  In this paper, we propose a scheme to generate entanglement between two
distant qubits (two-level atom) which are separately trapped in their own (in
general) non-Markovian dissipative cavities by utilizing entangling swapping.
We consider the case in which the qubits can move along their cavity axes
rather than a static state of motion. We first examine the role of movement of
the qubit by studying the entropy evolution for each subsystem. We calculate
the average entropy over the initial states of the qubit. Then by performing a
Bell state measurement on the fields leaving the cavities, we swap the
entanglement between qubit-field in each cavity into qubit-qubit and
field-field subsystems. We use the entangling power to measure the average
amount of swapped entanglement over all possible pure initial states. Our
results are presented in two weak and strong coupling regimes. Our results
illustrate the positive role of the movement of the qubits on the swapped
entanglement. It is revealed that by considering certain conditions for the
initial state of qubits, it is possible to achieve a maximally long-leaving
stationary entanglement (Bell state) which is entirely independent of the
environmental variables as well as the velocity of qubits. This happens when
the two qubits have the same velocities.
