Macroscopic Quantum Behaviour of Periodic Quantum Systems

Martín-Ruiz, A.; Bernal, Jorge; Carbajal-Domínguez, Adrian

doi:10.4236/jmp.2014.51007

Cited by 10 publications

(9 citation statements)

References 25 publications

(36 reference statements)

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“…This is a delicate issue because λ is regarded as a nonzero fundamental length scale of the polymer theory, and it cannot be removed when working in H poly , no matter how small is λ. This is analogous to the quantum-classical transition problem through → 0 limit, because is a nonzero fundamental constant of the quantum theory [15,16].…”

Section: The Polymer-schr öDinger Transitionmentioning

confidence: 92%

“…We observe that the polymer result exhibits small oscillations superimposed on the Moshinsky result. This situation resembles the quantum-classical transition problem, where the classical distribution follows the spatial local average of the quantum probability density for large quantum numbers [15,16]. In this framework, fig.…”

Section: The Shutter Problem In Polymer Quantum Mechanicsmentioning

confidence: 97%

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Diffraction in time of polymer particles

Martín-Ruiz

2014

Phys. Rev. D

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We study the quantum dynamics of a suddenly released beam of particles using a background independent (polymer) quantization scheme. We show that, in the first order of approximation, the low-energy polymer distribution converges to the standard quantum-mechanical result in a clear fashion, but also arises an additional small polymer correction term. We find that the high-energy polymer behaviour becomes predominant at short distances and short times. Numerical results are also presented. We find that particles whose wave functions satisfy the polymer wave equation do not exhibit the diffraction in time phenomena. The implementation of a lower bound to the possible resolution of times into the time-energy Heisenberg uncertainty relation is briefly discussed.

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Section: The Polymer-schr öDinger Transitionmentioning

confidence: 92%

Section: The Shutter Problem In Polymer Quantum Mechanicsmentioning

confidence: 97%

Diffraction in time of polymer particles

Martín-Ruiz

2014

Phys. Rev. D

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“…In H poly = L 2 (R d , dµ d ) this limit does not exist because λ is regarded as a fundamental length scale. This is analogous to the quantum-classical transition through → 0 limit, where is a nonzero fundamental constant of quantum theory [41,42].…”

Section: Polymer Quantizationmentioning

confidence: 91%

Casimir effect in polymer scalar field theory

2020

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In this paper, we study the Casimir effect in the classical geometry of two parallel conducting plates, separated by a distance L, due to the presence of a minimal length λ arising from a background independent (polymer) quantization scheme. To this end, we polymer-quantize the classical Klein-Gordon Hamiltonian for a massive scalar field confined between the plates and obtain the energy spectrum. The minimal length scale of the theory introduces a natural cutoff for the momenta in the plane parallel to the plates and a maximum number of discrete modes between the plates. The zero-point energy is calculated by summing over the modes, and by assuming λ L, we expressed it as an expansion in powers of 1/N , being N = L/λ the number of points between the plates. Closed analytical expressions are obtained for the Casimir energy in the cases of small and large scalar mass limits.

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“…In Refs. [1,27,28] the authors propose a simple mathematical method to derive the classical probability distribution of a quantum system from its corresponding quantum mechanical analogue. This method has been successfully applied to the harmonic oscillator, the infinite square well and the Kepler's problem.…”

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confidence: 99%

“…The methodology of our research is based on the one described in Refs. [1,27,28], but we include the nonrelativistic limit. The formulation of this article is purely in first quantization and we only consider single eigenstates of the 1-dimensional Klein-Gordon and Dirac equations.…”

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On the correspondence principle for the Klein-Gordon and Dirac Equations

Hernández,

Aguilar,

Bernal

2019

Preprint

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In this paper we apply the Bohr's correspondence principle to analize the asymptotic behavior of the Klein-Gordon and Dirac probability densities. It is found that in the non-relativistic limit, the densities reduce to their respective classical single-particle probability distributions plus a series of quantum corrections. The procedure is applied in two basic problems, the relativistic quantum oscillator and the relativistic particle in a box. The particle and antiparticle solutions are found to yield the same classical distribution plus quantum correction terms for the proposed limit. In the quantum oscillator case, a κ parameter modifies the probability distribution. Its origin is briefly discussed in terms of energy.

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Macroscopic Quantum Behaviour of Periodic Quantum Systems

Cited by 10 publications

References 25 publications

Diffraction in time of polymer particles

Diffraction in time of polymer particles

Casimir effect in polymer scalar field theory

On the correspondence principle for the Klein-Gordon and Dirac Equations

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