Quantum phase transitions of the Dirac oscillator in the Anti-Snyder model

Abstract

We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field within the Anti-Snyder modified uncertainty relation characterized by a momentum cut-off ($p\le p_{\text{max}}=1/\sqrt{\beta }$). In ordinary quantum mechanics ($\beta \to 0$) this system is known to have a single left-right chiral quantum phase transition (QPT). We show that a finite momentum cut-off modifies the spectrum introducing additional quantum phase transitions. It is also shown that the presence of momentum cut-off modifies the degeneracy of the states.

10 pages, 2 Figures. Accepted for publication by the Physical Review D

References in corpus (9)

• The electronic properties of graphene
• Germanene: a novel two-dimensional Germanium allotrope akin to Graphene and Silicene
• Chirality Quantum Phase Transition in the Dirac oscillator
• Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption
• Non-relativistic limit in the 2+1 Dirac Oscillator: A Ramsey Interferometry Effect
• Playing relativistic billiards beyond graphene
• Quantum phase transitions in the noncommutative Dirac Oscillator
• Quantum phase transitions of the Dirac oscillator in a minimal length scenario
• Generalized Relativistic Wave Equations with Intrinsic Maximum Momentum

Cited by in corpus (2)

• Quantization of nonlocal fractional field theories via the extension problem
• Non-Relativistic Anti-Snyder Model and Some Applications