Quantum trajectories for time-dependent adiabatic master equations

We develop a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension $N$ instead of a complex density matrix of dimension $N^2$, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor $N$ advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor $N^2$ is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for $8$-qubit quantum annealing examples. We also apply the quantum trajectories method to a $16$-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.Comment: 17 pages, 7 figure

ac Josephson effect in asymmetric superconducting quantum point contacts

We investigate ac Josephson effects between two superconductors connected by a single-mode quantum point contact, where the gap amplitudes in the two superconductors are unequal. In these systems, it was found in previous studies on the dc effects that, besides the Andreev bound-states, the continuum states can also contribute to the current. Using the quasiclassical formulation, we calculate the current-voltage characteristics for general transmission $D$ of the point contact. To emphasize bound versus continuum states, we examine in detail the low bias, ballistic (D=1) limit. It is shown that in this limit the current-voltage characteristics can be determined from the current-phase relation, if we pay particular attention to the different behaviors of these states under the bias voltage. For unequal gap configurations, the continuum states give rise to non-zero sine components. We also demonstrate that in this limit the temperature dependence of the dc component follows $\tanh(\Delta_s/2T)$, where $\Delta_s$ is the smaller gap, with the contribution coming entirely from the bound state.Comment: To appear in PR

Chemochemical caries removal: a review of the techniques and latest developments

Chemomechanical caries removal involves the chemical softening of carious dentine followed by its removal by gentle excavation. The reagent involved is generated by mixing amino acids with sodium hypochlorite; N-monochloroamino acids are formed which selectively degrade demineralised collagen in carious dentine. The procedure requires 5-15 minutes but avoids the painful removal of sound dentine thereby reducing the need for local anaesthesia. It is well suited to the treatment of deciduous teeth, dental phobics and medically compromised patients. The dentine surface formed is highly irregular and well suited to bonding with composite resin or glass ionomer. When complete caries removal is achieved, the dentine remaining is sound and properly mineralised. The system was originally marketed in the USA in the 1980's as Caridex. Large volumes of solution and a special applicator system were required. A new system, Carisolv, has recently been launched on to the market. This comes as a gel, requires volumes of 0.2-1.0 ml and is accompanied by specially designed instruments

An Open-Source 7-Axis, Robotic Platform to Enable Dexterous Procedures within CT Scanners

This paper describes the design, manufacture, and performance of a highly dexterous, low-profile, 7 Degree-of-Freedom (DOF) robotic arm for CT-guided percutaneous needle biopsy. Direct CT guidance allows physicians to localize tumours quickly; however, needle insertion is still performed by hand. This system is mounted to a fully active gantry superior to the patient's head and teleoperated by a radiologist. Unlike other similar robots, this robot's fully serial-link approach uses a unique combination of belt and cable drives for high-transparency and minimal-backlash, allowing for an expansive working area and numerous approach angles to targets all while maintaining a small in-bore cross-section of less than $16cm^2$. Simulations verified the system's expansive collision free work-space and ability to hit targets across the entire chest, as required for lung cancer biopsy. Targeting error is on average $<1mm$ on a teleoperated accuracy task, illustrating the system's sufficient accuracy to perform biopsy procedures. The system is designed for lung biopsies due to the large working volume that is required for reaching peripheral lung lesions, though, with its large working volume and small in-bore cross-sectional area, the robotic system is effectively a general-purpose CT-compatible manipulation device for percutaneous procedures. Finally, with the considerable development time undertaken in designing a precise and flexible-use system and with the desire to reduce the burden of other researchers in developing algorithms for image-guided surgery, this system provides open-access, and to the best of our knowledge, is the first open-hardware image-guided biopsy robot of its kind.Comment: 8 pages, 9 figures, final submission to IROS 201

Electronic thermal conductivity and the Wiedemann-Franz law for unconventional superconductors

We use the quasiclassical theory of superconductivity to calculate the electronic contribution to the thermal conductivity. The theory is formulated for low temperatures when heat transport is limited by electron scattering from random defects and for superconductors with nodes in the order parameter. We show that certain eigenvalues of the thermal conductivity tensor are universal at low temperature, $k_B T\ll \gamma$, where $\gamma$ is the bandwidth of impurity bound states in the superconducting phase. The components of the electrical and thermal conductivity also obey a Wiedemann-Franz law with the Lorenz ratio, $L(T)=\kappa/\sigma T$, given by the Sommerfeld value of $L_{\!S}=({\pi^2}/{3})(k_B/e)^2$ for $k_BT\ll\gamma$. For intermediate temperatures the Lorenz ratio deviates significantly from $L_{\!S}$, and is strongly dependent on the scattering cross section, and qualitatively different for resonant vs.\ nonresonant scattering. We include comparisons with other theoretical calculations and the thermal conductivity data for the high $T_c$ cuprate and heavy fermion superconductors.Comment: 17 pages, PostScript file compressed and uuencode

Synthesis of H_xLi_1-xLaTiO₄ from quantitative solid-state reactions at room temperature

The layered perovskite HLaTiO4 reacts stoichiometrically with LiOH·H2O at room temperature to give targeted compositions in the series HxLi1-xLaTiO4. Remarkably, the Li+ and H+ ions are quantitatively exchanged in the solid state and this allows stoichiometric control of ion exchange for the first time in this important series of compounds