vacuum with positive vacuum energy density to explain the accelerating expansion of the universe. Based on the possible large scale Lorentz violation, we define an effective cosmological constant which depends not only on the bare cosmological constant but also on the Lorentz violation effect. We find the evolution of the effective cosmological constant exhibits the behavior of quintessence potential when the bare cosmological constant is from string landscape in contrary to the existence of local minimum during evolution while the bare cosmological constant is supplied by the swampland. The critical value of bare cosmological constant is approximately zero for the behavior transition. The frozen large scale Lorentz violation can uplift the AdS vacua to an effective quintessence-like one in this sense.
A recent proposal for testing Lorentz symmetry violation (LSV) presents a formulation where the effect of violation is described as a local interaction [R. Shaniv, et al, Phys. Rev. Lett. 120, 103202 (2018)]. An entangled ion pair in a decoherence free subspace (DFS) is shown to double the signal to noise ratio (SNR) of one ion, while (even)-N/2 such DFS pairs in a collective entangled state improve SNR by N times, provided the state parity or the even/odd numbers of ions can be measured. It remains to find out, however, how such fiducial entangled states can be prepared at nonexponentially small success rates. This work suggests two types of many particle entangled states for testing LSV: the maximally entangled NOON state, which can achieve Heisenberg limited precision; and the balanced spin-1 Dicke state, which is readily available in deterministic fashion. We show that the latter also lives in a DFS and is immune to stray magnetic fields. It can achieve classical precision limit or the standard quantum limit (SQL) based on collective population measurement without individual atom resolution. Given the high interests in LSV and in entanglement assisted quantum metrology, our observation offers additional incentives for pursuing practical applications of many atom entangled states.
In this paper are presented the effects of Lorentz violation in superconductivity. Constructing a Lorentz-Violating Ginzburg-Landau theory of superconductivity we discuss the influence of the Lorentz-Violating tensor $hat{k}_a^i$ in the Londons depth penetration, in the coherence length and in the critical magnetic field. We also study the behavior of the magnetic field inside the superconductor for two different geometries, cylindrical and rectangular.
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