Generalized Dirac oscillators with position-dependent mass

Abstract

We study the (1 + 1) dimensional generalized Dirac oscillator with a position-dependent mass. In particular, bound states with zero energy as well as non zero energy have been obtained for suitable choices of the mass function/oscillator interaction. It has also been shown that in the presence of an electric field, bound states exist if the magnitude of the electric field does not exceed a critical value.

Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators

“…Graphs of these functions are shown in the right part of figure 2. In the form (20) of our Dirac equation, our function f stands for a generalized oscillator term, while in the equivalent form (21) we use (22) to determine the magnetic field that is represented by f . We obtain B(x) = 0, 0, −sech(x) 2 T .…”

“…For example, Dirac systems with magnetic fields were studied on a hyperbolic graphene surface [12], under the presence of nonuniform fields [15], within the minimal-length context [27], among others. Position-dependent masses were used in determining scattering states [7], systems with spatially variable Fermi velocity [32] [19] and generalized Dirac oscillators [21]. Such oscillators, initially introduced as systems linear in momentum and coordinate variables [29], are closely related to Dirac models coupled to magnetic fields.…”

The kinetic Hamiltonian with position-dependent mass

“…Position-dependent mass (PDM) models have been under regular development since the sixties and continuously improved up to present days. Particularly, in the last decade modeling quantum systems with PDM particles has grown as a consequence of its wide area of applications [11][12][13][14][15][16]. Among them, this technique has been applied to the understanding of the electronic properties of semiconductor heterostructures, crystal-growth techniques [5,17], quantum wells and quantum dots [18][19][20][21][22][23][24][25][26][27][28], helium clusters [29], graded crystals [30], quantum liquids [31], nanowire structures with size variations, impurities, dislocations, and geometry imperfections [32][33][34][35], as well as in superconductors investigations [4,5,7,17,30,[36][37][38][39][40].…”

On the Dirac oscillator in a spinning cosmic string spacetime in external magnetic fields: Investigation of energy spectrum and connection with the condensed matter physics

“…The Dirac oscillator was also studied in a noncommutative spacetime [16]. In the context of recent contributions, the Dirac oscillator was analyzed taking into account a scenario with position-dependent mass [17] and the inclusion of time-reversal symmetry [18].…”