Harmonic oscillator interacting with conical singularities

Furtado, C.; Moraes, Fernando

doi:10.1088/0305-4470/33/31/306

Cited by 162 publications

(173 citation statements)

References 19 publications

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“…[7], where the presence of the screw dislocation modifies the angular momentum [34] and gives rise to an Aharonov-Bohm-type effect for bound states [33], the presence of the spiral dislocation (an edge dislocation) gives no contribution to the angular momentum quantum number in the energy levels. In this sense, there is no Aharonov-Bohm-type effect for bound states [7,21,33]. Note that, by taking β = 0 in Eq.…”

Section: Tionmentioning

confidence: 99%

“…The common point between these areas of physics is the description of these defects made by the Volterra process [1,2,4,5]. Up to now, a great deal of study has explored quantum system in the presence of disclinations [6][7][8][9][10] and screw dislocations [5,[11][12][13][14][15][16] in the context of condensed matter physics. In particular, torsion effects related to the presence of topological defects are in the interests of studies of semiconductors [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Harmonic oscillator in an elastic medium with a spiral dislocation

Maia

Bakke

2018

Physica B: Condensed Matter

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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:

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Section: Tionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Harmonic oscillator in an elastic medium with a spiral dislocation

Maia

Bakke

2018

Physica B: Condensed Matter

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“…Gauge conditions (32)- (33) are first order equations by themselves and have some arbitrariness. Therefore, to fix a solution uniquely, we must impose additional boundary conditions on the vielbein for any given problem.…”

Section: Gauge Fixingmentioning

confidence: 99%

Geometric theory of defects

Katanaev¹

2005

Usp. Fiz. Nauk

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A description of dislocations and disclinations defects in terms of RiemannCartan geometry is given, with the curvature and torsion tensors being interpreted as the surface densities of the Frank and Burgers vectors, respectively. A new free energy expression describing the static distribution of defects is presented, and equations of nonlinear elasticity theory are used to specify the coordinate system. Application of the Lorentz gauge leads to equations for the principal chiral SO(3)-field. In the defect-free case, the geometric model reduces to elasticity theory for the displacement vector field and to a principal chiral SO(3)-field model for the spin structure. As illustrated by the example of a wedge dislocation, elasticity theory reproduces only the linear approximation of the geometric theory of defects. It is shown that the equations of asymmetric elasticity theory for the Cosserat media can also be naturally incorporated into the geometric theory as the gauge conditions. As an application of the theory, phonon scattering on a wedge dislocation is considered. The energy spectrum of impurity in the field of a wedge dislocation is also discussed.

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“…It is worth emphasizing that a spacetime with a space-like dislocation corresponds to a topological defect spacetime associated with the presence of torsion in the spacetime [38]. In quantum mechanics, the background defined by a spacetime with a space-like dislocation has been explored in studies of the Aharonov-Bohm effect for bound states [39], quantum scattering [40,41], harmonic oscillator [42], noninertial effects [43], Kaluza-Klein theory [44] and the Dirac oscillator [45].…”

Section: Introductionmentioning

confidence: 99%

Torsion effects on a relativistic position-dependent mass system

Vitória

Bakke

2016

Gen Relativ Gravit

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We analyse a relativistic scalar particle with a position-dependent mass in a spacetime with a space-like dislocation by showing that relativistic bound states solutions can be achieved. Further, we consider the presence of the Coulomb potential and analyse the relativistic position-dependent mass system subject to the Coulomb potential in the spacetime with a space-like dislocation. We also show that a new set of relativistic bound states solutions can be obtained, where there also exists the influence of torsion of the relativistic energy levels. Finally, we investigate an analogue of the Aharonov-Bohm effect for bound states in this position-dependent mass in a spacetime with a space-like dislocation.

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Harmonic oscillator interacting with conical singularities

Cited by 162 publications

References 19 publications

Harmonic oscillator in an elastic medium with a spiral dislocation

Harmonic oscillator in an elastic medium with a spiral dislocation

Geometric theory of defects

Torsion effects on a relativistic position-dependent mass system

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