THE QUANTUM REFRIGERATOR IN A TWO-QUBIT XXZ HEISENBERG MODEL

The four-level entangled quantum refrigerator (QR) is studied in the XXZ Heisenberg model for the two-qubits. The Hamiltonian of the problem includes the exchange parameters J(x) = J(y) = J and J(z) = alpha J along the x-, y- and z-directions, respectively, and constant external magnetic field B in the z-direction. The parameter alpha is introduced into the model which controls the strength of the exchange parameter J(z) in comparison to J(x) and J(y), thus, our investigation of QR includes the XX (alpha = 0.0), XXX (alpha = 1.0) and XXZ (for other alpha's) Heisenberg models. The two-qubits are assumed to be in contact with two heat reservoirs at different temperatures. The concurrences for a two-qubit are used as a measure of entanglement and then the expressions for the amount of heat transferred, the work performed and the efficiency are derived. The contour, i.e., the isoline maps, and some two-dimensional plots of the above mentioned thermodynamic quantities are illustrated