Quantum mechanics of spin transfer in coupled electron-spin chains

The manner in which spin-polarized electrons interact with a magnetized thin film is currently described by a semi-classical approach. This in turn provides our present understanding of the spin transfer, or spin torque phenomenon. However, spin is an intrinsically quantum mechanical quantity. Here, we make the first strides towards a fully quantum mechanical description of spin transfer through spin currents interacting with a Heisenberg-coupled spin chain. Because of quantum entanglement, this requires a formalism based on the density matrix approach. Our description illustrates how individual spins in the chain time-evolve as a result of spin transfer.Comment: 4 pages, 3 (colour) figure

What Is Dilution, Anyway?

Ever since the Supreme Court decided Moseley v. V Secret Catalogue, Inc. in 2003, an amendment to the Federal Trademark Dilution Act (“FTDA”) has appeared inevitable. Congress almost certainly meant to adopt a “likelihood of dilution” standard in the original statute, and the 2006 revisions correct its sloppy drafting. Substituting a “likelihood of dilution” standard for “actual dilution,” however, does not resolve a deeper philosophical question that has always lurked in the dilution debate: what is dilution, and how does one prove or disprove its probability? The statutory definition notwithstanding, this issue remains largely unanswered, leaving the courts with the responsibility—and the power—to delineate dilution’s scope. Judging from the ambiguous legislative history and the messy history of dilution in the states, courts will have broad discretion in exercising their authority. The absence of any consistent normative vision for dilution means that judges will shape that vision, along with the doctrinal framework for pursuing it. In doing so, they face a stark choice between one approach that largely comports with traditional trademark theory, and another that transforms the law’s purpose and effect. Because the more radical option imposes substantial costs without any obvious social benefits, courts would do well to adopt the more modest version

Is Napster a VCR--The Implications of Sony for Napster and Other Internet Technologies

The staple article of commerce doctrine must strike a balance between a copyright holder\u27s legitimate demand for effective-not merely symbolic-protection of the statutory monopoly, and the rights of others freely to engage in substantially unrelated areas of commerce. In Sony Corp. of America v. Universal City Studios, the Supreme Court created the copyright version of the so-called staple article of commerce doctrine. \u272 Its stated objective was to strike a balance between the incentive objectives of copyright3 and the interests of the public in access to new technology.4 As defined by the Court, the doctrine prevents copyright holders from interfering with the sale of technologies that may be used to infringe, but that also have substantial non-infringing uses. \u27

Magnetic Multilayer Edges in Bernal-Stacked Hexagonal Boron Nitride

Single-layer $\it{h}$-BN is known to have edges with unique magnetism, however, in the commonly fabricated multilayer $\text{AA}^{\prime}$-$\it{h}$-BN, edge relaxations occur that create interlayer bonds and eliminate the unpaired electrons at the edge. Recently, a robust method of growing the unconventional Bernal-stacked $\it{h}$-BN (AB-$\it{h}$-BN) has been reported. Here, we use theoretical approaches to investigate the nitrogen-terminated zigzag edges in AB-$\it{h}$-BN that can be formed in a controlled fashion using a high-energy electron beam. We find that these "open" edges remain intact in bilayer and multilayer AB-$\it{h}$-BN, enabling researchers potentially to investigate these edge states experimentally. We also investigate the thermodynamics of the spin configurations at the edge by constructing a lattice model that is based on parameters extracted from a set of first-principles calculations. We find that the edge spins in neighboring layers interact very weakly, resulting in a sequence of independent spin chains in multilayer samples. By solving this model using Monte Carlo simulations, we can determine nm-scale correlation lengths at liquid-N$_{2}$ temperatures and lower. At low temperatures, these edges may be utilized in magnetoresistance and spintronics applications

Copyright Law and Subject Matter Specificity: The Case of Computer Software

Drawing on recent work by Dan Burk and Mark Lemley in the patent context, this paper explores the extent to which courts have adapted pre-existing copyright doctrines to the special case of computer software. We argue that a number of courts have, as has been widely recognized, significantly adapted copyright doctrines to deal with special features of the computer software market. We further argue that these adaptations have, by and large, positively sought to strike a balance between the copyright act\u27s dual goals of incentive and access. Despite this general trend toward adaptation, however, we point to a handful of instances in which courts and legislatures have adopted a more wooden approach to software copyright questions. Given the nuanced nature of copyright law\u27s underlying goals, we contend that some level of flexibility and adaptation is critical in the software context, where network effects, interoperability, and functionality play a prominent role. We suggest that copyright law should-and indeed must-have some vehicle for considering these unique features of software markets, and we recommend a number of changes to maintain the more flexible, policy-lever approach to software copyright law

