Weak Energy: Form and Function

The equation of motion for a time-independent weak value of a quantum mechanical observable contains a complex valued energy factor - the weak energy of evolution. This quantity is defined by the dynamics of the pre-selected and post-selected states which specify the observable's weak value. It is shown that this energy: (i) is manifested as dynamical and geometric phases that govern the evolution of the weak value during the measurement process; (ii) satisfies the Euler-Lagrange equations when expressed in terms of Pancharatnam (P) phase and Fubini-Study (FS) metric distance; (iii) provides for a PFS stationary action principle for quantum state evolution; (iv) time translates correlation amplitudes; (v) generalizes the temporal persistence of state normalization; and (vi) obeys a time-energy uncertainty relation. A similar complex valued quantity - the pointed weak energy of an evolving state - is also defined and several of its properties in PFS-coordinates are discussed. It is shown that the imaginary part of the pointed weak energy governs the state's survival probability and its real part is - to within a sign - the Mukunda-Simon geometric phase for arbitrary evolutions or the Aharonov-Anandan (AA) phase for cyclic evolutions. Pointed weak energy gauge transformations and the PFS 1-form are discussed and the relationship between the PFS 1-form and the AA connection 1-form is established.Comment: To appear in "Quantum Theory: A Two-Time Success Story"; Yakir Aharonov Festschrif

Deformations at Earth's dayside magnetopause during quasi-radial IMF conditions: Global kinetic simulations and soft X-ray imaging

The Solar wind Magnetosphere Ionosphere Link Explorer (SMILE) is an ESA-CAS joint mission. Primary goals are investigating the dynamic response of the Earth's magnetosphere to the solar wind (SW) impact via simultaneous in situ magnetosheath (MS) plasma and magnetic field measurements, X-Ray images of the magnetosheath and magnetic cusps, and UV images of global auroral distributions. Magnetopause (MP) deformations associated with MS high speed jets (HSJs) under a quasi-parallel interplanetary magnetic field condition are studied using a three-dimensional (3-D) global hybrid simulation. Soft X-ray intensity calculated based on both physical quantities of solar wind proton and oxygen ions is compared. We obtain key findings concerning deformations at the MP: (1) MP deformations are highly coherent with the MS HSJs generated at the quasiparallel region of the bow shock, (2) X-ray intensities estimated using solar wind H+ and self-consistent O7+ ions are consistent with each other, (3) Visual spacecraft are employed to check the discrimination ability for capturing MP deformations on Lunar and polar orbits, respectively. The SMILE spacecraft on the polar orbit could be expected to provide opportunities for capturing the global geometry of the magnetopause in the equatorial plane. A striking point is that SMILE has the potential to capture small-scale MP deformations and MS transients, such as HSJs, at medium altitudes on its orbit

Use of metal/uranium mixtures to explore data uncertainties

A table of k{sub {infinity}} values for three homogenized metal/{sup 235}U systems calculated using both MCNP and the SCALE code system was presented in Ref. 3. The homogenized metal/{sup 235} U ratios were selected such that the MCNP analyses for each mixture provided k{sub {infinity}} {approx_equal} 1.0. The metals considered were Al, Zr, and Fe. These simplified systems were created in an effort to ease an investigation of discrepant results obtained using MCNP and SCALE to analyze large, dry systems of metal-clad, highly enriched fuel assemblies. Reference 3 has received considerable attention at ORNL and elsewhere because the reported k{sub {infinity}} values varied by as much as 38% between the MCNP results and those of SCALE. The ORNL approach was to analyze the systems using a broad range of codes and data and to seek an understanding of the discrepancies by studying differences in the basic data and processing methods. The continuous-energy codes and data applied in the ORNL study were (1) MCNP, using ENDF/B-V, ENDF/B-VI, and LANL data evaluations, (2) VIM, using ENDF/B-V data, and (3) MONK, using a 8,200-point library based on UKNDL evaluations and a preliminary JEF library. The VIM code provides treatment of unresolved resonances; MCNP does not. The MONK analyses provided a result using both an independent code and independent data evaluations. Although accessing continuous-energy data typically requires the use of Monte Carlo codes, 1-D deterministic codes can be used to accurately calculate K{sub {infinity}} values using a variety of multigroup data libraries and processing methods. The multigroup codes used in the study were MC and the CSAS1X sequence of the SCALE system. Both systems provide problem-dependent resonance processing of cross-section data and available fine-group libraries were used for the analyses. Broad-group libraries were not studied in any depth because there were non-readily available for intermediate-energy systems

Analytic study of properties of holographic p-wave superconductors

In this paper, we analytically investigate the properties of p-wave holographic superconductors in $AdS_{4}$-Schwarzschild background by two approaches, one based on the Sturm-Liouville eigenvalue problem and the other based on the matching of the solutions to the field equations near the horizon and near the asymptotic $AdS$ region. The relation between the critical temperature and the charge density has been obtained and the dependence of the expectation value of the condensation operator on the temperature has been found. Our results are in very good agreement with the existing numerical results. The critical exponent of the condensation also comes out to be 1/2 which is the universal value in the mean field theory.Comment: Latex, To appear in JHE

Inertial Mass of a Vortex in Cuprate Superconductors

We present here a calculation of the inertial mass of a moving vortex in cuprate superconductors. This is a poorly known basic quantity of obvious interest in vortex dynamics. The motion of a vortex causes a dipolar density distortion and an associated electric field which is screened. The energy cost of the density distortion as well as the related screened electric field contribute to the vortex mass, which is small because of efficient screening. As a preliminary, we present a discussion and calculation of the vortex mass using a microscopically derivable phase-only action functional for the far region which shows that the contribution from the far region is negligible, and that most of it arises from the (small) core region of the vortex. A calculation based on a phenomenological Ginzburg-Landau functional is performed in the core region. Unfortunately such a calculation is unreliable, the reasons for it are discussed. A credible calculation of the vortex mass thus requires a fully microscopic, non-coarse grained theory. This is developed, and results are presented for a s-wave BCS like gap, with parameters appropriate to the cuprates. The mass, about 0.5 $m_e$ per layer, for magnetic field along the $c$ axis, arises from deformation of quasiparticle states bound in the core, and screening effects mentioned above. We discuss earlier results, possible extensions to d-wave symmetry, and observability of effects dependent on the inertial mass.Comment: 27 pages, Latex, 3 figures available on request, to appear in Physical Review

Free flux flow resistivity in strongly overdoped high-T_c cuprate; purely viscous motion of the vortices in semiclassical d-wave superconductor

We report the free flux flow (FFF) resistivity associated with a purely viscous motion of the vortices in moderately clean d-wave superconductor Bi:2201 in the strongly overdoped regime (T_c=16K) for a wide range of the magnetic field in the vortex state. The FFF resistivity is obtained by measuring the microwave surface impedance at different microwave frequencies. It is found that the FFF resistivity is remarkably different from that of conventional s-wave superconductors. At low fields (H<0.2H_c2) the FFF resistivity increases linearly with H with a coefficient which is far larger than that found in conventional s-wave superconductors. At higher fields, the FFF resistivity increases in proportion to \sqrt H up to H_c2. Based on these results, the energy dissipation mechanism associated with the viscous vortex motion in "semiclassical" d-wave superconductors with gap nodes is discussed. Two possible scenarios are put forth for these field dependence; the enhancement of the quasiparticle relaxation rate and the reduction of the number of the quasiparticles participating the energy dissipation in d-wave vortex state.Comment: 9 pages 7 figures, to appear in Phys. Rev.

Metal-macrofauna interactions determine microbial community structure and function in copper contaminated sediments

Peer reviewedPublisher PD