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

The identification of 93 day periodic photometric variability for YSO YLW 16A

Aims. Periodic variability in young stellar objects (YSOs) offers indirect evidence for an active dynamical mechanism. Starspots, accretion, stellar companions, and disk veiling can contribute to the photometric variability of YSOs. Methods. As part of an ongoing study of the ρ Oph star forming region, we report the discovery of 92.6 day periodic variations for the Class I YSO YLW 16A, observed over a period of three years. A SED model was fit to available photometric data for the object. Results. We propose a triple-system with an inner binary with a period of 93 days eclipsed by a warped circum-binary disk. The nature of the secondary is unconstrained and could be stellar or sub-stellar. We confirm the discovery of a tertiary companion at a projected separation of ~40 AU that could account for the circum-binary disk warp. This light curve and model is similar to the model we proposed for WL 4 in previous work. Understanding these systems may lead to insights about the nature of stellar evolution and planetary formation, and provide valuable benchmarks for future theoretical modeling and near- and mid-infrared synoptic surveys of YSOs

A statistical model for the intrinsically broad superconducting to normal transition in quasi-two-dimensional crystalline organic metals

Although quasi-two-dimensional organic superconductors such as $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ seem to be very clean systems, with apparent quasiparticle mean-free paths of several thousand \AA, the superconducting transition is intrinsically broad (e.g $\sim 1$ K wide for $T_c \approx 10$ K). We propose that this is due to the extreme anisotropy of these materials, which greatly exacerbates the statistical effects of spatial variations in the potential experienced by the quasiparticles. Using a statistical model, we are able to account for the experimental observations. A parameter $\bar{x}$, which characterises the spatial potential variations, may be derived from Shubnikov-de Haas oscillation experiments. Using this value, we are able to predict a transition width which is in good agreement with that observed in MHz penetration-depth measurements on the same sample.Comment: 8 pages, 2 figures, submitted to J. Phys. Condens. Matte

Imaging the Algol Triple System in H Band with the CHARA Interferometer

Algol (Beta Per) is an extensively studied hierarchical triple system whose inner pair is a prototype semi-detached binary with mass transfer occurring from the sub-giant secondary to the main-sequence primary. We present here the results of our Algol observations made between 2006 and 2010 at the CHARA interferometer with the Michigan Infrared Combiner in the H band. The use of four telescopes with long baselines allows us to achieve better than 0.5 mas resolution and to unambiguously resolve the three stars. The inner and outer orbital elements, as well as the angular sizes and mass ratios for the three components are determined independently from previous studies. We report a significantly improved orbit for the inner stellar pair with the consequence of a 15% change in the primary mass compared to previous studies. We also determine the mutual inclination of the orbits to be much closer to perpendicularity than previously established. State-of-the-art image reconstruction algorithms are used to image the full triple system. In particular an image sequence of 55 distinct phases of the inner pair orbit is reconstructed, clearly showing the Roche-lobe-filling secondary revolving around the primary, with several epochs corresponding to the primary and secondary eclipses

Mechanical Control of Spin States in Spin-1 Molecules and the Underscreened Kondo Effect

The ability to make electrical contact to single molecules creates opportunities to examine fundamental processes governing electron flow on the smallest possible length scales. We report experiments in which we controllably stretch individual cobalt complexes having spin S = 1, while simultaneously measuring current flow through the molecule. The molecule's spin states and magnetic anisotropy were manipulated in the absence of a magnetic field by modification of the molecular symmetry. This control enabled quantitative studies of the underscreened Kondo effect, in which conduction electrons only partially compensate the molecular spin. Our findings demonstrate a mechanism of spin control in single-molecule devices and establish that they can serve as model systems for making precision tests of correlated-electron theories.Comment: main text: 5 pages, 4 figures; supporting information attached; to appear in Science

A New Interpretation of Flux Quantization

We study the effect of Aharonov-Bohm flux on the superconducting state in metallic cylinders. Although Byers and Yang attributed flux quantization to the flux-dependent minimum of kinetic energies of the Cooper pairs, it is shown that kinetic energies do not produce any discernible oscillations in the free energy of the superconducting state (relative to that of normal state) as a function of the flux. This result is indeed anticipated by the observation of persistent current in normal metal rings at low temperature. Instead, we have found that pairing interaction depends on the flux, leading to flux quantization. When the flux $(\Phi$) is given by $\Phi=n\times hc/2e$ (with integer n), the pairing interaction and the free energy become unchanged (even n) or almost unchanged (odd n), due to degenerate-state pairing resulting from the energy level crossing. As a result, flux quantization and Little-Parks oscillations follow.Comment: Revtex, 10 pages, 6 figures, For more information, send me an e-mail at [email protected]