Thermostatistical properties of the blackbody radiation and Debye crystal model through Fibonacci oscillators

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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A Study of q-Deformed Bosons, and Their Implications to Quantum Optics

Şenay

2024

SAUJS

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In this study, we investigate three types of q-deformed boson oscillators, focusing on their mathematical frameworks and thermodynamic properties. We calculate key thermodynamic quantities, such as internal energy and entropy, as functions of the deformation parameter q. Our results reveal that these oscillators are eigenstates of specific deformed boson annihilation operators. We also analyze their unique characteristics and implications in deformed quantum optics. Furthermore, we examine the impact of q-deformation on qutrit logic gates, including cycle, self-shift, controlled cycle, controlled self-shift, Feynman, ternary Toffoli, and Fredkin gates, highlighting their altered computational properties. This research contributes to a deeper understanding of q-deformed systems and their applications in quantum computing. Overall, it opens new avenues for exploring the interplay between deformation parameters and quantum information processing.

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Thermostatistical properties of the blackbody radiation and Debye crystal model through Fibonacci oscillators

Cited by 3 publications

References 139 publications

Intermediate statistics: Addressing the thermoelectric properties of solids

Intermediate statistics: Addressing the thermoelectric properties of solids

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

A Study of q-Deformed Bosons, and Their Implications to Quantum Optics

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