Effect of Adiabatic Phonons on Striped and Homogeneous Ground States

The effects of adiabatic phonons on a spin-fermion model for high T_c cuprates are studied using numerical simulations. In the absence of electron-phonon interactions (EPI), stripes in the ground state are observed for certain dopings while homogeneous states are stabilized in other regions of parameter space. Different modes of adiabatic phonons are added to the Hamiltonian:breathing, shear and half-breathing modes. Diagonal and off-diagonal electron-phonon couplings are considered. It is observed that strong diagonal EPI generate stripes in previously homogeneous states, while in striped ground states an increase in the diagonal couplings tends to stabilize the stripes, inducing a gap in the density of states (DOS) and rendering the ground state insulating. The off-diagonal terms, on the other hand, destabilize the stripes creating inhomogeneous ground states with a pseudogap at the chemical potential in the DOS. The breathing mode stabilizes static diagonal stripes; while the half-breathing (shear) modes stabilize dynamical (localized) vertical and horizontal stripes. The EPI induces decoherence of the quasi-particle peaks in the spectral functions.Comment: latex, 9 pages,13 figure

From Grimm to Glory: Simulated Oral Argument as a Component of Legal Education\u27s Signature Pedagogy

The past two years have been a period of landmark transformation in legal education. With the issuance of the Carnegie and Best Practices for Legal Education Reports, law schools and law professors have revisited the essential process of analyzing and transforming legal pedagogy. This widespread reexamination of the law school curriculum has yielded two important changes in legal education; first, law schools-including those in the top tier-have begun radically to amend their curricular goals and structures; and, second, legal scholars have begun to turn their attention to the theory and implementation of better legal education. As Carnegie and Best Practices note, this nascent metamorphosis in scholarly thought about legal education has the potential to transform both the law school and the law practice experience, as well-grounded pedagogy will remove the barriers to learning that some law students have historically experienced while better preparing them to practice law. This Article represents one of the first concrete responses to Carnegie and Best Practices. In proposing that law professors regularly use simulated oral argument exercises to supplement traditional Socratic dialogue, it meets head on the concerns expressed by Best Practices and Carnegie that over-reliance on the Langdell method neither mimics law practice nor nurtures student learning. It also responds directly to the suggestion in both Reports that simulation exercises may yield better legal analysis and knowledge. Finally, this Article advances a novel theory directly related to the objectives and conclusions of the Reports: namely, thatfor experienced advocates and law students alike, practice oral argument may be a starting point, rather than a mere end point, for teaching, learning, and executing the fundamentals of legal analysis. In the style of the transcribed classroom conversations of the Carnegie Report, it discusses and demonstrates by example a simulation exercise designedfor professors to use in introducing this teaching methodology. The exercise, based on seven fairy tales used as precedent cases, provides a familiar, non-threatening technique for students to learn about rule synthesis, weight of authority, analogy and distinction, and theme through oral argument

Inhomogeneous charge textures stabilized by electron-phonon interactions in the t-J model

We study the effect of diagonal and off-diagonal electron-phonon coupling in the ground state properties of the t-J model. Adiabatic and quantum phonons are considered using Lanczos techniques. Charge tiles and stripe phases with mobile holes (localized holes) are observed at intermediate (large) values of the diagonal electron-phonon coupling. The stripes are stabilized by half-breathing modes, while the tiles arise due to the development of extended breathing modes. Off-diagonal terms destabilize the charge inhomogeneous structures with mobile holes by renormalizing the diagonal coupling but do not produce new phases. Buckling modes are also studied and they seem to induce a gradual phase separation between hole rich and hole poor regions. The pairing correlations are strongly suppressed when the holes are localized. However, in charge inhomogeneous states with mobile holes no dramatic changes, compared with the uniform state, are observed in the pairing correlations indicating that D-wave pairing and moderate electron-phonon interactions can coexist.Comment: minor changes; to appear in Physical Review

The temperature dependence of the local tunnelling conductance in cuprate superconductors with competing AF order

Based on the $t-t'-U-V$ model with proper chosen parameters for describing the cuprate superconductors, it is found that near the optimal doping at low temperature ($T$), only the pure d-wave superconductivity ($d$SC) prevails and the antiferromagnetic (AF) order is completely suppressed. At higher $T$, the AF order with stripe modulation and the accompanying charge order may emerge, and they could exist above the $d$SC transition temperature. We calculate the local differential tunnelling conductance (LDTC) from the local density of states (LDOS) and show that their energy variations are rather different from each other as $T$ increases. Although the calculated modulation periodicity in the LDTC/LDOS and bias energy dependence of the Fourier amplitude of LDTC in the "pseudogap" region are in good agreement with the recent STM experiment [Vershinin $et al.$, Science {\bf 303}, 1995 (2004)], we point out that some of the energy dependent features in the LDTC do not represent the intrinsic characteristics of the sample

Hydrogen-oxygen proton-exchange membrane fuel cells and electrolyzers

Hydrogen-oxygen solid polymer electrolyte (SPE) fuel cells and SPE electrolyzers (products of Hamilton Standard) both use a Proton-Exchange Membrane (PEM) as the sole electrolyte. These solid electrolyte devices have been under continuous development for over 30 years. This experience has resulted in a demonstrated ten-year SPE cell life capability under load conditions. Ultimate life of PEM fuel cells and electrolyzers is primarily related to the chemical stability of the membrane. For perfluorocarbon proton exchange membranes an accurate measure of the membrane stability is the fluoride loss rate. Millions of cell hours have contributed to establishing a relationship between fluoride loss rates and average expected ultimate cell life. This relationship is shown. Several features have been introduced into SPE fuel cells and SPE electrolyzers such that applications requiring greater than or equal to 100,000 hours of life can be considered. Equally important as the ultimate life is the voltage stability of hydrogen-oxygen fuel cells and electrolyzers. Here again the features of SPE fuel cells and SPE electrolyzers have shown a cell voltage stability in the order of 1 microvolt per hour. That level of stability has been demonstrated for tens of thousands of hours in SPE fuel cells at up to 500 amps per square foot (ASF) current density