A lower bound on the partition function for a classical charge symmetric system

A lower bound is obtained for the grand canonical partition function (and hence for the pressure) of a charge symmetric system with positive definite interaction. For the Coulomb interaction the lower bound on the pressure is the Debye-Hückel approximation.     

Impact of silica environment on hyperfine interactions in 𝜖-Fe2O3 nanoparticles

Magnetic nanoparticles have found broad applications in medicine, especially for cell targeting and transport, and as contrast agents in MRI. Our samples of ??-Fe₂O₃ nanoparticles were prepared by annealing in silica matrix, which was leached off and the bare particles were then coated with amorphous silica layers of various thicknesses. The distribution of particle sizes was determined from the TEM pictures giving the average size ～20 nm and the thickness of silica coating ～5; 8; 12; 19 nm. The particles were further characterized by the XRPD and DC magnetic measurements. The nanoparticles consisted mainly of ??-Fe₂O₃ with admixtures of ～1 % of the α phase and less than 1 % of the γ phase. The hysteresis loops displayed coercivities of ～2 T at room temperature. The parameters of hyperfine interactions were derived from transmission Mössbauer spectra. Observed differences of hyperfine fields for nanoparticles in the matrix and the bare ones are ascribed to strains produced during cooling of the composite. This interpretation is supported by slight changes of their lattice parameters and increase of the elementary cell volume deduced from XRD. The temperature dependence of the magnetization indicated a two-step magnetic transition of the ??-Fe₂O₃ nanoparticles spread between ～85 K and ～150 K, which is slightly modified by remanent tensile stresses in the case of nanoparticles in the matrix. The subsequent coating of the bare particles by silica produced no further change in hyperfine parameters, which indicates that this procedure does not modify magnetic properties of nanoparticles.     

Torelli Theorem for the Deligne–Hitchin Moduli Space

Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let denote the corresponding Deligne–Hitchin moduli space. We prove that the complex analytic space determines (up to an isomorphism) the unordered pair , where is the Riemann surface defined by the opposite almost complex structure on X.     

Bragg grating writing through the polyimide coating of high NA optical fibres with femtosecond IR radiation

Bragg gratings are written with ultrafast 800 nm radiation and a phase mask through the polyimide polymer coatings of commercially available high NA fibres that are both unloaded and loaded with high pressure hydrogen gas. For polyimide coated fibres with very high germanium core concentrations, index modulations greater than 1 × 10⁻⁴ are induced. Stable core index modulations 60% of their original value were present after 115 h at 500 °C.     

Laser excitation of positronium in the Paschen-Back regime

Zeeman mixing of singlet and triplet 2P states of positronium (Ps) atoms, followed by decay back to the ground state, can effectively turn a long-lived triplet atom into a short-lived singlet state, which would seem to preclude laser cooling of Ps in a magnetic field. Here we report experiments which show that, in fact, because of the large splitting of the n=2 states in a high magnetic field (the Paschen-Back regime), the amount of such mixing diminishes approximately exponentially with an increasing magnetic field >0.01 T and is essentially eliminated above ～2 T. Thus, laser cooling of Ps should be feasible at high fields, which will facilitate the production of a Ps Bose-Einstein condensate.