Harmonic oscillator in an elastic medium with a spiral dislocation

Abstract

We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schrödinger equation for harmonic oscillator in the presence of a spiral dislocation can be solved analytically. Further, we discuss the effects of this topological defect on the confinement to a hard-wall confining potential.In both cases, we analyse if the effects of the topology of the spiral dislocation gives rise to an Aharonov-Bohm-type effect for bound states.PACS numbers:

Aharonov–Bohm-type effect in the background of a distortion of a vertical line into a vertical spiral

“…The Aharonov-Bohm effect for bound states that arises from the presence of linear topological defects in an elastic medium has been investigated in several quantum systems [9][10][11][12][13][14][15][16][17][18][19][20]23]. In particular, by considering the distortion of a circular curve into a vertical spiral (a screw dislocation), it has been shown in Ref.…”

“…Therefore, the angular momentum in Eq. (20) is defined in terms of the effective operator (21). Besides, sinceĤ 0 is determined by Eqs.…”

“…In recent decades, the Katanaev-Volovich approach [2] has been widely used in the literature with the purpose of investigating topological effects associated with screw dislocations in quantum rings [9][10][11], electrons subject to the deformed Kratzer potential [12], electron gas in a cylindrical shell [13], quantum holonomies [14] and with an electron in a uniform magnetic field [15][16][17][18]. Furthermore, topological effects associated with a spiral dislocation have been made with geometric quantum phases [19] and the harmonic oscillator [20].…”

On an electron in an elastic medium with a spiral dislocation

“…where the constant β is the parameter related to the dislocation (0 < β < 1). The general form of the time-independent Schrödinger equation for an electron in the presence of a spiral dislocation is given by [9,25] (we shall use the units = 1 and c = 1)…”

“…On the other hand, based on the Katanaev-Volovich approach [8], topological effects on quantum systems that stem from the presence of a spiral dislocation in an elastic medium have just been reported recently. For instance, in studies of geometric quantum phases [24] and the harmonic oscillator [25].…”