Landau levels in the presence of a cosmic string in rainbow gravity

Abstract

In this paper we analyze the energy levels of a charged scalar particle placed in the static cosmic string spacetime, under the action of a uniform magnetic field parallel to the string, in the context of the semi-classical approach of the rainbow gravity. Firstly, we focus on the non-relativistic regime by solving the corresponding Schrödinger equation, following by a complete relativistic treatment of the problem in which we considered the Klein-Gordon equation. In both cases we find exact expressions for the Landau levels in terms of the rainbow functions, used to characterize a rainbow gravity model. In order to achieve the results of this paper we considered three different rainbow gravity models mostly used in the literature and compare the resulting modifications in the Landau levels with the standard case, namely without rainbow gravity.

PDM Klein-Gordon oscillators in cosmic string spacetime in magnetic and Aharonov-Bohm flux fields within the Kaluza-Klein theory

“…Moreover, we have observed that square the energies in (18) (i.e., E 2 ) resembles the Landau-type energies-squared with an irrational magnetic quantum number γ that indulges within the Aharonov-Bohm flux field effect. We may argue, therefore, that the additional compact dimension of the Kaluza-Klein theory offers quasi-Landau energy levels (e.g., [6,64,67]). Hereby, the behaviour of the energy levels E nr ,ℓ is found to follow two different trends of clustering and batching up for the curvature parameter α ≈ 0 and α ≫ 1.…”

“…where n r = 0, 1, 2, • • • is the radial quantum number (denotes number of nodes in the wave function) (c.f., e.g., [60,[64][65][66]). Hence, the KG-oscillator of ( 16) admits exact energy levels given by…”

“…It is interesting to know that this is manifestly introduced by the coupling between the compact Kaluza-Klein fifth-dimension u and the ϕ coordinate. As such, we may argue that the additional compact dimension of the Kaluza-Klein theory offers quasi-Landau energy levels (e.g., [6,64,67]). Moreover, one should be aware that the four possible KG-oscillators' settings discussed above, with some straightforward parametric substitutions, admit exact solvability as in (18) and (19).…”

Effects of modified dispersion relations on free Fermi gas: equations of state and applications in astrophysics

“…where the exponential form of these functions is useful to explain observational data of gamma ray bursts at cosmological distances [26,27].…”

Quantum dynamics of scalar particles in the space-time of a cosmic string in the context of gravity's rainbow

“…In the scenario of gravity's rainbow, the Landau levels [33] and the Dirac oscillator [34] in the presence of a cosmic string have been studied. In the present paper, we will consider scalar particles in a cosmic string space-time in the context of gravity's rainbow and obtain the solutions of the KG equation, with both minimum (Coulomb-like) and non-minimum coupling (KG oscillator) in two scenarios of the gravity's rainbow, and analyze their consequences.…”