q-Deformed Tamm-Dancoff oscillators: Representation, fermionic extension and physical application

In this paper, the q-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 q-fermion algebra of Tamm-Dancoff type are also studied. Second, the high-temperature thermostatistical properties of a gas of Tamm-Dancoff type q-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 q. 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.