There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This book presents the conceptual framework underlying the atomistic theory of matter, emphasizing those aspects that relate to current flow. This includes some of the most advanced concepts of non-equilibrium quantum statistical mechanics. No prior acquaintance with quantum mechanics is assumed. Chapter 1 provides a description of quantum transport in elementary terms accessible to a beginner. The book then works its way from hydrogen to nanostructures, with extensive coverage of current flow. The final chapter summarizes the equations for quantum transport with illustrative examples showing how conductors evolve from the atomic to the ohmic regime as they get larger. Many numerical examples are used to provide concrete illustrations and the corresponding Matlab codes can be downloaded from the web. Videostreamed lectures, keyed to specific sections of the book, are also available through the web. This book is primarily aimed at senior and graduate students.

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Quantum Transport: Atom to Transistor

Advanced gravitational wave interferometers, currently under realization, will soon permit the detection of gravitational waves from astronomical sources. To open the era of precision gravitational wave astronomy, a further substantial improvement in sensitivity is required. The future space-based Laser Interferometer Space Antenna and the third-generation ground-based observatory Einstein Telescope (ET) promise to achieve the required sensitivity improvements in frequency ranges. The vastly improved sensitivity of the third generation of gravitational wave observatories could permit detailed measurements of the sources' physical parameters and could complement, in a multi-messenger approach, the observation of signals emitted by cosmological sources obtained through other kinds of telescopes. This paper describes the progress of the ET project which is currently in its design study phase.

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The Einstein Telescope: a third-generation gravitational wave observatory

The Advanced LIGO gravitational wave detectors are next generation instruments which will replace the existing initial LIGO detectors. They are currently being constructed and installed. Advanced LIGO strain sensitivity is designed to be about a factor 10 better than initial LIGO over a broad band and usable to 10 Hz, in contrast to 40 Hz for initial LIGO. This is expected to allow for detections and significant astrophysics in most categories of gravitational waves. To achieve this sensitivity, all hardware subsystems are being replaced with improvements. Designs and expected performance are presented for the seismic isolation, suspensions, optics and laser subsystems. Possible enhancements to Advanced LIGO, either to resolve problems that may arise and/or to allow for improved performance, are now being researched. Some of these enhancements are discussed along with some potential technology being considered for detectors beyond Advanced LIGO.

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Advanced LIGO: the next generation of gravitational wave detectors

This review provides a theoretical basis for understanding the current-phase relation (CPhiR) for the stationary (dc) Josephson effect in various types of superconducting junctions The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CPhiR from the standard sinusoidal form A new experimental tool for measuring the CPhiR is described and its practical applications are discussed The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy A number of examples illustrate the importance of the CPhiR measurements for both fundamental physics and applications

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The current-phase relation in Josephson junctions

Low temperature permeability and current noise of ferromagnetic pickup coils

On the base of our experiments on thin film Josephson junctions in mesa geometry we discuss the quasiparticle branches of the intrinsic arrays within a tunnelling model using d-wave superconductor density of states. We find temperature dependent current contributions and a zero bias anomaly. The coherent behaviour is studied for intrinsic arrays with an additional side-wall shunt. The existence of thresholds of phase locking at small as well as at large inductances is demonstrated. We discuss the problems with experimental realisation of the shunts as well as with an alternative concept to enhance phase locking in such arrays towards application as oscillators in the frequency range up to some THz.

Quasiparticle current and phase locking of intrinsic Josephson junctions

The resistively shunted junction (RSJ) model of a Josephson junction in a microwave field is studied using both analog and digital simulators. A comparison of the two methods shows very good agreement. Voltage-current characteristics of the Josephson junction in the low-frequency limit and their transition to chaotic behavior due to the punchthrough effect are investigated. The inverse ac effect on high-β
 c
 junctions is simulated. Fractional inverse steps are found.

Simulation of Josephson junction in a microwave field

${\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8\ensuremath{-}x}$ films on vicinal $\mathrm{La}\mathrm{Al}{\mathrm{O}}_{3}$ having different misorientation angles (10\ifmmode^\circ\else\textdegree\fi{}, 15\ifmmode^\circ\else\textdegree\fi{}, 20\ifmmode^\circ\else\textdegree\fi{}, 25\ifmmode^\circ\else\textdegree\fi{}) grow with their $\mathrm{Cu}{\mathrm{O}}_{2}$ planes tilted with respect to the substrate surface. We found intrinsic Josephson behavior in microbridges patterned out of these films for misorientation angles equal to or larger than 15\ifmmode^\circ\else\textdegree\fi{}. Here we report on the fabrication process, structural, and electrical properties. Structural analyses include secondary electron microscopy images and x-ray analysis of the crystallographic structure. We also present the current voltage characteristics, which exhibit a different behavior for the 15\ifmmode^\circ\else\textdegree\fi{} films than for 20\ifmmode^\circ\else\textdegree\fi{} and 25\ifmmode^\circ\else\textdegree\fi{} films: 15\ifmmode^\circ\else\textdegree\fi{} films show enhanced critical currents, while 25\ifmmode^\circ\else\textdegree\fi{} films show giant collective switching events, indicating a very small spread of critical currents. We discuss these effects with the possibility of shunts in the case of the 15\ifmmode^\circ\else\textdegree\fi{} films and with the existence of collective modes in the case of the 25\ifmmode^\circ\else\textdegree\fi{} films. In the latter case, we also discuss the possibility of synchronization.

Intrinsic Josephson junctions in misaligned Tl 2 Ba 2 Ca Cu 2 O 8 − x thin films with different tilt angles

The differential conductivities of Bi2Sr2CaCu2O8+x/Au and YBa2Cu3O7−δ/Au point contacts were measured. The superconducting order parameter Δ and the Fermi velocity vF of both superconductors were determined making use of the modified Blonder—Tinkham—Klapwijk theory. The coherence length and penetration depth of Bi2Sr2CaCu2O8+x and YBa2Cu3O7−δ were calculated from Δ and vF, by applying a weak-coupling theory of superconductors with anisotropic single-particle dispersion and order parameter. Our results are compared to other experimental data.

Paul Seidel

Papers

Low temperature permeability and current noise of ferromagnetic pickup coils

Quasiparticle current and phase locking of intrinsic Josephson junctions

Simulation of Josephson junction in a microwave field

Intrinsic Josephson junctions in misaligned Tl 2 Ba 2 Ca Cu 2 O 8 − x thin films with different tilt angles

Superconducting parameters of YBCO and BSCCO from ‘tunneling’ spectroscopy