Generalized coherent states under deformed quantum mechanics with maximum momentum

Yeo

2017

Int. J. Mod. Phys. A

We examine the (2+1)-dimensional Dirac equation in a homogenous magnetic field under the non-relativistic anti-Snyder model which is relevant to doubly/deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigen-solutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states n max due to the orthogonality of the polynomials and the maximum energy is truncated at n max . Similar to the minimal length case, the degeneracy of the Dirac-Landau levels in anti-Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit β → 0. By taking m → 0, we explore the motion of effective massless charged fermions in graphene like material and obtained a maximum bound of deformed parameter β max . Furthermore, we consider the modified energy dispersion relations and it's application in describing the behavior of neutrinos oscillation under modified commutation relations.

“…There is an upper bound for the maximum number of bound states. We interpret this as the genuine effects induced by MCR with maximum momentum cutoff, see [14,16,[26][27][28][29][30][31].…”

Section: (2+1)-dimensional Relativistic Dirac-landau Problem With Maxmentioning

confidence: 89%

Nonrelativistic anti-Snyder model and some applications

Yeo

2017

Int. J. Mod. Phys. A

“…Similar behavior is observed in our results on both KMM-even (odd) cat states. However, [4] showed that it is possible for ADV-deformed GK coherent states to exhibit both type of quantum statistics that depends on γ factor. This generic behavior is in different to their cat states counterpart in our ADV models.…”

Section: Photon Statistics and Number Squeezing Of Gkscsmentioning

confidence: 99%

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mentioning

confidence: 99%

Deformed Gazeau-Klauder Schrödinger cat states with modified commutation relations

2019

Phys. Rev. D

Generalized coherent states (GCs) under deformed quantum mechanics which exhibit intrinsic minimum length and maximum momentum have been well studied following Gazeau-Klauder approach in Refs. [1][2][3][4]. In this paper, as an extension to the study of quantum deformation, we investigate the famous Schrödinger cat states (SCs) under these two classes of quantum deformation. Following the concept of generalized Gazeau-Klauder Schrödinger cat states (GKSCs) in [5], we construct the deformed-GKSCs for both phenomenological models that exhibit intrinsic minimum length and/or maximum momentum. All comparisons between minimum length and maximum momentum deformations are illustrated and plots are done in even and odd cat states since they are one of the most important classic statistical characteristics of SCs. Probability distribution and entropies are studied. In general, deformed cat states do not possess the original even and odd states statistical properties. Nonclassical properties of the deformed-GKSCs are explored in terms of Mandel Q parameter, quadrature squeezing (∆X q ) · (∆Y q ) as well as Husimi quasi-probability distribution Q. Some of these distinguishing quantum-gravitational features may possibly be realized qualitatively and even be measured quantitatively in future experiments with the advanced development in quantum atomic and optics technology.

“…We show that, for spinless particle satisfies KG wave equation, the energy spectrum is bounded from above and hence the number of the bound state solutions is finite. This is the generic result of MCR's with intrinsic maximum momentum cutoff as in their nonrelativistic counterpart [20][21][22]. In Sect.…”

Section: Introductionmentioning

confidence: 99%

“…We have investigated large classes of deformed quantum mechanics of the latter type and used it to study several quantum mechanical systems such as deformed harmonic oscillator (DHO) [20], a particle in potential well/barrier and their bound/scattering states [21] as well as generalized coherent states with maximum momentum [22].…”

Section: Introductionmentioning

confidence: 99%

Generalized relativistic wave equations with intrinsic maximum momentum

2014

Mod. Phys. Lett. A

Self Cite

We examine the nonperturbative effect of instrinsic maximum momentum on the relativistic wave equations. Using the momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and Dirac oscillator. Similar to the undeformed case, bound state solutions are only possible when the strength of scalar potential are stronger than vector potential. The energy spectrum of the systems studied are bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have relevant applications in quarkonium confinement and quantum gravity phenomenology.