  We introduce a variation of the discrete time quantum walk, the nonreversal
quantum walk, which does not step back onto a position which it has just
occupied. This allows us to simulate a dimer and we achieve it by introducing a
new type of coin operator. The nonrepeating walk, which never moves in the same
direction in consecutive time steps, arises by a permutation of this coin
operator. We describe the basic properties of both walks and prove that the
even-order joint moments of the nonrepeating walker are independent of the
initial condition, being determined by five parameters derived from the coin
instead. Numerical evidence suggests that the same is the case for the
nonreversal walk. This contrasts strongly with previously studied coins, such
as the Grover operator, where the initial condition can be used to control the
standard deviation of the walker.
