Quantum Mpemba prediction in three-qubit XYZ spin chains using low fractional orders

In this work, we investigate the possibility of predicting the phenomena of the quantum Mpemba fractionally, where it is assumed that a single qubit, which is initially prepared in three different cases, hottest, hotter and colder states, interacting with its surroundings made up of two qubits via XYZ chain model in the presence of Dzyaloshinskii–Moriya interaction ( DM ). The trace distance between the equilibrium and time fractional evolution of the system is used to predict the Mpemba phenomena. The impact of the interaction parameters and the fractional orders on the stabilization behavior of the qubit is discussed. It is shown that thermalization case is reached at small fraction order during a short interaction time. However, as one increases the fractional orders, the thermalization is observed at large interaction time. For ferromagnetic case and large strength of DM interaction, the stabilization behavior is predicted at small interaction time, while for anti-ferromagnetic and small values of DM , the stabilization is reached at large interaction time.