Zitterbewegung study in Dirac oscillator with laser pulse

Wang, Y.X.; Cao, Jie; Xiong, Shi‐Jie

doi:10.1140/epjb/e2012-30243-7

Cited by 20 publications

(13 citation statements)

References 28 publications

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“…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 realized experimentally [31] for the first time.…”

Section: Introductionmentioning

confidence: 99%

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Quantum phase transitions in the noncommutative Dirac oscillator

Panella

Roy

2014

Phys. Rev. A

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We study the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field in the noncommutative plane. It is shown that the effect of non-commutativity is twofold: i) momentum non commuting coordinates simply shift the critical value (B cr ) of the magnetic field at which the well known left-right chiral quantum phase transition takes place (in the commuting phase); ii) non-commutativity in the space coordinates induces a new critical value of the magnetic field, B * cr , where there is a second quantum phase transition (right-left), -this critical point disappears in the commutative limit-. The change in chirality associated with the magnitude of the magnetic field is examined in detail for both critical points. The phase transitions are described in terms of the magnetisation of the system. Possible applications to the physics of silicene and graphene are briefly discussed.

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Section: Introductionmentioning

confidence: 99%

“…Note that this is the only change that will affect the eigenfunctions of H 2D• (ũ nr,M ) and their normalisation constants C nr,M with respect to those of H 2D • (u nr,M and C nr,M ), c.f. Eqs (27,28)…”

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confidence: 99%

Quantum phase transitions in the noncommutative Dirac oscillator

Panella

Roy

2014

Phys. Rev. A

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“…Since the time of its proposal it has been the object of considerable attention in various branches of theoretical physics. For instance, it appears in mathematical physics [2][3][4][5][6][7][8][9][10][11], nuclear physics [12][13][14], quantum optics [15][16][17][18], supersymmetry [19][20][21], and noncommutativity [22][23][24][25]. Recently, the first experimental realization of the Dirac oscillator was realized by J.…”

Section: Introductionmentioning

confidence: 99%

On the κ-Dirac oscillator revisited

et al. 2014

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This Letter is based on the κ-Dirac equation, derived from the κ-Poincaré-Hopf algebra. It is shown that the κ-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac oscillator prescription, p → p − imωβr, in the κ-Dirac equation, one obtains the κ-Dirac oscillator. Using a decomposition in terms of spin angular functions, one achieves the deformed radial equations, with the associated deformed energy eigenvalues and eigenfunctions. The deformation parameter breaks the infinite degeneracy of the Dirac oscillator. In the case where ε = 0, one recovers the energy eigenvalues and eigenfunctions of the Dirac oscillator.

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“…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].…”

Section: Introductionmentioning

confidence: 99%

Re-entrant phase transitions in non-commutative quantum mechanics

Panella

Roy

2016

J. Phys.: Conf. Ser.

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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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Zitterbewegung study in Dirac oscillator with laser pulse

Cited by 20 publications

References 28 publications

Quantum phase transitions in the noncommutative Dirac oscillator

Quantum phase transitions in the noncommutative Dirac oscillator

On the κ-Dirac oscillator revisited

Re-entrant phase transitions in non-commutative quantum mechanics

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