Understanding Heisenberg's 'Magical' Paper of July 1925: a New Look at the Calculational Details

In July 1925 Heisenberg published a paper [Z. Phys. 33, 879-893 (1925)] which ended the period of `the Old Quantum Theory' and ushered in the new era of Quantum Mechanics. This epoch-making paper is generally regarded as being difficult to follow, perhaps partly because Heisenberg provided few clues as to how he arrived at the results which he reported. Here we give details of calculations of the type which, we suggest, Heisenberg may have performed. We take as a specific example one of the anharmonic oscillator problems considered by Heisenberg, and use our reconstruction of his approach to solve it up to second order in perturbation theory. We emphasize that the results are precisely those obtained in standard quantum mechanics, and suggest that some discussion of the approach - based on the direct computation of transition amplitudes - could usefully be included in undergraduate courses in quantum mechanics.Comment: 24 pages, no figures, Latex, submitted to Am. J. Phy

Normal state properties of high angle grain boundaries in (Y,Ca)Ba2Cu3O7-delta

By lithographically fabricating an optimised Wheatstone bridge geometry, we have been able to make accurate measurements of the resistance of grain boundaries in Y1-xCaxBa2Cu3O7-d between the superconducting transition temperature, Tc, and room temperature. Below Tc the normal state properties were assessed by applying sufficiently high currents. The behaviour of the grain boundary resistance versus temperature and of the conductance versus voltage are discussed in the framework charge transport through a tunnel barrier. The influence of misorientation angle, oxygen content, and calcium doping on the normal state properties is related to changes of the height and shape of the grain boundary potential barrier.Comment: 17 pages, 1 table, 5 figures, submitted to PR

POMICS: A Simulation Disease Model for Timing Fungicide Applications in Management of Powdery Mildew of Cucurbits

A weather-based simulation model, called Powdery Mildew of Cucurbits Simulation (POMICS), was constructed to predict fungicide application scheduling to manage powdery mildew of cucurbits. The model was developed on the principle that conditions favorable for Podosphaera xanthii, a causal pathogen of this crop disease, generate a number of infection cycles in a single growing season. The model consists of two components that (i) simulate the disease progression of P. xanthii in secondary infection cycles under natural conditions and (ii) predict the disease severity with application of fungicides at any recurrent disease cycles. The underlying environmental factors associated with P. xanthii infection were quantified from laboratory and field studies, and also gathered from literature. The performance of the POMICS model when validated with two datasets of uncontrolled natural infection was good (the mean difference between simulated and observed disease severity on a scale of 0 to 5 was 0.02 and 0.05). In simulations, POMICS was able to predict high- and low-risk disease alerts. Furthermore, the predicted disease severity was responsive to the number of fungicide applications. Such responsiveness indicates that the model has the potential to be used as a tool to guide the scheduling of judicious fungicide applications

Induced magnetization in La0.7_{0.7}Sr0.3_{0.3}MnO3_3/BiFeO3_3 superlattices

Using polarized neutron reflectometry (PNR), we observe an induced magnetization of 75$\pm$ 25 kA/m at 10 K in a La$_{0.7}$Sr$_{0.3}$MnO$_3$ (LSMO)/BiFeO$_3$ superlattice extending from the interface through several atomic layers of the BiFeO$_3$ (BFO). The induced magnetization in BFO is explained by density functional theory, where the size of bandgap of BFO plays an important role. Considering a classical exchange field between the LSMO and BFO layers, we further show that magnetization is expected to extend throughout the BFO, which provides a theoretical explanation for the results of the neutron scattering experiment.Comment: 5 pages, 4 figures, with Supplemental Materials. To appear in Physical Review Letter

An estimate for the Morse index of a Stokes wave

Stokes waves are steady periodic water waves on the free surface of an infinitely deep irrotational two dimensional flow under gravity without surface tension. They can be described in terms of solutions of the Euler-Lagrange equation of a certain functional. This allows one to define the Morse index of a Stokes wave. It is well known that if the Morse indices of the elements of a set of non-singular Stokes waves are bounded, then none of them is close to a singular one. The paper presents a quantitative variant of this result.Comment: This version contains an additional reference and some minor change

