Relaxation rates and collision integrals for Bose-Einstein condensates

Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, $\mathcal{G}^{12}$, $\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals conserve momentum and energy during bogolon collisions, but only $\mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the contribution of only two collision integrals, $\mathcal{G}^{22}$ and $\mathcal{G}^{12}$. In this work, we show that the third collision integral $\mathcal{G}^{31}$ makes a significant contribution to the bogolon number relaxation rate and needs to be retained when computing relaxation properties of the BEC. We provide values of relaxation rates in a form that can be applied to a variety of dilute Bose-Einstein condensates.Comment: 18 pages, 4 figures, accepted by Journal of Low Temperature Physics 7/201

Use and abuse of zircon-based thermometers: A critical review and a recommended approach to identify antecrystic zircons

Zircon- and bulk-rock Zr-based thermometric parameters have become fundamental to petrogenetic models of magmatism, from which broader geochronological and tectonic implications are being made. In particular, petrogenetic models have become increasingly reliant on Ti concentration in zircon geothermometry (T<font size="small">_ZircTi</font>) and zircon saturation temperature (T<font size="small">_Zircsat</font>). A feature of many of these studies is an implicit assumption that all zircons present in the host igneous rock are autocrystic, that is, crystallised from the surrounding melt. However, it has long been recognised that zircons present in an igneous rock can be inherited either from the surrounding country rock or source region (xenocrysts), or from earlier phases of magmatism or the magmatic plumbing system (antecrysts). Distinguishing these different origins for zircon crystals or domains within crystals is not straightforward.\ud \ud Here, we first review the utility and reliability of zircon-based thermometers for petrogenetic studies and show that T<font size="small">_Zircsat</font> is a theoretical temperature and cannot be used to constrain magmatic or partial melting temperatures. It is a dynamic variable that changes during magma crystallisation, and essentially increases as fractional crystallisation proceeds, whereas true magmatic temperatures (T<font size="small">_Magma</font>) decrease. Generally, in Temperature-SiO₂ space, the cross-over point of these two temperatures is magmatic system dependent, and also affected by the type of calibration used for the T<font size="small">_Zircsat</font> calculations. Consequently, each magmatic system needs to be evaluated independently to assess the validity and usefulness of T<font size="small">_Zircsat</font>. A fundamental conclusion of T<font size="small">_Zircsat</font> and T<font size="small">_Magma</font> relationships assessed here is that new zircon generally only crystallises in silicic (granitic/rhyolitic) melt compositions, and thus autocrystic zircons should not be assumed to be present in igneous rocks with bulk compositions < 64 wt% SiO₂, although inherited and minor zircons crystallising from late-stage differentiated melt pockets can be present. This highlights the importance of discriminating autocrystic from inherited zircons in igneous rocks.\ud \ud We then review techniques available to discriminate autocrystic from inherited zircons, and propose a new methodology to assist in the identification of autocrystic zircons for emplacement age determination and separate evaluation of inherited zircon components. The approach uses two strands of data: 1) zircon data such as zircon morphologies, textures, compositions and U-Pb ages, and 2) whole-rock data, in particular SiO₂ and coupled geothermometry (T<font size="small">_Zircsat</font> and T<font size="small">_Magma</font>) to estimate whether the magma was zircon-saturated or undersaturated. To test this new protocol, we use as examples, several Phanerozoic granitic rocks intersected by drilling in Queensland where contextual information is limited, and show how antecrystic and xenocrystic zircons and monazites can be distinguished. In contrast, where zircons are metamict (for example, high U and Th-rich zircons), much of the ability to discriminate is impacted because such zircons have suffered Pb loss and have modified compositions (e.g., higher T<font size="small">_ZircTi</font>). We recommend an integrated approach incorporating whole-rock chemistry, independent geothermometric constraints, zircon composition, textures and ages obtained by routine cathodoluminescence and LA-ICP-MS or ion microprobe analysis to provide increased confidence for the discrimination of inherited zircons from autocrystic zircons and determination of the emplacement age