Re-entrant phase transitions in non-commutative quantum mechanics

Abstract

Abstract. We discuss the (2+1)-dimensional Dirac oscillator in a magnetic field in non commutative quantum mechanics. The system is known to be characterised by a left rightchiral phase transition in ordinary Quantum mechanics. We show that the momentum noncommutativity shifts the know phase transition while the space non commutativity introduces a new right-left chiral quantum phase transition giving rise to the intriguing phenomenon of re-entrant phase transition observed in condensed matter as well as in black hole physics. IntroductionOn the basis that both string theory and quantum gravity indicate that space-time can be non-commutative [1-4] several quantum mechanical systems have been studied by a number of authors to determine the role of noncommutativity parameters on a variety of physical observables [5][6][7][8][9][10][11][12][13][14].The Dirac oscillator on the other hand is one of the very few relativistic systems which is exactly solvable [15][16][17][18][19][20][21][22]. In mathematical physics the Dirac oscillator has become a paradigm for the realization of covariant quantum models and it has found applications both in nuclear [23][24][25] and subnuclear [26,27] physics as well as in quantum optics [28][29][30]. Very recently a one dimensional version of the Dirac oscillator has been realised experimentally [31] for the first time with realistic prospects to realise in the near future the two dimensional version of the Dirac oscillator which may be feasible using networks of microwave coaxial cables [32][33][34]. It is interesting to note that a further interaction in the form of a homogeneous magnetic field can still be incorporated in the Dirac oscillator keeping the system still exactly solvable [28,[35][36][37][38] and this combined system has quite interesting properties. In some recent papers it has been shown that for this combined system there is a chirality phase transition if the magnitude of the magnetic field either exceeds or is less than a critical value B cr (which also depends on the oscillator strength) [39,40]. A consequence of this chirality phase transition is that the spectrum is different for B > B cr and B < B cr , B being the magnetic field strength.Our objective here is to analyse the same system, a 2D Dirac oscillator within a constant magnetic field, but in the framework of non-commutative space and momentum coordinates. It will be shown that in this case the critical value of the magnetic field depends not only on the oscillator strength but on the non-commutativity parameters as well. The interesting feature which we would like to emphasise, is that beside the two left-and right-chiral phases present also in the commutative case, in the non-commutative scenario there appear also a new third

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“…Since their discovery, reentrant phase transitions have been commonly observed in multicomponent fluid systems, gels, ferroelectrics, liquid crystals, and binary gases, where the reentrant behavior often emerges as a consequence of two (or more) 'competing driving mechanisms'. It can also take place in non-commutative spacetimes [166]. We refer the interested reader to a topical review [167] for more details.…”

Microscopic origin of black hole reentrant phase transitions

“…This phenomenon was first discovered in the nicotine/water mixture during a procedure in which, by increasing the temperature at a sufficient fixed percentage of nicotine, the homogeneous mixed state separated into distinct nicotine/water phases and then the homogeneous state reappeared [1]. More often, as a result of two (or more) competing driving mechanisms, such behavior has also been observed in multicomponent fluid systems, gels, ferroelectrics, liquid crystals, and binary gases as well as non-commutative spacetimes [2] (for more details, see the review [3]).…”

Ruppeiner Geometry, Reentrant Phase transition and Microstructure of Born-Infeld AdS Black Hole

“…[7]. This phenomenon is not limited to condensed matter physics, for example, in a (2 + 1) dimensional Dirac oscillator, in a magnetic field, in non-commutative spacetime a similar phase transition is observed [8].…”