On the construction of probabilistic Newton-type algorithms

It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start assembling probabilistic Newton-type algorithms, applicable in situations where we only have access to noisy observations of the cost function and its derivatives. This is where our interest lies. We make contributions to the use of the non-parametric and probabilistic Gaussian process models in solving these stochastic optimisation problems. Specifically, we present a new algorithm that unites these approximations together with recent probabilistic line search routines to deliver a probabilistic quasi-Newton approach. We also show that the probabilistic optimisation algorithms deliver promising results on challenging nonlinear system identification problems where the very nature of the problem is such that we can only access the cost function and its derivative via noisy observations, since there are no closed-form expressions available

Charge Transport in Voltage-Biased Superconducting Single-Electron Transistors

Charge is transported through superconducting SSS single-electron transistors at finite bias voltages by a combination of coherent Cooper-pair tunneling and quasiparticle tunneling. At low transport voltages the effect of an ``odd'' quasiparticle in the island leads to a $2e$-periodic dependence of the current on the gate charge. We evaluate the $I-V$ characteristic in the framework of a model which accounts for these effects as well as for the influence of the electromagnetic environment. The good agreement between our model calculation and experimental results demonstrates the importance of coherent Cooper-pair tunneling and parity effects.Comment: RevTeX, 12 pages, 4 figure

Strongly enhanced shot noise in chains of quantum dots

We study charge transport through a chain of quantum dots. The dots are fully coherent among each other and weakly coupled to metallic electrodes via the dots at the interface, thus modelling a molecular wire. If the non-local Coulomb interactions dominate over the inter-dot hopping we find strongly enhanced shot noise above the sequential tunneling threshold. The current is not enhanced in the region of enhanced noise, thus rendering the noise super-Poissonian. In contrast to earlier work this is achieved even in a fully symmetric system. The origin of this novel behavior lies in a competition of "slow" and "fast" transport channels that are formed due to the differing non-local wave functions and total spin of the states participating in transport. This strong enhancement may allow direct experimental detection of shot noise in a chain of lateral quantum dots.Comment: 4 pages, 2 figures, submitted to PR

Properties of the energy landscape of network models for covalent glasses

We investigate the energy landscape of two dimensional network models for covalent glasses by means of the lid algorithm. For three different particle densities and for a range of network sizes, we exhaustively analyse many configuration space regions enclosing deep-lying energy minima. We extract the local densities of states and of minima, and the number of states and minima accessible below a certain energy barrier, the 'lid'. These quantities show on average a close to exponential growth as a function of their respective arguments. We calculate the configurational entropy for these pockets of states and find that the excess specific heat exhibits a peak at a critical temperature associated with the exponential growth in the local density of states, a feature of the specific heat also observed in real glasses at the glass transition.Comment: RevTeX, 19 pages, 7 figure

The possible explanation of electric-field-doped C60 phenomenology in the framework of Eliashberg theory

In a recent paper (J.H. Schon, Ch. Kloc, R.C. Haddon and B. Batlogg, Nature 408 (2000) 549) a large increase in the superconducting critical temperature was observed in C60 doped with holes by application of a high electric field. We demonstrate that the measured Tc versus doping curves can be explained by solving the (four) s-wave Eliashberg equations in the case of a finite, non-half-filled energy band. In order to reproduce the experimental data, we assume a Coulomb pseudopotential depending on the filling in a very simple and plausible way. Reasonable values of the physical parameters involved are obtained. The application of the same approach to new experimental data (J.H. Schon, Ch. Kloc and B. Batlogg, Science 293 (2001) 2432) on electric field-doped, lattice-expanded C60 single crystals (Tc=117 K in the hole-doped case) gives equally good results and sets a theoretical limit to the linear increase of Tc at the increase of the lattice spacing.Comment: latex2e, 6 pages, 7 figures, 1 table, revised versio

Co-tunneling current and shot noise in quantum dots

We derive general expressions for the current and shot noise, taking into account non-Markovian memory effects. In generalization of previous approaches our theory is valid for arbitrary Coulomb interaction and coupling strength and is applicable to quantum dots and more complex systems like molecules. A diagrammatic expansion up to second-order in the coupling strength, taking into account co-tunneling processes, allows for a study of transport in a regime relevant to many experiments. As an example, we consider a single-level quantum dot, focusing on the Coulomb-blockade regime. We find super-Poissonian shot noise due to spin-flip co-tunneling processes at an energy scale different from the one expected from first-order calculations, with a sensitive dependence on the coupling strength.Comment: 4 pages, three figures, submitted to PR

Effect of Measurement on the Periodicity of the Coulomb Staircase of a Superconducting Box

We report on the effect of the back-action of a Single Cooper Pair Transistor electrometer (E) on the measurement of charge on the island of a superconducting box (B). The charge is e-periodic in the gate bias of B when E is operated near voltages 2Delta/e or 4Delta/e. We show that this is due to quasiparticle poisoning of B at a rate proportional to the number of quasiparticle tunneling events in E per second. We are able to eliminate this back action and recover 2e charge periodicity using a new measurement method based on switching current modulation of E.Comment: 4 pages, 4 figures, revised versio

Strong coupling of a qubit to shot noise

We perform a nonperturbative analysis of a charge qubit in a double quantum dot structure coupled to its detector. We show that strong detector-dot interaction tends to slow down and halt coherent oscillations. The transitions to a classical and a low-temperature quantum overdamping (Zeno) regime are studied. In the latter, the physics of the dissipative phase transition competes with the effective shot noise.Comment: 5 pages, 4 figure

Kinetics of non-equilibrium quasiparticle tunneling in superconducting charge qubits

We directly observe low-temperature non-equilibrium quasiparticle tunneling in a pair of charge qubits based on the single Cooper-pair box. We measure even- and odd-state dwell time distributions as a function of temperature, and interpret these results using a kinetic theory. While the even-state lifetime is exponentially distributed, the odd-state distribution is more heavily weighted to short times, implying that odd-to-even tunnel events are not described by a homogenous Poisson process. The mean odd-state dwell time increases sharply at low temperature, which is consistent with quasiparticles tunneling out of the island before reaching thermal equilibrium.Comment: Replaced Figure 1 with color version, corrected more typos. Version submitted to PR