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 $\beta \to 0$.

7 pages, 1 figure

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Cited by in corpus (1)

• Symmetry operators and separation of variables in the $(2+1)$-dimensional Dirac equation with external electromagnetic field