Enhancement of Critical Current Density in low level Al-doped MgB2

Two sets of MgB2 samples doped with up to 5 at. % of Al were prepared in different laboratories using different procedures. Decreases in the a and c lattice parameters were observed with Al doping confirming Al substitution onto the Mg site. The critical temperature (Tc) remained largely unchanged with Al doping. For 1 - 2.5 at.% doping, at 20K the in-field critical current densities (Jc's) were enhanced, particularly at lower fields. At 5K, in-field Jc was markedly improved, e.g. at 5T Jc was enhanced by a factor of 20 for a doping level of 1 at.% Al. The improved Jcs correlate with increased sample resistivity indicative of an increase in the upper critical field, Hc2, through alloying.Comment: 17 pages, 4 figures, to be published in Superconductor Science and Technolog

Strongly Enhanced Current Densities in Superconducting Coated Conductors of YBa2Cu3O7-x + BaZrO3

There are numerous potential applications for superconducting tapes, based on YBa2Cu3O7-x (YBCO) films coated onto metallic substrates. A long established goal of more than 15 years has been to understand the magnetic flux pinning mechanisms which allow films to maintain high current densities out to high magnetic fields. In fact, films carry 1-2 orders of magnitude higher current densities than any other form of the material. For this reason, the idea of further improving pinning has received little attention. Now that commercialisation of conductors is much closer, for both better performance and lower fabrication costs, an important goal is to achieve enhanced pinning in a practical way. In this work, we demonstrate a simple and industrially scaleable route which yields a 1.5 to 5-fold improvement in the in-field current densities of already-high-quality conductors

Colossal terahertz magnetoresistance at room temperature in epitaxial La0.7Sr0.3MnO3 nanocomposites and single-phase thin films

Colossal magnetoresistance (CMR) is demonstrated at terahertz (THz) frequencies by using terahertz time-domain magnetospectroscopy to examine vertically-aligned nanocomposites (VANs) and planar thin films of La_0.7Sr_0.3MnO_3. At the Curie temperature (room temperature) the THz conductivity of the VAN was dramatically enhanced by over 2 orders of magnitude under the application of a magnetic field, with a non-Drude THz conductivity that increased with frequency. The dc CMR of the VAN is controlled by extrinsic magnetotransport mechanisms such as spin-polarized tunneling between nano-grains. In contrast, we find that THz CMR is dominated by intrinsic, intragrain transport: the mean free path was smaller than the nanocolumn size, and the planar thin-film exhibited similar THz CMR to the VAN. Surprisingly, the observed colossal THz magnetoresistance suggests that the magnetoresistance can be large for ac motion on nanometre length scales, even when the magnetoresistance is negligible on the macroscopic length scales probed by dc transport. This suggests that colossal magnetoresistance at THz frequencies may find use in nanoelectronics and in THz optical components controlled by magnetic fields. The VAN can be scaled in thickness while retaining a high structural quality, and offers a larger THz CMR at room temperature than the planar film

Long-term effects of delayed-release dimethyl fumarate in multiple sclerosis: Interim analysis of ENDORSE, a randomized extension study

