Comment: Numerical calculation of thermal noise-voltage in a Josephson junction of finite capacitance

The autocorrelation function of the Langevin force in the model introduced in the cited paper is calculated and verified to be correct.Comment: 2 pages, to appear in Annalen der Physik; dedicated to Ulrich Eckern on the occasion of his 60th birthda

Entropy and Time

The emergence of a direction of time in statistical mechanics from an underlying time-reversal-invariant dynamics is explained by examining a simple model. The manner in which time-reversal symmetry is preserved and the role of initial conditions are emphasized. An extension of the model to finite temperatures is also discussed.Comment: 9 pages, 8eps figures. To appear in the theme issue of the American Journal of Physics on Statistical Physic

Width and Magnetic Field Dependence of Transition Temperature in Ultranarrow Superconducting Wires

We calculate the transition temperature in ultranarrow superconducting wires as a function of wire width, resistance and applied magnetic field. We compare the results of first-order perturbation theory and the non-perturbative resummation technique developed by Oreg and Finkel'stein. The latter technique is found to be superior as it is valid even in the strong disorder limit. In both cases the predicted additional suppression of the transition temperature due to the reduced dimensionality is strongly dependent upon the boundary conditions used. When we use the correct (zero-gradient) boundary conditions, we find that theory and experiment are consistent, although more experimental data is required to verify this systematically. We calculate the magnetic field dependence of the transition temperature for different wire widths and resistances in the hope that this will be measured in future experiments. The predicted results have a rich structure - in particular we find a dimensional crossover which can be tuned by varying either the width of the wire or its resistance per square.Comment: 12 pages, 1 table, 7 figures. The changes made to the paper are ones of emphasis. The comparison between theory and experiment has been altered, and detailed comparisons of various approximations have been omitted, although the results are summarised in the paper. Much more emphasis has been placed on the new predictions of the effect of an applied magnetic field on transition temperature in wires (Figs. 5-7

Decoherence without dissipation?

In a recent article, Ford, Lewis and O'Connell (PRA 64, 032101 (2001)) discuss a thought experiment in which a Brownian particle is subjected to a double-slit measurement. Analyzing the decay of the emerging interference pattern, they derive a decoherence rate that is much faster than previous results and even persists in the limit of vanishing dissipation. This result is based on the definition of a certain attenuation factor, which they analyze for short times. In this note, we point out that this attenuation factor captures the physics of decoherence only for times larger than a certain time t_mix, which is the time it takes until the two emerging wave packets begin to overlap. Therefore, the strategy of Ford et al of extracting the decoherence time from the regime t < t_mix is in our opinion not meaningful. If one analyzes the attenuation factor for t > t_mix, one recovers familiar behaviour for the decoherence time; in particular, no decoherence is seen in the absence of dissipation. The latter conclusion is confirmed with a simple calculation of the off-diagonal elements of the reduced density matrix.Comment: 8 pages, 4 figure

Decoherence in weak localization II: Bethe-Salpeter calculation of Cooperon

This is the second in a series of two papers (I and II) on the problem of decoherence in weak localization. In paper I, we discussed how the Pauli principle could be incorporated into an influence functional approach for calculating the Cooperon propagator and the magnetoconductivity. In the present paper II, we check and confirm the results so obtained by diagrammatically setting up a Bethe-Salpeter equation for the Cooperon, which includes self-energy and vertex terms on an equal footing and is free from both infrared and ultraviolet divergencies. We then approximately solve this Bethe-Salpeter equation by the Ansatz C(t) = C^0 (t) e^{-F(t)}, where the decay function F(t) determines the decoherence rate. We show that in order to obtain a divergence-free expression for the decay function F(t), it is sufficient to calculate C^1 (t), the Cooperon in the position-time representation to first order in the interaction. Paper II is independent of paper I and can be read without detailed knowledge of the latter.Comment: 18 pages, 3 figures. This is the second of a series of two papers on decoherence. The first introduces an influence functional approach, the second obtains equivalent results using a diagrammatic Bethe-Salpeter equation. For a concise summary of the main results and conclusions, see Section II of the first pape

Loss of Pi-Junction Behaviour in an Interacting Impurity Josephson Junction

Using a generalization of the non-crossing approximation which incorporates Andreev reflection, we study the properties of an infinite-U Anderson impurity coupled to two superconducting leads. In the regime where $\Delta$ and $T_K$ are comparable, we find that the position of the sub-gap resonance in the impurity spectral function develops a strong anomalous phase dependence-- its energy is a minimum when the phase difference between the superconductors is equal to $\pi$. Calculating the Josephson current through the impurity, we find that $\pi$-junction behaviour is lost as the position of the bound-state moves above the Fermi energy.Comment: 4 pages, 4 figures; labelling of Fig. 3 corrected; final published form, only trivial change

Effect of Magnetic Impurities on Suppression of the Transition Temperature in Disordered Superconductors

We calculate the first-order perturbative correction to the transition temperature $T_c$ in a superconductor with both non-magnetic and magnetic impurities. We do this by first evaluating the correction to the effective potential, $\Omega(\Delta)$, and then obtain the first-order correction to the order parameter, $\Delta$, by finding the minimum of $\Omega(\Delta)$. Setting $\Delta=0$ finally allows $T_c$ to be evaluated. $T_c$ is now a function of both the resistance per square, $R_\square$, a measure of the non-magnetic disorder, and the spin-flip scattering rate, $1/\tau_s$, a measure of the magnetic disorder. We find that the effective pair-breaking rate per magnetic impurity is virtually independent of the resistance per square of the film, in agreement with an experiment of Chervenak and Valles. This conclusion is supported by both the perturbative calculation, and by a non-perturbative re-summation technique.Comment: 29 pages, 9 figure

Effect of Level Statistics on Superconductivity in Ultrasmall Metallic Grains

We examine the destruction of superconducting pairing in metallic grains as their size is decreased for both even and odd numbers of electrons. This occurs when the average level spacing d is of the same order as the BCS order parameter. The energy levels of these grains are randomly distributed according to random matrix theory, and we must work statistically. We find that the average value of the critical level spacing is larger than for the model of equally spaced levels for both parities, and derive numerically the probabilities $P_{o,e}(d)$ that a grain of mean level spacing d shows pairing.Comment: 12 pages, 2 PostScript files, RevTex format, submitted to PR

Andreev Scattering and the Kondo Effect

We examine the properties of an infinite-$U$ Anderson impurity coupled to both normal and superconducting metals. Both the cases of a quantum dot and a quantum point contact containing an impurity are considered; for the latter, we study both one and two-channel impurities. Using a generalization of the noncrossing approximation which incorporates multiple Andreev reflection, we compute the impurity spectral function and the linear-response conductance of these devices. We find generically that the Kondo resonance develops structure at energies corresponding to the superconducting gap, and that the magnitude of the resonance at the Fermi energy is altered. This leads to observable changes in the zero-bias conductance as compared to the case with no superconductivity.Comment: 8 pages, 7 figures; expanded version to appear in PR