Quantum phase transitions of the Dirac oscillator in a minimal length scenario

Abstract

We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field within a minimal length ($\Delta x_0=\hslash \sqrt{\beta }$), or generalised uncertainty principle (GUP) scenario. This system in ordinary quantum mechanics has a single left-right chiral quantum phase transition (QPT). We show that a non zero minimal length turns on a infinite number of quantum phase transitions which accumulate towards the known QPT when $\beta \to 0$. It is also shown that the presence of the minimal length modifies the degeneracy of the states and that in this case there exist a new class of states which do not survive in the ordinary quantum mechanics limit $\beta \to 0$.

arXiv comment7 pages, 1 figure

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Cited by in corpus (9)

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• $1+1$-dimensional Dirac oscillator with deformed algebra with minimal uncertainty in position and maximal in momentum
• Symmetry operators and separation of variables in the $(2+1)$-dimensional Dirac equation with external electromagnetic field
• Non-Relativistic Anti-Snyder Model and Some Applications
• Kinetic energy properties and weak equivalence principle in a space with GUP
• Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions
• Exact continuity equation in a space with minimal length