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arXiv · 1411.5278

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

L. Menculini·O. Panella·P. Roy
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Abstract

We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field within a minimal length ($Δx_0=\hbar \sqrtβ$), 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 $β\to 0$. 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 $β\to 0$.

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L. Menculini, O. Panella, P. Roy. 2014-11-19. Quantum phase transitions of the Dirac oscillator in a minimal length scenario. https://doi.org/10.1103/physrevd.91.045032

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