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International Journal of Modern Physics B

q-Deformed Tamm–Dancoff oscillators: Coherent state and thermostatistics

Won Sang Chung, Abdullah Algin

Published May 20, 2014• 6 citations
Publisher

Abstract

The q-deformed bosonic Tamm–Dancoff oscillator algebra is considered. The coherent state of the q-deformed bosonic Tamm–Dancoff oscillator algebra is first constructed in detail. Second, the high-temperature thermostatistical properties of a gas of the Tamm–Dancoff oscillators are investigated. For high temperatures, the specific heat, the entropy and the equation of state for the system are derived in terms of the real deformation parameter q. The results obtained by the effects of Tamm–Dancoff type q-deformation show that they could be useful for further researches on understanding of mutual interactions between bosons and fermions in many-body quantum systems.

DOI
10.1142/s0217979214501306

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The q-deformed bosonic Tamm–Dancoff oscillator algebra is considered. The coherent state of the q-deformed bosonic Tamm–Dancoff oscillator algebra is first constructed in detail. Second, the high-temperature thermostatistical properties of a gas of the Tamm–Dancoff oscillators are investigated. For high temperatures, the specific heat, the entropy and the equation of state for the system are derived in terms of the real deformation parameter q. The results obtained by the effects of Tamm–Dancoff type q-deformation show that they could be useful for further researches on understanding of mutual interactions between bosons and fermions in many-body quantum systems.
In this paper, the [Formula: see text]-deformed bosonic Tamm–Dancoff oscillator algebra is considered. First, the quantum algebraic and representative properties of these deformed bosons are analyzed in detail. The representations of the [Formula: see text]-fermion algebra of Tamm–Dancoff type are also studied. Second, the high-temperature thermostatistical properties of a gas of Tamm–Dancoff type [Formula: see text]-fermions are investigated. The fermionic distribution function and the other important thermodynamic functions such as the entropy and the specific heat are derived in terms of the real deformation parameter [Formula: see text]. Finally, the time evaluation of a two-level atom in a Tamm–Dancoff oscillator trap interacting with a single-mode traveling light field is concisely discussed.
Abstract 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.
In this paper, we propose a full characterization of a generalized q-deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the condition satisfied by the deformed q-number to define the algebra structure function. Particular Fock spaces involving finite and infinite dimensions are examined. A deformed calculus is performed as well as a coordinate realization for this algebra. A relevant example is exhibited. Associated coherent states are constructed. Finally, some thermodynamics aspects are computed and 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 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 Tc of standard case of bosons condensation. Similar results are presented for the deformed Bose gas model of the Tamm–Dancoff (TD) type.