Prediction of High Temperature Superconductivity in Experimentally Observed Solid Hydrogen

Recent experimental developments in hydrogen-rich materials in high pressures have put this class of materials above others in the race toward room temperature superconductivity. As it is the basis of all the materials in this class, the efforts to determine the properties of pure solid hydrogen at high pressures remain intense. Most notably, a recent experimental study of the metallization of hydrogen identified the crystal phase of the solid as the C2/c-24 molecular phase up to ~425 GPa. It is possible that the observed metallization is caused by band structure effects and not a structural phase transition, and the material remains in this crystal phase up to higher pressures. Therefore it is of crucial importance to determine the superconducting properties of the C2/c-24 phase. Here, we employ a Wannier function-based dense k-point and q-point sampling to compute the electron-phonon coupling and superconducting properties of molecular hydrogen in the C2/c-24 phase. We find that the material has a high superconducting transition temperature of 242 K at 500 GPa. We also find that the transition temperature rapidly increases with pressure in the 400 - 500 GPa range

Observed Metallization of Hydrogen Interpreted as a Band Structure Effect

A recent experimental study of the metallization of hydrogen tracked the direct band gap and vibron frequency via infrared measurements up to ~425 GPa [P. Loubeyre et al., Nature 577, 631 (2020)]. Above this pressure, the direct gap has a discontinuous drop to below the minimum experimentally accessible energy (~0.1 eV). The authors suggested that this observation is caused by a structural phase transition between the C2/c-24 molecular phase to another molecular phase such as Cmca-12. Here, through ab initio calculations of pressure dependent vibron frequency and direct band gap, we find that the experimental data is consistent with the C2/c-24 phase up to 425 GPa, and suggest that this consistency extends beyond that pressure. Specifically, we find that qualitative changes in the band structure of the C2/c-24 phase lead to a discontinuous drop of the direct band gap, which can explain the observed drop without a structural transition. This alternative scenario naturally explains the absence of hysteresis in the measurements

Modelling the dynamics of intramammary E. coli infections in dairy cows: understanding mechanisms that distinguish transient from persistent infections

The majority of intramammary infections with Escherichia coli in dairy cows result in transient infections with duration of about 10 days or less, although more persistent infections (2 months or longer) have been identified. We apply a mathematical model to explore the role of an intracellular mammary epithelial cell reservoir in the dynamics of infection. We included biological knowledge of the bovine immune response and known characteristics of the bacterial population in both transient and persistent infections. The results indicate that varying the survival duration of the intracellular reservoir reproduces the data for both transient and persistent infections. Survival in an intracellular reservoir is the most likely mechanism that ensures persistence of E. coli infections in mammary glands. Knowledge of the pathogenesis of persistent infections is essential to develop preventive and treatment programmes for these important infections in dairy cows

Anisotropy and Isotope Effect in Superconducting Solid Hydrogen

Elucidating the phase diagram of solid hydrogen is a key objective in condensed matter physics. Several decades ago, it was proposed that at low temperatures and high pressures, solid hydrogen would be a metal with a high superconducting transition temperature. This transition to a metallic state can happen through the closing of the energy gap in the molecular solid or through a transition to an atomic solid. Recent experiments have managed to reach pressures in the range of 400-500 GPa, providing valuable insights. There is strong evidence suggesting that metallization via either of these mechanisms occurs within this pressure range. Computational and experimental studies have identified multiple promising crystal phases, but the limited accuracy of calculations and the limited capabilities of experiments prevent us from determining unequivocally the observed phase or phases. Therefore, it is crucial to investigate the superconducting properties of all the candidate phases. Recently, we reported the superconducting properties of the C2/c-24, Cmca-12, Cmca-4 and I41/amd-2 phases, including anharmonic effects. Here, we report the effects of anisotropy on superconducting properties using Eliashberg theory. Then, we investigate the superconducting properties of deuterium and estimate the size of the isotope effect for each phase. We find that the isotope effect on superconductivity is diminished by anharmonicity in the C2/c-24 and Cmca-12 phases and enlarged in the Cmca-4 and I41/amd-2 phases. Our anharmonic calculations of the C2/c-24 phase of deuterium agree closely with the most recent experiment by Loubeyre et al. [Phys. Rev. Lett. 29, 035501 (2022)], indicating that the C2/c-24 phase remains the leading candidate in this pressure range, and has a strong anharmonic character. These characteristics can serve to distinguish among crystal phases in experiment