Validity of the Adiabatic Approximation

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the "standard criterion" for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic {\em theorem} and the adiabatic {\em approximation}, two quite different although closely related ideas.Comment: 4 pages, 1 figur

A new perturbative approach to the adiabatic approximation

A new and intuitive perturbative approach to time-dependent quantum mechanics problems is presented, which is useful in situations where the evolution of the Hamiltonian is slow. The state of a system which starts in an instantaneous eigenstate of the initial Hamiltonian is written as a power series which has a straightforward diagrammatic representation. Each term of the series corresponds to a sequence of "adiabatic" evolutions, during which the system remains in an instantaneous eigenstate of the Hamiltonian, punctuated by transitions from one state to another. The first term of this series is the standard adiabatic evolution, the next is the well-known first correction to it, and subsequent terms can be written down essentially by inspection. Although the final result is perhaps not terribly surprising, it seems to be not widely known, and the interpretation is new, as far as we know. Application of the method to the adiabatic approximation is given, and some discussion of the validity of this approximation is presented.Comment: 9 pages. Added references, discussion of previous results, expanded upon discussion of main result and application of i

Interplay of Spin-Orbit Interaction and Electron Correlation on the Van Vleck Susceptibility in Transition Metal Compounds

We have studied the effects of electron correlation on Van Vleck susceptibility ($\chi_{\rm{VV}}$) in transition metal compounds. A typical crossover behavior is found for the correlation effect on $\chi_{\rm{VV}}$ as sweeping spin-orbit interaction, $\lambda$. For a small $\lambda$, orbital fluctuation plays a dominant role in the correlation enhancement of $\chi_{\rm{VV}}$; however, the enhancement rate is rather small. In contrast, for an intermediate $\lambda$, $\chi_{\rm{VV}}$ shows a substantial increase, accompanied by the development of spin fluctuation. We will discuss the behavior of $\chi_{\rm{VV}}$ in association with the results of Knight-shift experiments on Sr$_2$RuO$_4$ and an anomalously large magnetic susceptibility observed for $5d$ Ir compounds.Comment: 5 pages, 3 figures, to appear in J. Phys. Soc. Jp

From double Lie groupoids to local Lie 2-groupoids

We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.Comment: 23 pages, a few minor changes, including a correction to Lemma 6.

Photoemission Quasi-Particle Spectra of Sr2_2RuO4_4

Multi-band quasi-particle calculations based on perturbation theory and dynamical mean field methods show that the creation of a photoemission hole state in Sr$_2$RuO$_4$ is associated with a highly anisotropic self-energy. Since the narrow Ru-derived $d_{xz,yz}$ bands are more strongly distorted by Coulomb correlations than the wide $d_{xy}$ band, charge is partially transferred from $d_{xz,yz}$ to $d_{xy}$, thereby shifting the $d_{xy}$ van Hove singularity close to the Fermi level.Comment: 4 pages, to be published in PRB Rapid Com

A Novel Use for the Rigid Cystoscope: The Removal of Sacral Tacks after a Coloanal Anastamosis Dehiscence

A 69-year-old female presented as an emergency with atrial fibrillation, which was treated with warfarin. She subsequently developed fresh rectal bleeding and after further investigations a Dukes B adenocarcinoma of the rectum was found. She subsequently underwent a low anterior resection, coloanal anastamosis and a defunctioning ileostomy. Three sterile surgical metallic tacks (pins) were inserted into the sacrum to stop brisk bleeding from the presacral venous plexus. Following discharge, she was readmitted with septic shock and a CT scan revealed a presacral fluid collection in the area surrounding the sacral tacks (pins) and an anastamotic dehiscence. The patient was not fit for further pelvic surgery to remove the tacks, so an alternative minimally invasive cystoscopic procedure was performed. The sacral tacks (pins) were removed by the urologist using a rigid cystoscope and cold cup biopsy forceps. To our knowledge, this is the first reported case in the literature

Anisotropic Energy Gaps of Iron-based Superconductivity from Intra-band Quasiparticle Interference in LiFeAs

If strong electron-electron interactions between neighboring Fe atoms mediate the Cooper pairing in iron-pnictide superconductors, then specific and distinct anisotropic superconducting energy gaps \Delta_i(k) should appear on the different electronic bands i. Here we introduce intra-band Bogoliubov quasiparticle scattering interference (QPI) techniques for determination of \Delta_i(k) in such materials, focusing on LiFeAs. We identify the three hole-like bands assigned previously as \gamma, \alpha_2 and \alpha_1, and we determine the anisotropy, magnitude and relative orientations of their \Delta_i(k). These measurements will advance quantitative theoretical analysis of the mechanism of Cooper pairing in iron-based superconductivity

The de Haas-van Alphen effect across the metamagnetic transition in Sr3_3Ru2_2O7_7

We report a study of the de Haas-van Alphen (dHvA) effect on the itinerant metamagnet Sr$_3$Ru$_2$O$_7$. Extremely high sample purity allows the observation of dHvA oscillations both above and below the metamagnetic transition field of 7.9 T. The quasiparticle masses are fairly large away from the transition, and are enhanced by up to an extra factor of three as the transition is approached, but the Fermi surface topography change is quite small. The results are qualitatively consistent with a field-induced Stoner transition in which the mass enhancement is the result of critical fluctuations.Comment: 4 pages, 3 figure

Upper critical field in layered superconductors

The theoretical statements about a restoration of a superconductivity at magnetic fields higher than the quasiclassical upper critical field and a reentrance of superconductivity at temperatures $T_c(H)\approx T_c(0)$ in the superconductors with open Fermi surfaces are reinvestigated taking into account a scattering of quasiparticles on the impurities. The system of integral equations for determination of the upper critical field parallel to the conducting planes in a layered conventional and unconventional superconductors with impurities are derived. The $H_{c2}(T)$ values for the "clean" case in the Ginzburg-Landau regime and at any temperature in the "dirty" case are found analytically. The upper limit of the superconductor purity when the upper critical field definately has a finite value is established.Comment: 10 page

The mean field infinite range p=3 spin glass: equilibrium landscape and correlation time scales

We investigate numerically the dynamical behavior of the mean field 3-spin spin glass model: we study equilibrium dynamics, and compute equilibrium time scales as a function of the system size V. We find that for increasing volumes the time scales $\tau$ increase like $\ln \tau \propto V$. We also present an accurate study of the equilibrium static properties of the system.Comment: 6 pages, 9 figure