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Remanent magnetization in geological samples may record the past intensity and direction of planetary magnetic fields. Traditionally, this magnetization is analyzed through measurements of the net magnetic moment of bulk millimeter to centimeter sized samples. However, geological samples are often mineralogically and texturally heterogeneous at submillimeter scales, with only a fraction of the ferromagnetic grains carrying the remanent magnetization of interest. Therefore, characterizing this magnetization in such cases requires a technique capable of imaging magnetic fields at fine spatial scales and with high sensitivity. To address this challenge, we developed a new instrument, based on nitrogen-vacancy centers in diamond, which enables direct imaging of magnetic fields due to both remanent and induced magnetization, as well as optical imaging, of room-temperature geological samples with spatial resolution approaching the optical diffraction limit. We describe the operating principles of this device, which we call the quantum diamond microscope (QDM), and report its optimized image-area-normalized magnetic field sensitivity (20 uT.um/Hz^1/2), spatial resolution (5 um), and field of view (4 mm), as well as trade-offs between these parameters. We also perform an absolute magnetic field calibration for the device in different modes of operation, including three-axis (vector) and single-axis (projective) magnetic field imaging. Finally, we use the QDM to obtain magnetic images of several terrestrial and meteoritic rock samples, demonstrating its ability to resolve spatially distinct populations of ferromagnetic carriers., Comment: 41 pages, 14 figures

Let a discrete group $G$ act on a unital simple C$^*$-algebra $A$ by outer automorphisms. We establish a Galois correspondence $H\mapsto A\rtimes_{\alpha,r}H$ between subgroups of $G$ and C$^*$-algebras $B$ satisfying $A\subseteq B \subseteq A\rtimes_{\alpha,r}G$, where $A\rtimes_{\alpha,r}G$ denotes the reduced crossed product. For a twisted dynamical system $(A,G,\alpha,\sigma)$, we also prove the corresponding result for the reduced twisted crossed product $A\rtimes^\sigma_{\alpha,r}G$., Comment: As pointed out to us by Prof. Yuhei Suzuki, there is an error in Lemma 2.9 of v1. Lemmas 2.8 and 2.9 in v1 are replaced by Lemmas 2.8-2.12 in v2. The main results of the paper are unchanged. A correction will be sent to Canad. J. Math

Let $G$ be a discrete group acting on a von Neumann algebra $M$ by properly outer $*$-automorphisms. In this paper we study the containment $M \subseteq M\rtimes_\alpha G$ of $M$ inside the crossed product. We characterize the intermediate von Neumann algebras, extending earlier work of other authors in the factor case. We also determine the $M$-bimodules that are closed in the Bures topology and which coincide with the $w^*$-closed ones under a mild hypothesis on $G$. We use these results to obtain a general version of Mercer's theorem concerning the extension of certain isometric $w^*$-continuous maps on $M$-bimodules to $*$-automorphisms of the containing von Neumann algebras., Comment: 27 pages. Minor revisions after referee's comments. Internat. J. Math., to appear

Zircon crystals offer a unique combination of suitability for high-precision radiometric dating and high resistance to alteration. Paleomagnetic experiments on ancient zircons may potentially constrain the earliest geodynamo, which holds broad implications for the early Earth interior and atmosphere. However, the ability of zircons to record accurately the geomagnetic field has not been fully demonstrated. Here we conduct thermal and room temperature alternating field (AF) paleointensity experiments on 767.1 thousand year old (ka) zircons from the Bishop Tuff, California. The rapid emplacement of these zircons in a well-characterized magnetic field provides a high-fidelity test of the zircons intrinsic paleomagnetic recording accuracy. Successful dual heating experiments on nine zircons measured using a superconducting quantum interference device (SQUID) microscope yield a mean paleointensity of 46.2 +/- 18.8 microtesla (1sigma), which agrees closely with high-precision results from Bishop Tuff whole rock (43.0 +/- 3.2 microtesla). High-resolution quantum diamond magnetic mapping, electron microscopy, and X-ray tomography indicate that the bulk of the remanent magnetization in Bishop Tuff zircons is carried by Fe oxides associated with apatite inclusions, which would be susceptible to destruction via metamorphism and aqueous alteration in older zircons. As such, while zircons can reliably record the geomagnetic field, robust zircon-derived paleomagnetic results require careful characterization of the ferromagnetic carrier and demonstration of their occurrence in primary inclusions. We further conclude that a combination of quantum diamond magnetometry and high-resolution imaging can provide detailed, direct characterization of the ferromagnetic mineralogy of geological samples., Comment: In review in Earth and Planetary Science Letters

We show that a number of key structural properties transfer between sufficiently close II$_1$ factors, including solidity, strong solidity, uniqueness of Cartan masas and property $\Gamma$. We also examine II$_1$ factors close to tensor product factors, showing that such factors also factorise as a tensor product in a fashion close to the original., Comment: Minor typos corrected. Munster J. Math., to appear. 16 pages, section 2 contains material from arXiv:1209.4116v2 which was removed from the final published version (v3)

We investigate numerically conditions for order and chaos in the dynamics of an interacting Bose- Einstein condensate (BEC) confined by an external trap cut off by a hard-wall box potential. The BEC is stirred by a laser to induce excitations manifesting as irregular spatial and energy oscillations of the trapped cloud. Adding laser stirring to the external trap results in an effective time-varying trapping frequency in connection with the dynamically changing combined external+laser potential trap. The resulting dynamics are analyzed by plotting their trajectories in coordinate phase space and in energy space. The Lyapunov exponents are computed to confirm the existence of chaos in the latter space. Quantum effects and trap anharmonicity are demonstrated to generate chaos in energy space, thus confirming its presence and implicating either quantum effects or trap anharmonicity as its generator. The presence of chaos in energy space does not necessarily translate into chaos in coordinate space. In general, a dynamic trapping frequency is found to promote chaos in a trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved by increasing the characteristic scale of the external trap with respect to the condensate size., Comment: 19 pages, 14 pages

We offer second year students the opportunity to explore Current Topics in Biophysics in a course co-taught by a physicist and a biologist. The interdisciplinary course allows university students to engage in analytical thinking that integrates physics and biology. The students are either biophysics majors (50%) or from a diversity of science majors (about 30% life sciences). All will have taken first year courses in biology, physics and mathematics. The course is divided into: 1) The application of physical approaches to biological problems using case studies (how high can a tree grow? and biological pumps are two examples); 2) An introduction to physics concepts for which potential applications are explored (biophotonics and its application in fluorescence microscopy and photodynamic therapy is one example); and 3) Presentations from industry and university researchers who describe careers, research and clinical applications of biophysics. Over the six years the course has been offered, students have achieved a B average independent of declared major. In course evaluations, students expressed a high level of satisfaction the course overall (91% were positive). However, students expressed reservations about the open-ended nature of assignments and test questions that approach biological problems using an analytical framework grounded in physics -the real challenge when implementing an open-ended problem solving approach to pedagogy.