Quantum groups and their applications in nuclear physics

Bonatsos, Dennis; Daskaloyannis, C.

doi:10.1016/s0146-6410(99)00100-3

Cited by 198 publications

(210 citation statements)

References 381 publications

(620 reference statements)

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“…It is useful to notice that the the q-boson operators can be expressed in terms of ordinary boson operators [4]. …”

Section: A Q-deformed Objectsmentioning

confidence: 99%

“…(3,4). Since this Hamiltonian operator is diagonal in the basis |n , the spectrum can be easily found:…”

Section: B Q-deformed Harmonic Oscillatormentioning

confidence: 99%

“…One can use the q-rotor to describe the rotational nuclear spectra of pair-pair nuclei [4]. The following expression defines the q-rotor:…”

Section: E Applications A) Rotational Spectra Of Pair-pair Nucleimentioning

confidence: 99%

“…So stretching effects can be taken into account by the deformation [4]. b) Vibrational and Rotational Spectra of Molecules The q-deformed rotor and oscillator can be used in the description of the energy spectrum of atoms and molecules.…”

Section: E Applications A) Rotational Spectra Of Pair-pair Nucleimentioning

confidence: 99%

“…These algebraic structures are usually called q-algebras, qdeformed algebras or quantum groups. In current theoretical investigations there have been extensive applications of qalgebras to many branches of physics [3,4,5]. In a sense, many successful standard applications of group theory in the past may be extended to a quantum group symmetry.…”

Section: Introductionmentioning

confidence: 99%

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Some unusual algebraic structures and their applications in many-body problems

Avancini¹

2003

Braz. J. Phys.

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In this paper, we introduce the q-deformed and quon algebras formalism. Some applications of these algebraic structures are considered. A possible connection of the quon algebra with composite particle systems is discussed and perspectives on using such mathematical objects in the Bose-Einstein condensation is presented. I IntroductionThe identification of algebraic structures in quantum physical systems has been an important tool for their understanding. Concepts of symmetry, invariance and group theory have shown to be of great utility from the beginning of quantum mechanics [1]. In a more recent context some unusual algebraic structures related to quantum inverse scattering methods and statistical mechanics models have appeared [2]. These algebraic structures are usually called q-algebras, qdeformed algebras or quantum groups. In current theoretical investigations there have been extensive applications of qalgebras to many branches of physics [3,4,5]. In a sense, many successful standard applications of group theory in the past may be extended to a quantum group symmetry. The aim of this paper is to discuss the use of q-algebras in the framework of many-body problems. We introduce the mathematical fundamentals as simply as possible and consider applications to q-deformed pseudo-spin models. These models can be considered as convenient theoretical laboratories where one can test the properties of these algebraic structures. We also show that the q-algebra formalism may be useful in the context of boson mappings,i. e., when the substitution of fermion pairs by bosons is convenient. A q-deformed algebra has a closely related algebraic structure which is called the quon algebra [6,7]. Such algebra was proposed to describe particles that violate statistics by a small amount. We consider the applications of quon algebras in boson mappings and nuclear models. We also show that they may be relevant in the study of composite bosonic particles (particles composed by fermion pairs), since deviations of a true bosonic particle could be accommodated in a natural way through the quon algebra. This formalism can also be applied to the study of Bose-Einstein condensation in trapped atoms [8]. This paper is organized as follows: In Sec.II quantum groups or q-algebras are defined and some of their properties and applications are analysed, in Sec.III the quon algebra formalism is considered and ,finally, in Sec.IV we present our conclusions. II q-deformed algebras or quantum groupsThe q-algebras or quantum groups are generalizations of classical Lie groups and Lie algebras and involve two fundamental ideas: Deformation and Non-commutative comultiplication [5]. Next, these two concepts will be discussed in detail. A. q-deformed objectsA q-boson algebra [9,10] (deformed harmonic oscillator) is a set of elements called q-boson operators: a (annihilation), a † (creation), N (number), which satisfy the following commutation relations:Note that the first and second commutation relations are equal to the common harmonic oscillator, ho...

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“…It is useful to notice that the the q-boson operators can be expressed in terms of ordinary boson operators [4]. …”

Section: A Q-deformed Objectsmentioning

confidence: 99%

“…(3,4). Since this Hamiltonian operator is diagonal in the basis |n , the spectrum can be easily found:…”

Section: B Q-deformed Harmonic Oscillatormentioning

confidence: 99%

“…One can use the q-rotor to describe the rotational nuclear spectra of pair-pair nuclei [4]. The following expression defines the q-rotor:…”

Section: E Applications A) Rotational Spectra Of Pair-pair Nucleimentioning

confidence: 99%

Section: E Applications A) Rotational Spectra Of Pair-pair Nucleimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Some unusual algebraic structures and their applications in many-body problems

Avancini¹

2003

Braz. J. Phys.

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Transparency and Enhancement in Fast and Slow Light in q‐Deformed Optomechanical System

Kundu

Miszczak

2022

Annalen der Physik

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Nonclassical phenomena can be enhanced by introducing q-deformation in optomechanical systems. This motivates investigation of the optical response in a q-deformed linearly coupled optomechanical system. The system consists of two deformed cavities that are linearly coupled to the motion of mechanical mirrors, and the cavities are coupled to each other by transmission strength parameter. This study shows that compared to non-deformed cases, the deformed system exhibits more rapid phase transition at the positions of transparency windows, causing stronger and enhanced fast and slow light phenomena. Moreover, in the region 0 < q < 0.5, the optomechanical system results in gain. Additionally, for a fixed deformation of cavities, by tuning the tunneling strength and optomechanical coupling, one can observe a delay and advancement in probe field in the order of milliseconds and even above milliseconds for fine-tuning of the coupling parameters. Finally, the bridge between mathematical and physical models is built by assuming the deformation to be a primitive root of unity, which indicates a class of anyon models. These results demonstrate that q-deformation provides a novel method for manipulating and significantly enhancing optical phenomena not only in arbitrarily deformed optomechanical systems but also in anyon models.

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Quantum (or q$$ q $$‐) operator equations and associated partial differential equations for bivariate Laguerre polynomials with applications to the q$$ q $$‐Hille‐Hardy type formulas

Cao,

Srivastava,

Zhang

2024

Math Methods in App Sciences

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Based on the extensive application of the ‐series and ‐polynomials including (for example) the ‐Laguerre polynomials in several fields of the mathematical and physical sciences, we attach great importance to the equations and related application issues involving the ‐Laguerre polynomials. The mission of this paper is to find the general ‐operational equation together with the expansion issue of the bivariate ‐Laguerre polynomials from the perspective of ‐partial differential equations. We also give some applications including some ‐Hille‐Hardy type formulas. In addition, we present the Rogers‐type formulas and the ‐type generating functions for the bivariate ‐Laguerre polynomials by the technique based upon ‐operational equations. Moreover, we derive a new generalized Andrews‐Askey integral and a new transformation identity involving the bivariate ‐Laguerre polynomials by applying ‐operational equations.

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Quantum groups and their applications in nuclear physics

Cited by 198 publications

References 381 publications

Some unusual algebraic structures and their applications in many-body problems

Some unusual algebraic structures and their applications in many-body problems

Transparency and Enhancement in Fast and Slow Light in q‐Deformed Optomechanical System

Quantum (or q$$ q $$‐) operator equations and associated partial differential equations for bivariate Laguerre polynomials with applications to the q$$ q $$‐Hille‐Hardy type formulas

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