Accordingly, an adiabatic pump operation is based on varying more than one parameter, while for non-adiabatic pumps modulation of a single parameter may suffice for DC current generation. The best known example is the peristaltic mechanism that combines a cyclic squeezing operation with on/off switching of entrance/exit valves. Adiabatic quantum pumping is closely related to a class of current-driven nanomotors named Adiabatic quantum motor. While in a quantum pump, the periodic movement of some classical parameters pumps quantum particles from one reservoir to another, in a quantum motor a DC current of quantum particles induce the cyclic motion of the classical device. Said relation is due to the Onsager reciprocal relations between electric currents and current-induced forces , taken as generalized fluxes on one hand, and the chemical potentials biases and the velocity of the control parameters , taken as generalized forces on the other hand., . where and are indexes over the mechanical degrees of freedom and the leads respectively, and the subindex "" implies that the quantities should be evaluated at equilibrium, i.e. and . Integrating the above equation for a system with two leads yields the well known relation between the pumped charge per cycle , the work done by the motor , and the voltage bias , . The Kubo approach to quantum stirring Consider a closed system which is described by a Hamiltonian that depends on some control parameters . If is an Aharonov Bohm magnetic flux through the ring, then by Faraday law is the electro motive force. If linear response theory applies we have the proportionality , where is the called the Ohmic conductance. In complete analogy if we change the current is , and if we change the current is , where and are elements of a conductance matrix. Accordingly, for a full pumping cycle: The conductance can be calculated and analyzed using the Kubo formula approach to quantum pumping, which is based on the theory of adiabatic processes. Here we write the expression that applies in the case of low frequency "quasi static" driving process (the popular terms "DC driving" and "adiabatic driving" turn out to be misleading so we do not use them): where is the current operator, and is the generalized force that is associated with the control parameter . Though this formula is written using quantum mechanical notations it holds also classically if the commutator is replaced by