Fluctuating "order parameter" for a quantum chaotic system with partially broken time-reversal symmetry

The functional defined as the squared modulus of the spatial average of the wave function squared, plays the role of an ``order parameter'' for the transition between Hamiltonian ensembles with orthogonal and unitary symmetry. Upon breaking time-reversal symmetry, the order parameter crosses over from one to zero. We compute its distribution in the crossover regime and find that it has large fluctuations around the ensemble average. These fluctuations imply long-range spatial correlations in the eigenfunction and non-Gaussian perturbations of eigenvalues, in precise agreement with results by Fal'ko and Efetov and by Taniguchi, Hashimoto, Simons, and Altshuler. As a third implication of the order-parameter fluctuations we find correlations in the response of an eigenvalue to independent perturbations of the system.Comment: 4 pages, REVTeX-3.0, 1 figure. Reference added to Y. V. Fyodorov and A. D. Mirlin, Phys. Rev. B 51, 13403 (1995

Finite size effects and localization properties of disordered quantum wires with chiral symmetry

Finite size effects in the localization properties of disordered quantum wires are analyzed through conductance calculations. Disorder is induced by introducing vacancies at random positions in the wire and thus preserving the chiral symmetry. For quasi one-dimensional geometries and low concentration of vacancies, an exponential decay of the mean conductance with the wire length is obtained even at the center of the energy band. For wide wires, finite size effects cause the conductance to decay following a non-pure exponential law. We propose an analytical formula for the mean conductance that reproduces accurately the numerical data for both geometries. However, when the concentration of vacancies increases above a critical value, a transition towards the suppression of the conductance occurs. This is a signature of the presence of ultra-localized states trapped in finite regions of the sample.Comment: 5 figures, revtex

Nonequilibrium theory of Coulomb blockade in open quantum dots

We develop a non-equilibrium theory to describe weak Coulomb blockade effects in open quantum dots. Working within the bosonized description of electrons in the point contacts, we expose deficiencies in earlier applications of this method, and address them using a 1/N expansion in the inverse number of channels. At leading order this yields the self-consistent potential for the charging interaction. Coulomb blockade effects arise as quantum corrections to transport at the next order. Our approach unifies the phase functional and bosonization approaches to the problem, as well as providing a simple picture for the conductance corrections in terms of renormalization of the dot's elastic scattering matrix, which is obtained also by elementary perturbation theory. For the case of ideal contacts, a symmetry argument immediately allows us to conclude that interactions give no signature in the averaged conductance. Non-equilibrium applications to the pumped current in a quantum pump are worked out in detail.Comment: Published versio

Distributions of the Conductance and its Parametric Derivatives in Quantum Dots

Full distributions of conductance through quantum dots with single-mode leads are reported for both broken and unbroken time-reversal symmetry. Distributions are nongaussian and agree well with random matrix theory calculations that account for a finite dephasing time, $\tau_\phi$, once broadening due to finite temperature $T$ is also included. Full distributions of the derivatives of conductance with respect to gate voltage $P(dg/dV_g)$ are also investigated.Comment: 4 pages (REVTeX), 4 eps figure

Distribution of parametric conductance derivatives of a quantum dot

The conductance G of a quantum dot with single-mode ballistic point contacts depends sensitively on external parameters X, such as gate voltage and magnetic field. We calculate the joint distribution of G and dG/dX by relating it to the distribution of the Wigner-Smith time-delay matrix of a chaotic system. The distribution of dG/dX has a singularity at zero and algebraic tails. While G and dG/dX are correlated, the ratio of dG/dX and $\sqrt{G(1-G)}$ is independent of G. Coulomb interactions change the distribution of dG/dX, by inducing a transition from the grand-canonical to the canonical ensemble. All these predictions can be tested in semiconductor microstructures or microwave cavities.Comment: 4 pages, RevTeX, 3 figure

Assessing the impact of a cattle risk-based trading scheme on the movement of bovine tuberculosis infected animals in England and Wales

The adoption of bovine tuberculosis (bTB) risk-based trading (RBT) schemes has the potential to reduce the risk of bTB spread. However, any scheme will have cost implications that need to be balanced against its likely success in reducing bTB. This paper describes the first stochastic quantitative model assessing the impact of the implementation of a cattle risk-based trading scheme to inform policy makers and contribute to cost–benefit analyses. A risk assessment for England and Wales was developed to estimate the number of infected cattle traded using historic movement data recorded between July 2010 and June 2011. Three scenarios were implemented: cattle traded with no RBT scheme in place, voluntary provision of the score and a compulsory, statutory scheme applying a bTB risk score to each farm. For each scenario, changes in trade were estimated due to provision of the risk score to potential purchasers. An estimated mean of 3981 bTB infected animals were sold to purchasers with no RBT scheme in place in one year, with 90% confidence the true value was between 2775 and 5288. This result is dependent on the estimated between herd prevalence used in the risk assessment which is uncertain. With the voluntary provision of the risk score by farmers, on average, 17% of movements was affected (purchaser did not wish to buy once the risk score was available), with a reduction of 23% in infected animals being purchased initially. The compulsory provision of the risk score in a statutory scheme resulted in an estimated mean change to 26% of movements, with a reduction of 37% in infected animals being purchased initially, increasing to a 53% reduction in infected movements from higher risk sellers (score 4 and 5). The estimated mean reduction in infected animals being purchased could be improved to 45% given a 10% reduction in risky purchase behaviour by farmers which may be achieved through education programmes, or to an estimated mean of 49% if a rule was implemented preventing farmers from the purchase of animals of higher risk than their own herd. Given voluntary trials currently taking place of a trading scheme, recommendations for future work include the monitoring of initial uptake and changes in the purchase patterns of farmers. Such data could be used to update the risk assessment to reduce uncertainty associated with model estimates

Effects of localization and amplification on distribution of intensity transmitted through random media

We numerically study the statistical distribution of intensity transmitted through quasi-one dimensional random media by varying the dimensionless conductance $g$ and the amount of absorption or gain. Markedly non-Rayleigh distribution is found to be well fitted by the analytical formula of Nieuwenhuizen {\it et al}, Phys. Rev. Lett. {\bf 74}, 2674 (1995) with a single parameter $g^\prime$. We show that in the passive random system $g^\prime$ is uniquely related to $g$, while in amplifying/absorbing random media $g^\prime$ also depends on gain/absorption coefficient.Comment: 4 pages, 4 figures, 1 tabl

The Thermopower of Quantum Chaos

The thermovoltage of a chaotic quantum dot is measured using a current heating technique. The fluctuations in the thermopower as a function of magnetic field and dot shape display a non-Gaussian distribution, in agreement with simulations using Random Matrix Theory. We observe no contributions from weak localization or short trajectories in the thermopower.Comment: 4 pages, 3 figures, corrected: accidently omitted author in the Authors list, here (not in the article