In general formula_35 can be written as a sum of two terms: one has to do with dissipation, while the other, denoted as formula_36 has to do with geometry. The dissipative part vanishes in the strict quantum adiabatic limit, while the geometrical part formula_36 might be non-zero. It turns out that in the strict adiabatic limit formula_36 is the "Berry curvature" (mathematically known as ``two-form"). Using the notations formula_39 and formula_40 we can rewrite the formula for the amount of pumped particles as  where we define the normal vector formula_42 as illustrated. The advantage of this point of view is in the intuition that it gives for the result: formula_1 is related to the flux of a field formula_44 which is created (so to say) by "magnetic charges" in formula_45 space. In practice the calculation of formula_44 is done using the following formula:  This formula can be regarded as the quantum adiabatic limit of the Kubo formula. The eigenstates of the system are labeled by the index formula_48. These are in general many body states, and the energies are in general many body energies. At finite temperatures a thermal average over formula_49 is implicit. The field formula_36 can be regarded as the rotor of "vector potential" formula_51 (mathematically known as the "one-form"). Namely, formula_52. The ``Berry phase" which is acquired by a wavefunction at the end of a closed cycle is  Accordingly, one can argue that the "magnetic charge" that generates (so to say) the formula_36 field consists of quantized "Dirac monopoles". It follows from gauge invariance that the degeneracies of the system are arranged as vertical Dirac chains. The "Dirac monopoles" are situated at formula_45 points where formula_49 has a degeneracy with another level. The Dirac monopoles picture is useful for charge transport analysis: the amount of transported charge is determined by the number of the Dirac chains encircled by the pumping cycle. Optionally it is possible to evaluate the transported charge per pumping cycle from the Berry phase by differentiating it with respect to the Aharonov–Bohm flux through the device. The Ohmic conductance of a mesoscopic device that is connected by leads to reservoirs is given by the Landauer formula: in dimensionless units the Ohmic conductance of an open channel equals its transmission.