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By applying high magnetic and electric fields to a semiconductor superlattice (SL) we create quasi-one-dimensional or quasi-zero-dimensional electronic states. This reduced dimensionality restricts the range of inelastic scattering processes available to the conduction electrons, leading to an increase of the inelastic scattering time and a corresponding decrease of the electrical conductance. Our study reveals the fundamental link between current flow and energy dissipation in low-dimensional conductors, which is relevant to the exploitation of artificial nanowires and quantum dot SLs for novel applications, including recently proposed thermoelectric devices.