Reduced Quantum Anomaly in a Quasi-Two-Dimensional Fermi Superfluid: Significance of the Confinement-Induced Effective Range of Interactions.

A two-dimensional (2D) harmonically trapped interacting Fermi gas is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale-invariant value ω_{B}=2ω_{⊥}, where ω_{⊥} is the trapping frequency. The predicted maximum quantum anomaly (∼10%) has not been confirmed in experiments. Here, we theoretically investigate the zero-temperature density equation of state and the breathing mode frequency of an interacting Fermi superfluid at the dimensional crossover from three to two dimensions. We find that the simple model of a 2D Fermi gas with a single s-wave scattering length is not adequate to describe the experiments in the 2D limit, as commonly believed. A more complete description of quasi-2D leads to a much weaker quantum anomaly, consistent with the experimental observations. We clarify that the reduced quantum anomaly is due to the significant confinement-induced effective range of interactions.

Synthesis, chiroptical properties, and their theoretical simulation of some highly rotating benzotricamphor derivatives.

The large molecules 1-3 (69, 90, and 102 atoms, respectively), prepared by cyclotrimerization of enantiomerically pure derivatives of (-)-bornyl acetate, show intense ECD spectra, high optical rotation (OR) values (200-1300, in absolute value) dominated in sign and order of magnitude by the lowest-energy Cotton effects, that is, they are the ideal candidates to test the reliability of our "approximate" (TDDFT/B3LYP/6-31G* or smaller basis set) approach to the calculation of chiroptical properties. As a matter of fact, a correct simulation of the OR values and ECD spectra of 1 and 2 can be obtained even using STO-3G basis set and semiempirical or molecular mechanics input geometries: for 1, at the TDDFT/B3LYP/STO-3G level, the OR values are of the order of 500-550, versus an experimental value ranging between 660 and 690, depending on the solvent. On the contrary, the case of 3 (exp. OR between -1330 and -1500) is really complex (for instance, the OR values range between -3216 and -729 (TDDFT/B3LYP/6-31G* calculations) or -1824 and -444 (TDDFT/B3LYP/STO-3G calculations)), making the comparison between calculated and experimental values more difficult. The behavior of 3 is due to its molecular flexibility, whereas 1 is a really rigid molecules and 2 behaves (vide infra) as it were a rigid system. These observations strongly indicate that the conformational freedom constitutes one of the major difficulties for a correct but simple simulation of the chiroptical properties.