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Journal of Physics A Mathematical and General

Real Planck distribution for a complex Q-boson gas

Pinelopi Angelopoulou, Sotirios Baskoutas, Leonardo Falco, A. D. Jannussis, R Mignani, A A Sotiropoulou

Published Sep 7, 1994• 9 citations
Publisher

Abstract

We discuss the energy-density distribution for a gas of q-bosons with complex deformation parameter by exploiting a new q-complex oscillator algebra in which both the number operator and the energy eigenvalues are real. The corresponding Planck distribution generalizes the results obtained for a real q-boson gas, including Wien's and Stephan's laws, and the role of an effective Planck constant depending on the parameter modulus.

DOI
10.1088/0305-4470/27/17/002

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We discuss the energy-density distribution for a gas of q-bosons with complex deformation parameter by exploiting a new q-complex oscillator algebra in which both the number operator and the energy eigenvalues are real. The corresponding Planck distribution generalizes the results obtained for a real q-boson gas, including Wien's and Stephan's laws, and the role of an effective Planck constant depending on the parameter modulus.
Complex-q boson gas as an application of complex-q oscillator algebra is reinvestigated by using an algebra that was introduced recently by us 5 as an improvement over the earlier studies of Gupta et al.2 and Angelopoulou et al.3 The improvements are in terms of the use of Hermitian operators (real eigenvalues) and constant boson number. The formalism is therefore exact and results in the modifications of some of the approximate results of Gupta et al.2 A possible connection of the q-deformed, effective Planck constant to the (minimum) q-uncertainty relation is also discussed.
In the study of many-particle systems both the interaction of particles can be essential and such feature as their internal (composite) structure. To describe these aspects, the theory of deformed oscillators is very efficient. Viewing the particles as p,q-deformed bosons, in the corresponding p,q-Bose gas model we obtain in explicit form virial expansion along with the 2nd to 5th virial coefficients. The obtained virial coefficients depend on the deformation parameters p,q in the form symmetric under p<->q, and at p->1, q->1 turn into those known for usual bosons. Besides real parameters, we analyze the case of complex mutually conjugate p and q and find interesting implications. Also, the critical temperature is derived (for the p,q-Bose gas) and compared with the T_c of standard case of Bose condensation. Similar results are presented for the deformed Bose gas model of the Tamm-Dancoff type.
In the framework of the q -deformed oscillator algebra we investigate the nature of the interaction among the particles of a free q -boson gas with a view to interpreting the interaction in terms of the general properties of the q -deformation. It is shown that many thermodynamic quantities characterizing the q -boson system can be expressed as power series in the number of particles operator or as a series in the deformation parameter q , implying that the q -deformation can originate from the interaction among the particles of the ensemble. As an example, we derive the virial expansion of the q -boson gas, showing that the lowest order coefficient reduces to the standard virial coefficient of an undeformed boson gas, while the higher order coefficients contain effects arising from interaction.
Using the exact realization of the Morse oscillator problem in terms of SO(2,1) symmetry and its bosonization, the corresponding q deformation is performed. The ground-state energy is found to remain constant for all arbitrary (zero, real, imaginary, or complex) values of the q-deformation parameter. By fitting the resulting q-deformed energy-level spectrum to data for the hydrogen molecule in its ground electronic state, it is shown that, depending upon the value of the scaling constant, a considerable improvement results for the real and/or imaginary q deformation over the corresponding result for the classical Morse oscillator, and that the best fit is obtained in the q-deformed case with a complex value of the deformation parameter.