Effects of rotation on the Landau levels in an elastic medium with a spiral dislocation

About the effects of rotation on the Landau levels in an elastic medium with a spiral dislocation

“…When r = 0 then y = y 0 = mδβ 2 /2 and the correct boundary condition for the differential equation ( 2) is g(y 0 ) = 0. The choice y 0 = 0 is rather unphysical 3 because it leads to r 2 = −β 2 ; however, Maia and Bakke [1] stated that they could resort to this approximation without loss of generality because β 2 ≪ 1 as mentioned above. In what follows we analyze to which extent this approximation is reasonable.…”

“…In what follows we analyze to which extent this approximation is reasonable. To begin with, note that the behaviour at origin of the solution to the differential equation ( 1) is h ∼ r 2 while, on the other hand, the behaviour at origin of the solution to (2) chosen by Maia and Bakke [1] is g ∼ y |γ|/2 . Under the approximation β ∼ 0 it leads to g ∼ r |γ| that is consistent with the correct asymptotic behaviour at origin only when |γ| = 2.…”

“…In a recent paper Maia and Bakke [1] analyzed the effects of rotation on the interaction of a point charge with a uniform magnetic field in an elastic medium with a spiral dislocation. In order to obtain analytical solutions to the Schrödinger equation in a rotating frame with a constant angular velocity Maia and Bakke [1] changed the boundary conditions of the model. Based on this approximation they concluded that both the topology of the defect and rotation modify the degeneracy of the Landau levels.…”

“…The purpose of this paper is to analyze the effect of the change of the left boundary condition on the results because Maia and Bakke [1] did not discuss this point in detail and their weak argument leaves much to be desired. In section 2 we derive the analytical results by means of the Frobenius method because it is clearer than the approach based on the confluent hypergeometric function followed by Maia and Bakke [1]. In section 3 we solve the eigenvalue equation with the correct left boundary condition and compare the numerical results thus obtained with the analytical ones.…”

Interaction of the magnetic quadrupole moment of a non-relativistic particle with an electric field in the background of screw dislocations with a rotating frame

“…In Ref. [63] it is shown that the topology of a screw dislocation that corresponds to the distortion of a circular curve into a vertical spiral makes such transformation and also showed that the effective operator of the z-component of the angular momentum does not commute with the Hamiltonian. Next, the effects of rotation on this nonrelativistic system are investigated by Ω. LΨ (t, r) (the second term of the left-hand side of Eq.…”