It is well known that a Bose-Einstein (BE) condensate of atoms exists in a system of interacting Bose atoms at $T\lesssim T^{(i)}_{c}$, where $T^{(i)}_{c}$ is the BE condensation temperature of an ideal gas. It is also generally accepted that BE condensation is impossible at ``ultrahigh'' temperatures $T\gg T^{(i)}_{c}$. While the latter property has been theoretically proven for an ideal gas, no such proof exists for an interacting system, to our knowledge. In this paper, we propose an approximate mathematical proof for a finite, nonrelativistic, periodic system of $N$ spinless interacting bosons. The key point is that, at $T\gg T^{(i)}_{c}$, the main contribution to the occupation number $N_{0}=\frac{1}{Z}\sum_{\wp}e^{-E_{\wp}/k_{B}T}\langle Ψ_{\wp}|\hat{a}^{+}_{\mathbf{0}}\hat{a}_{\mathbf{0}}|Ψ_{\wp}\rangle$, corresponding to atoms with zero momentum, originates from the states containing $N$ elementary quasiparticles. These states do not contain the BE condensate of zero-momentum atoms, implying that an ultrahigh temperature should ``blur'' such a condensate.
Gas phase nuclear magnetic resonance (NMR) spectroscopy is a powerful method, determining physical and chemical properties of molecules and giving insight into internal spin dynamics. Work has been done to significantly expand the known database of gas phase proton and carbon chemical shieldings obtained in the zero-pressure limit, which provide a comparison to computational NMR methods performed in vacuo. The combination of new knowledge of gas phase shieldings and high-resolution capabilities are demonstrated on analysis of natural gas and volatile fractions of crude oil, which gives new applications of gas phase NMR towards the petroleum industry. Furthermore, more insight has been obtained in regards to gas spin-relaxation, particularly in multiple-quantum relaxation through comprehensive pulse sequences to filter double- and zero-quantum coherences. Finally, results will be given of efforts in 13C hyperpolarization via the Haupt effect, as most notably observed in γ-picoline. New enhancements in γ-picoline were obtained through careful sample preparation and more understanding has been achieved though examining the time periods of liquid helium immersion required to generate the hyperpolarization. The hyperpolarization in γ-picoline served as a proof of concept for the application of this paradigm to smaller molecules. Results are given of matrix-isolation techniques in gas phase methyl-rotors with intention to create hyperpolarization through A/E state rotor imbalance of methyl groups at 4.2 Kelvin.
The applicability to a quantum liquid of the standard classical formula connecting the compressibility with the coherent scattering cross section for large wavelengths, questioned by the author in a previous paper, is examined. The correctness of the standard formula is proved (a) at absolute zero (the density fluctuations being infranormal); (b) under quantum conditions for all temperatures at which the Wigner expansion converges (it is conjectured that for liquid helium the expansion may diverge below the lambdapoint); and (c) for a one-dimensional crystal for all temperatures. These results, while they stop short of a complete proof of the standard classical formula for all conditions, do extend considerably our knowledge of its range of validity.