BACKGROUND: Delayed-release dimethyl fumarate (DMF) demonstrated strong efficacy and a favorable benefit-risk profile for patients with relapsing-remitting multiple sclerosis (RRMS) in phase 3 DEFINE/CONFIRM studies. ENDORSE is an ongoing long-term extension of DEFINE/CONFIRM. OBJECTIVE: We report efficacy and safety results of a 5-year interim analysis of ENDORSE (2 years DEFINE/CONFIRM; minimum 3 years ENDORSE). METHODS: In ENDORSE, patients randomized to DMF 240 mg twice (BID) or thrice daily (TID) in DEFINE/CONFIRM continued this dosage, and those initially randomized to placebo (PBO) or glatiramer acetate (GA) were re-randomized to DMF 240 mg BID or TID. RESULTS: For patients continuing DMF BID (BID/BID), annualized relapse rates were 0.202, 0.163, 0.139, 0.143, and 0.138 (years 1-5, respectively) and 63%, 73%, and 88% were free of new or enlarging T2 hyperintense lesions, new T1 hypointense lesions, and gadolinium-enhanced lesions, respectively, at year 5. Adverse events (AEs; serious adverse events (SAEs)) were reported in 91% (22%; BID/BID), 95% (24%; PBO/BID), and 88% (16%; GA/BID) of the patients. One case of progressive multifocal leukoencephalopathy was reported in the setting of severe, prolonged lymphopenia. CONCLUSION: Treatment with DMF was associated with continuously low clinical and magnetic resonance imaging (MRI) disease activity in patients with RRMS. These interim data demonstrate a sustained treatment benefit and an acceptable safety profile with DMF

Safety and efficacy of bexarotene in patients with relapsing-remitting multiple sclerosis (CCMR One): a randomised, double-blind, placebo-controlled, parallel-group, phase 2a study

Background: Progressive disability in multiple sclerosis occurs because CNS axons degenerate as a late consequence of demyelination. In animals, retinoic acid receptor RXR-gamma agonists promote remyelination. We aimed to assess the safety and efficacy of a non-selective retinoid X receptor agonist in promoting remyelination in people with multiple sclerosis. Methods: This randomised, double-blind, placebo-controlled, parallel-group, phase 2a trial (CCMR One) recruited patients with relapsing-remitting multiple sclerosis from two centres in the UK. Eligible participants were aged 18–50 years and had been receiving dimethyl fumarate for at least 6 months. Via a web-based system run by an independent statistician, participants were randomly assigned (1:1), by probability-weighted minimisation using four binary factors, to receive 300 mg/m2 of body surface area per day of oral bexarotene or oral placebo for 6 months. Participants, investigators, and outcome assessors were masked to treatment allocation. MRI scans were done at baseline and at 6 months. The primary safety outcome was the number of adverse events and withdrawals attributable to bexarotene. The primary efficacy outcome was the patient-level change in mean lesional magnetisation transfer ratio between baseline and month 6 for lesions that had a baseline magnetisation transfer ratio less than the within-patient median. We analysed the primary safety outcome in the safety population, which comprised participants who received at least one dose of their allocated treatment. We analysed the primary efficacy outcome in the intention-to-treat population, which comprised all patients who completed the study. This study is registered in the ISRCTN Registry, 14265371, and has been completed. Findings: Between Jan 17, 2017, and May 17, 2019, 52 participants were randomly assigned to receive either bexarotene (n=26) or placebo (n=26). Participants who received bexarotene had a higher mean number of adverse events (6·12 [SD 3·09]; 159 events in total) than did participants who received placebo (1·63 [SD 1·50]; 39 events in total). All bexarotene-treated participants had at least one adverse event, which included central hypothyroidism (n=26 vs none on placebo), hypertriglyceridaemia (n=24 vs none on placebo), rash (n=13 vs one on placebo), and neutropenia (n=10 vs none on placebo). Five (19%) participants on bexarotene and two (8%) on placebo discontinued the study drug due to adverse events. One episode of cholecystitis in a placebo-treated participant was the only serious adverse event. The change in mean lesional magnetisation transfer ratio was not different between the bexarotene group (0·25 percentage units [pu; SD 0·98]) and the placebo group (0·09 pu [0·84]; adjusted bexarotene–placebo difference 0·16 pu, 95% CI –0·39 to 0·71; p=0·55). Interpretation: We do not recommend the use of bexarotene to treat patients with multiple sclerosis because of its poor tolerability and negative primary efficacy outcome. However, statistically significant effects were seen in some exploratory MRI and electrophysiological analyses, suggesting that other retinoid X receptor agonists might have small biological effects that could be investigated in further studies. Funding: Multiple Sclerosis Society of the United Kingdom