The EUP Dirac Oscillator: A Path Integral Approach

Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass

“…GUP has been applied in problems of quantum mechanics and quantum gravity, whose modified relation commutation between position and linear momentum depends on one or both operators [46][47][48][49][50][51][52][53] . Consequently, this could be interpreted as an effective mass dependent on the position or the linear momentum (see references 51-53 for more details).…”

“…Furthermore, effects of the gravitational field in quantum mechanics have been characterized by generalizations of the standard commutation relationship between the position and the linear momentum, giving place to the generalized uncertainty principles (GUP). [46][47][48][49][50][51][52][53] In this context, some theoretical frameworks have been developed to mimic the effect of the PDM by means of deformed algebraic structures. [51][52][53] One of these formulations is derived from a a) Electronic mail: bruno.costa@ifsertao-pe.edu.br b) Electronic mail: cardoso.genilson@outlook.com c) Electronic mail: ignacio.sebastian@ufba.br translation operator that causes non-additive displacements of the type Tγ (ε)|x = |x + (1 + γx)ε , being γ a deformation parameter with inverse length dimension.…”

“…[46][47][48][49][50][51][52][53] In this context, some theoretical frameworks have been developed to mimic the effect of the PDM by means of deformed algebraic structures. [51][52][53] One of these formulations is derived from a a) Electronic mail: bruno.costa@ifsertao-pe.edu.br b) Electronic mail: cardoso.genilson@outlook.com c) Electronic mail: ignacio.sebastian@ufba.br translation operator that causes non-additive displacements of the type Tγ (ε)|x = |x + (1 + γx)ε , being γ a deformation parameter with inverse length dimension. [54][55][56][57][58][59][60][61][62][63][64][65][66][67] This translation operator leads to a position-dependent linear momentum operator pγ that generates non-additive translations.…”

Exact Green’s function for 2D dirac oscillator in constant magnetic field within curved snyder space, and its thermal properties

“…Moreover, the anti-de Sitter commutation relations give rise to the appearance of minimal uncertainty and then in [15] it is described the Dirac oscillator in one dimension using the position space representation, where analysis is performed on the thermodynamic properties of relativistic harmonic oscillators at high-temperatures. Later, Benzair et al computed the energy spectrum of the Dirac Oscillator (DO) using the path integral formulation in one and two dimensions, respectively, within the extended uncertainty principle framework [16,17]. Moreover, the investigation of thermodynamic properties for relativistic oscillator particles under deformed algebra resonated in this aspect, as evidenced by the references [14,[17][18][19][20][21][22].…”

One dimensional Bose–Einstein condensate under the effect of the extended uncertainty principle

“…Furthermore, it is important to study quantum effects over large distances [12]. In this context, numerous applications have emerged, including the one-dimensional Klein-Gordan and Dirac oscillators [13], two-dimensional Dirac oscillator [14], three-dimensional relativistic Coulomb potential [15], the two-dimensional Dirac equation with Aharonov-Bohm-Coulomb interaction [16], and scalar and vector potentials for the Klein-Gordon equation in one dimension [17].…”