Seminarium Fizyki Materii Skondensowanej

Recent experimental work by Gasparini and coworkers examined small cubicalboxes of about 1 nm edge inscribed in a regular pattern on a silicon waferand filled with liquid 4He. The boxes are then coupled by addition of more He4 to form a thin supernatant film or via channels. Something most remarkable happens: even though the boxes have a mesoscopic spacing, calorimetric measurements show clear evidence of coupling between different boxes. The authors did not offer any theoretical analysis, but they made the intriguing suggestion that action at a distance effects of this type might be a common feature of critical systems, both quantum (like 4He) and classical. In our work, we have constructed a theoretical model of boxes containing a fluid phase below its critical temperature but at coexistence. The boxes are coupled together by rods (of arbitrary length) also containing the fluid; in this way, we can assemble lattices of coupled boxes like those of Gasparini et al. We have analysed this model using mesoscopic description and by Monte-Carlo simulation, which confirms our phenomenological results. We have shown that, by appropriate tuning of parameters, the lattice of boxes develops long ranged order, even though the rods are very long compared to their lateral dimensions; the simulations produce associated thermodynamic signatures. If we consider two boxes coupled by a single rod, then we have a model system that may have relevance as a potential mechanism for biological control. Our ideas may also be useful for networks in social science. Finally, we suspect that our ideas extend to quantum spin models and maybe even to systems of coupled quantum dots.