Graphene coherent states

Díaz-Bautista, Erik; C., David J. Fernández

doi:10.1140/epjp/i2017-11794-y

Cited by 37 publications

(52 citation statements)

References 48 publications

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“…Now, we focus on the second part of the theorem concerning the number of bound states (33). The key feature is the existence of an integer s 0 for which…”

Section: Discussionmentioning

confidence: 99%

“…For this proof, we use the number of bound states given in Eq. (33) of Theorem 1 in order to obtain n = 0 ∀ > max . (B.8) Note that in the derivation of (33), we have not used the assumption of the existence of max that appears at the beginning of "Appendix B.1" so there is no circular reasoning.…”

Section: B2 Proof Of Theoremmentioning

confidence: 99%

“…Although Dirichlet BC can also be reached with the δ potential alone, the strength going to infinity could be troublesome for the Casimir self-energy of a sphere [25,26]. Some other discussions on properties of contact potentials are given in [20,[27][28][29], and their use in supersymmetric quantum mechanics is shown in [30][31][32][33][34][35] and references quoted therein. We do not intend to be exhaustive and just mention the recent literature.…”

Section: Introductionmentioning

confidence: 99%

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An approximation to the Woods–Saxon potential based on a contact interaction

et al. 2020

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We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial δ − δ contact interaction at the well edge. This contact potential is defined by appropriate matching conditions for the radial functions, thereby fixing a self-adjoint extension of the non-singular Hamiltonian. Since this model admits exact solutions for the wave function, we are able to characterize and calculate the number of bound states. We also extend some well-known properties of certain spherically symmetric potentials and describe the resonances, defined as unstable quantum states. Based on the Woods-Saxon potential, this configuration is implemented as a first approximation for a mean-field nuclear model. The results derived are tested with experimental and numerical data in the double magic nuclei 132 Sn and 208 Pb with an extra neutron.

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“…Now, we focus on the second part of the theorem concerning the number of bound states (33). The key feature is the existence of an integer s 0 for which…”

Section: Discussionmentioning

confidence: 99%

Section: B2 Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An approximation to the Woods–Saxon potential based on a contact interaction

et al. 2020

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“…However, depending on such a function f (N ), one would have the possibility to introduce a different description from the harmonic oscillator to get a deformed dynamics in phase space [10,11]. Therefore, in order to describe the effects of strain on the NLCS, in the following sections we consider some particular forms for the function f (N + 1) in Θ − f [31]. Moreover, we make use of use some physical quantities to analyze such quantum states, including the probability density ρ α (x), the mean energy H , the occupation number distribution P α (n) and the Heisenberg uncertainty relation (HUR).…”

Section: Some Examplesmentioning

confidence: 99%

Barut–Girardello coherent states for anisotropic 2D-Dirac materials

Díaz-Bautista

Concha‐Sánchez

Raya

2019

J. Phys.: Condens. Matter

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We construct the Barut-Girardello coherent states for charge carriers in anisotropic 2D-Dirac materials immersed in a constant homogeneous magnetic field which is orthogonal to the sample surface. For that purpose, we solve the anisotropic Dirac equation and identify the appropriate arising and lowering operators. Working in a Landau-like gauge, we explicitly construct nonlinear coherent states as eigenstates of a generalized annihilation operator with complex eigenvalues which depends on an arbitrary function f of the number operator. In order to describe the anisotropy effects on these states, we obtain the Heisenberg uncertainty relation, the probability density, mean energy value and occupation number distribution for three different functions f . For the case in which the anisotropy is caused by uniaxial strain, we obtain that when a stress is applied along the x-axis of the material surface, the probability density for the nonlinear coherent states is smaller compared to when the material is stressed along the orthogonal axis. * ediaz@fis.cinvestav.mx † yconcha@umich.mx ‡

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“…This framework can be considered as a generalization of Refs. [15,34]. From here, we start the construction of coherent states, which we outline in the remaining of this article, organized as follows: In Sec.…”

Section: Introductionmentioning

confidence: 99%

Coherent states in magnetized anisotropic 2D Dirac materials

Díaz-Bautista¹,

Oliva-Leyva²,

Concha‐Sánchez³

et al. 2020

J. Phys. A: Math. Theor.

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In this work, we construct coherent states for electrons in anisotropic 2D-Dirac materials immersed in a uniform magnetic field perpendicularly oriented to the sample. In order to describe the bidimensional effects on electron dynamics in a semiclassical approach, we adopt the symmetric gauge vector potential to describe the external magnetic field through a vector potential. By solving a Dirac-like equation with an anisotropic Fermi velocity, we identify two sets of scalar ladder operators that allow us to define generalized annihilation operators, which are generators of either the Heisenberg-Weyl or su(1, 1) algebra. We construct both bidimensional and su(1, 1) coherent states as eigenstates of such annihilation operators with complex eigenvalues. In order to illustrate the effects of the anisotropy on these states, we obtain their probability density and mean energy value. Depending upon the anisotropy, expressed by the ration between the Fermi velocities along the x-and y-axes, the shape of the probability density is modified on the xy-plane with respect to the isotropic case and according to the classical dynamics. * ediaz@fis.cinvestav.mx † moliva@fis.cinvestav.mx ‡ yconcha@umich.mx § raya@ifm.umich.mx arXiv:1907.06551v1 [quant-ph]

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Graphene coherent states

Cited by 37 publications

References 48 publications

An approximation to the Woods–Saxon potential based on a contact interaction

An approximation to the Woods–Saxon potential based on a contact interaction

Barut–Girardello coherent states for anisotropic 2D-Dirac materials

Coherent states in magnetized anisotropic 2D Dirac materials

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