Hom-Lie-Virasoro symmetries in Bloch electron systems and quantum plane in tight binding models

Aizawa, Naruhiko; Sato, Haru-Tada

doi:10.1016/j.nuclphysb.2023.116336

Cited by 3 publications

(1 citation statement)

References 70 publications

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“…In conclusion, the present construction on the q-deformed quantum mechanics and the related q-calculus along with all the results above can be applied to analyze a non-linear behavior in complex systems in diverse fields of research, where both the undeformed quantum mechanics and the standard quantum statistics do not work. When we consider the recent developments on some other potential application areas of deformed oscillators such as in studies on describing the Bose polaron based on a bath of non-interacting q-deformed bosons [51], addressing the non-classicality of the states in an optical quantum communication process [110], constructing three-level quantum states (qutrits) for quantum computation [31], discussing the symmetry properties in a discrete Bloch electron system [111], the present TD-deformed boson model along with its quantum and statistical features developed here may be used to understand the details about the interaction mechanism in the same systems. It may also provide physical insight into several research issues such as in determining the quality of signal propagation in waveguides due to some defects in a given material, approaching the properties of dark matter constituents with the use of TD type q-deformed statistics, analyzing a non-linearity in electromagnetic field vibrations, studying vibrational characteristics of diatomic and polyatomic molecules and understanding the details about electron-phonon interactions such as in an ionic crystal.…”

Section: Discussionmentioning

confidence: 99%

q-Deformed quantum mechanics related to the Tamm-Dancoff oscillator algebra and some physical applications

Chung,

Algin

2024

Phys. Scr.

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In this paper, we consider a system of the q-deformed bosonic Tamm-Dancoff oscillators, whose spectrum has some exponential cutoff factors at high energies. We first investigate the q-calculus in the Tamm-Dancoff (TD) boson algebra, and within this framework, the q-derivative, q-integral and q-exponential function are introduced. Using these properties, we construct a new formalism for the q-deformed quantum mechanics, which accordingly involve the q-adjoint operator and the q-Hermitian operator properties. We then derive the q-deformed Heisenberg relation, and develop the q-Hermitian momentum operator. The q-deformed Schrödinger equation is introduced, and as applications, we study the momentum eigenfunction and one-dimensional box problem. Another application of the TD type deformation onto lattice oscillations is also discussed through a model of the q-deformed Debye solid. Finally, other potential applications of the TD-oscillators gas model are concisely pointed out.

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Section: Discussionmentioning

confidence: 99%

q-Deformed quantum mechanics related to the Tamm-Dancoff oscillator algebra and some physical applications

Chung,

Algin

2024

Phys. Scr.

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Moyal product and generalized Hom-Lie-Virasoro symmetries in Bloch electron systems

Sato

2024

Nuclear Physics B

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Two-parameter deformed quantum mechanics based on Fibonacci calculus and Debye crystal model of two-parameter deformed quantum statistics

Algin,

Chung

2024

Eur. Phys. J. Plus

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Starting on the basis of Fibonacci calculus and Fibonacci oscillator algebra, we introduce the main properties to develop a new formalism for the two-parameter $$({q}_{1},{q}_{2})$$ ( q 1 , q 2 ) -deformed quantum mechanics, where $${q}_{1}$$ q 1 and $${q}_{2}$$ q 2 are real positive independent deformation parameters. As applications of such a two-parameter deformed formalism, we investigate the behavior of a quantum particle in some different physical phenomena covering the free particle and the inverse-harmonic potential case. The effect of two deformation parameters on the wave functions for these applications is studied. Another application is carried out onto the quantum statistics of lattice oscillations through a model of the $$({q}_{1},{q}_{2})$$ ( q 1 , q 2 ) -deformed phonon gas, and it is shown that the high- and low-temperature behavior of the model specific heat differs notably from the classical theories for the interval $$0<({q}_{1},{q}_{2})<\infty $$ 0 < ( q 1 , q 2 ) < ∞ . We also construct a two-parameter deformed non-extensive entropy based on some elements of the Fibonacci calculus and discuss its possible connection with the Tsallis entropy in non-extensive statistical mechanics. Finally, other possible application areas of the present two-parameter $$({q}_{1},{q}_{2})$$ ( q 1 , q 2 ) -deformed construction on quantum mechanics are discussed.

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Hom-Lie-Virasoro symmetries in Bloch electron systems and quantum plane in tight binding models

Cited by 3 publications

References 70 publications

q-Deformed quantum mechanics related to the Tamm-Dancoff oscillator algebra and some physical applications

q-Deformed quantum mechanics related to the Tamm-Dancoff oscillator algebra and some physical applications

Moyal product and generalized Hom-Lie-Virasoro symmetries in Bloch electron systems

Two-parameter deformed quantum mechanics based on Fibonacci calculus and Debye crystal model of two-parameter deformed quantum statistics

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