Earlier work has confirmed that (i) observers can judge divergent receding lines, placed directly in front of them, to be parallel, and (ii) converging lines which are displaced laterally, so that they are viewed obliquely, can also be judged to be parallel. The former observation is in accord with traditional views of perspective while the latter, which is in accord with the depictions of obje...

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We consider two-flavor chiral perturbation theory ($\chi$PT) at finite isospin chemical potential $\mu_I$ and temperature $T$. calculate the effective quark pion condensates as functions of $T$ to next-to-leading order in low-energy expansion presence a pionic source. map out phase diagram $\mu_I$--$T$ plane. Numerically, we find that transition pion-condensed is second region validity $\chi$PT...

Using first-principles calculations, we show manifestations of the quantum size effect in the dielectric function ε(2) of free-standing Al(1 1 1) ultrathin films of 1 monolayer to 20 monolayers, taking into account size dependent contributions from both interband and intraband electronic transitions. Overall the in-plane components (interband transition) of ε(2) increase with film thickness at ...