Real Planck distribution for a complex Q-boson gas

Angelopoulou, Pinelopi; Baskoutas, Sotirios; Falco, L. De; Jannussis, A.; Mignani, Roberto; Sotiropoulou, A

doi:10.1088/0305-4470/27/17/002

Cited by 12 publications

(5 citation statements)

References 11 publications

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“…A problem associated with complex deformations as the ones considered above is that the energy eigenvalues become complex as well. A way to avoid this problem has been introduced recently by Jannussis and collaborators 284,285 .…”

Section: The Question Of Complete Breaking Of Symmetries and Some App...mentioning

confidence: 99%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

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Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools (q-numbers, q-analysis, q-oscillators, q-algebras), the su q (2) rotator model and its extensions, the construction of deformed exactly soluble models (u(3)⊃so (3) model, Interacting Boson Model, Moszkowski model), the 3-dimensional q-deformed harmonic oscillator and its relation to the nuclear shell model, the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to the structure of molecules and of atomic clusters, as well as an outlook are also given.

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Section: The Question Of Complete Breaking Of Symmetries and Some App...mentioning

confidence: 99%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

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“…One of the most typical examples is the case of the so called q-oscillators, which satisfy an algebra in terms of deformed commutation relations rather than an algebra covariant under quantum group transformations. A recent application of the q-fermionic algebra [7] to the Lipkin model can be found in Reference [8], and some approaches dealing with the thermodynamics of q-bosons are given in References [9,10,11,12,13].…”

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confidence: 99%

Thermodynamics of a free SUq(2) fermionic system

Ubriaco

1996

Physics Letters A

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“…In conclusion, the relevance of the q ↔ q −1 symmetry is well-known in q-oscillators from the mathematical structure as well as in applications [15][16][17][18]. Similarly we expect the symmetric Tsallis thermostatistics to be useful in many future investigations.…”

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confidence: 59%

GENERALIZED SYMMETRIC NONEXTENSIVE THERMOSTATISTICS AND q-MODIFIED STRUCTURES

Lavagno

Swamy

1999

Mod. Phys. Lett. B

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We formulate a convenient generalization of the q-expectation value, based on the analogy of the symmetric quantum groups and q-calculus, and show that the q ↔ q −1 symmetric nonextensive entropy preserves all of the mathematical structure of thermodynamics just as in the case of non-symmetric Tsallis statistics. Basic properties and analogies with quantum groups are discussed.PACS: 05.20.-y; 05.70.-a; 05.30.-d In the last few years there has been much interest in nonextensive classical and quantum physics. The nonextensive statistical mechanics proposed by Tsallis [1,2], has been the source of inspiration for many investigations in systems which represent multifractal properties, long-range interactions and/or long-range memory effects [3]. On the other hand, quantum groups and the derived q-deformed algebraic structure such as q-oscillators, based on the deformation of standard oscillator commutation-anticommutation relations, have created considerable interest in mathematical physics and in several applications [4]. The investigations described above are only two apparently unrelated areas in nonextensive physics. Although a complete understanding of the connection between nonextensive statistics and q-deformed structure is still lacking, many papers are devoted to the study of a deep connection between these two non-extensive formalisms [5][6][7][8][9].Tsallis statistics is a q-nonsymmetric formalism i.e., not invariant under q ↔ q −1 . Recently Abe [6] has employed a connection between Tsallis entropy and the non-symmetric Jackson derivative. Because the requirement of invariance under q ↔ q −1 is very important in quantum groups [10], the above connection allows him to extend the Tsallis entropy to the q-symmetric one by means of a symmetric Jackson derivative. However, Abe has not extended the definition of the expectation value of an observable to the symmetric case and thus unable to formulate the thermostatistics which will preserve the Legendre transformation of standard thermodynamics in contrast to the Tsallis statistics which does. We would like to point out that Ref.[7] introduces a two-parameter modification for the entropy and for the expectation value of an observable but does not also produce a consistent formulation of thermostatistics.The purpose of this letter is to show how the q ↔ q −1 symmetric generalization of the Tsallis entropy together with a natural generalization of the q-expectation value produces a 1

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Real Planck distribution for a complex Q-boson gas

Cited by 12 publications

References 11 publications

Quantum groups and their applications in nuclear physics

Quantum groups and their applications in nuclear physics

Thermodynamics of a free SUq(2) fermionic system

GENERALIZED SYMMETRIC NONEXTENSIVE THERMOSTATISTICS AND q-MODIFIED STRUCTURES

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