A novel “photovoltaics (PV) + electrolyzer” concept is presented using a simple, small, and completely stand-alone non-biased device for solar-driven overall water splitting. Three or four spherical-shaped p-n junction silicon balls were successfully connected in series, named “SPHELAR.” SPHELAR possessed small projected areas of 0.20 (3PVs) and 0.26 cm2 (4PVs) and exhibited working voltages sufficient for water electrolysis. Impacts of the configuration on the PV module performance were carefully analyzed, revealing that a drastic increase in the photocurrent (≈20%) was attained by the effective utilization of a reflective sheet. Separate investigations on the electrocatalyst performance showed that non-noble metal based materials with reasonably small sizes (<0.80 cm2) exhibited substantial currents at the PV working voltage. By combining the observations of the PV characteristics, light management and electrocatalyst performance, solar-driven overall water splitting was readily achieved, reaching solar-to-hydrogen efficiencies of 7.4% (3PVs) and 6.4% (4PVs).

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A quantum theory of noncommutative fields was recently proposed by Carmona, Cortez, Gamboa and Mendez ([1]). The implications of the noncommutativity of the fields, intended as the requirements [φ,, were analyzed on the basis of an analogy with previous results on the so-called "noncommutative harmonic oscillator construction". Some departures from Lorentz symmetry turned out to play a key role in the emerging framework. We first consider the same hamiltonian proposed in [1], and we show that the theory can be analyzed straightforwardly within the framework of Heisenberg evolution equation without any need of making reference to the "noncommutative harmonic oscillator construction". We then consider a rather general class of alternative hamiltonians, and we observe that violations of Lorentz invariance are inevitably encountered. These violations must therefore be viewed as intrinsically associated with the proposed type of noncommutativity of fields, rather than as a consequence of a specific choice of hamiltonian.