Energy absorption by "sparse" systems: beyond linear response theory

The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between energy levels is essential. The Kubo formula is modified, replacing the "algebraic" average over the squared matrix elements by a "resistor network" average. Consequently the response becomes semi-linear rather than linear. Some novel results have been obtained in the context of two prototype problems: the heating rate of particles in Billiards with vibrating walls; and the Ohmic Joule conductance of mesoscopic rings driven by electromotive force. Respectively, the obtained results are contrasted with the "Wall formula" and the "Drude formula".Comment: 8 pages, 7 figures, short pedagogical review. Proceedings of FQMT conference (Prague, 2011). Ref correcte

Origin of strong scarring of wavefunctions in quantum wells in a tilted magnetic field

The anomalously strong scarring of wavefunctions found in numerical studies of quantum wells in a tilted magnetic field is shown to be due to special properties of the classical dynamics of this system. A certain subset of periodic orbits are identified which are nearly stable over a very large interval of variation of the classical dynamics; only this subset are found to exhibit strong scarring. Semiclassical arguments shed further light on why these orbits dominate the experimentally observed tunneling spectra.Comment: RevTeX, 5 page

The shape of invasion perclation clusters in random and correlated media

The shape of two-dimensional invasion percolation clusters are studied numerically for both non-trapping (NTIP) and trapping (TIP) invasion percolation processes. Two different anisotropy quantifiers, the anisotropy parameter and the asphericity are used for probing the degree of anisotropy of clusters. We observe that in spite of the difference in scaling properties of NTIP and TIP, there is no difference in the values of anisotropy quantifiers of these processes. Furthermore, we find that in completely random media, the invasion percolation clusters are on average slightly less isotropic than standard percolation clusters. Introducing isotropic long-range correlations into the media reduces the isotropy of the invasion percolation clusters. The effect is more pronounced for the case of persisting long-range correlations. The implication of boundary conditions on the shape of clusters is another subject of interest. Compared to the case of free boundary conditions, IP clusters of conventional rectangular geometry turn out to be more isotropic. Moreover, we see that in conventional rectangular geometry the NTIP clusters are more isotropic than TIP clusters

Smoothed universal correlations in the two-dimensional Anderson model

We report on calculations of smoothed spectral correlations in the two-dimensional Anderson model for weak disorder. As pointed out in (M. Wilkinson, J. Phys. A: Math. Gen. 21, 1173 (1988)), an analysis of the smoothing dependence of the correlation functions provides a sensitive means of establishing consistency with random matrix theory. We use a semiclassical approach to describe these fluctuations and offer a detailed comparison between numerical and analytical calculations for an exhaustive set of two-point correlation functions. We consider parametric correlation functions with an external Aharonov-Bohm flux as a parameter and discuss two cases, namely broken time-reversal invariance and partial breaking of time-reversal invariance. Three types of correlation functions are considered: density-of-states, velocity and matrix element correlation functions. For the values of smoothing parameter close to the mean level spacing the semiclassical expressions and the numerical results agree quite well in the whole range of the magnetic flux.Comment: 12 pages, 14 figures submitted to Phys. Rev.

Semiclassical cross section correlations

We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth classical limit the autocorrelation function of such matrix elements has two contributions with relative weights determined by classical dynamics. We show how the random matrix result can be obtained if the operator approaches a projector onto a single initial state. The expressions are verified in calculations for the kicked rotor.Comment: 6 pages, 2 figure

Identification of Specific Inhibitors of Trypanosoma cruzi Malic Enzyme Isoforms by Target-Based HTS.

Trypanosoma cruzi is the causative agent of Chagas disease. The lack of an efficient and safe treatment supports the research into novel metabolic targets, with the malic enzyme (ME) representing one such potential candidate. T. cruzi expresses a cytosolic (TcMEc) and a mitochondrial (TcMEm) ME isoform, with these activities functioning to generate NADPH, a key source of reducing equivalents that drives a range of anabolic and protective processes. To identify specific inhibitors that target TcMEs, two independent high-throughput screening strategies using a diversity library containing 30,000 compounds were employed. IC50 values of 262 molecules were determined for both TcMEs, as well as for three human ME isoforms, with the inhibitors clustered into six groups according to their chemical similarity. The most potent hits belonged to a sulfonamide group that specifically target TcMEc. Moreover, several selected inhibitors of both TcMEs showed a trypanocidal effect against the replicative forms of T. cruzi. The chemical diversity observed among those compounds that inhibit TcMEs activity emphasizes the druggability of these enzymes, with a sulfonamide-based subset of compounds readily able to block TcMEc function at a low nanomolar range.The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Sao Paulo Research Foundation (FAPESP) (process numbers 2013/03983-5, 2012/23682-7, and 2015/03336-5)

Complex Periodic Orbits and Tunnelling in Chaotic Potentials

We derive a trace formula for the splitting-weighted density of states suitable for chaotic potentials with isolated symmetric wells. This formula is based on complex orbits which tunnel through classically forbidden barriers. The theory is applicable whenever the tunnelling is dominated by isolated orbits, a situation which applies to chaotic systems but also to certain near-integrable ones. It is used to analyse a specific two-dimensional potential with chaotic dynamics. Mean behaviour of the splittings is predicted by an orbit with imaginary action. Oscillations around this mean are obtained from a collection of related orbits whose actions have nonzero real part

A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems

We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit corrections; each orbit is weighted by the usual Gutzwiller factor times $A_p B_p ...$, where $A_p$ is the average of the classical observable $A$ along the periodic orbit $p$. This structure for the orbit corrections was previously proposed by Main and Wunner (chao-dyn/9904040) on the basis of numerical evidence.Comment: 8 pages; analysis made more rigorous in the revised versio

Current noise of a superconducting single electron transistor coupled to a resonator

We analyze the current and zero-frequency current noise properties of a superconducting single electron resonator (SSET) coupled to a resonator, focusing on the regime where the SSET is operated in the vicinity of the Josephson quasiparticle resonance. We consider a range of coupling strengths and resonator frequencies to reflect the fact that in practice the system can be tuned to quite a high degree with the resonator formed either by a nanomechanical oscillator or a superconducting stripline fabricated in close proximity to the SSET. For very weak couplings the SSET acts on the resonator like an effective thermal bath. In this regime the current characteristics of the SSET are only weakly modified by the resonator. Using a mean field approach, we show that the current noise is nevertheless very sensitive to the correlations between the resonator and the SSET charge. For stronger couplings, the SSET can drive the resonator into limit cycle states where self-sustained oscillation occurs and we find that regions of well-defined bistability exist. Dynamical transitions into and out of the limit cycle state are marked by strong fluctuations in the resonator energy, but these fluctuations are suppressed within the limit cycle state. We find that the current noise of the SSET is strongly influenced by the fluctuations in the resonator energy and hence should provide a useful indicator of the resonator's dynamics.Comment: Reduced quality figures for arXiv version; v2 minor correction

Partnership, ownership and control: the impact of corporate governance on employment relations

Prevailing patterns of dispersed share ownership and rules of corporate governance for UK listed companies appear to constrain the ability of managers to make credible, long-term commitments to employees of the kind needed to foster effective labour-management partnerships. We present case study evidence which suggests that such partnerships can nevertheless emerge where product market conditions and the regulatory environment favour a stakeholder orientation. Proactive and mature partnerships may also be sustained where the board takes a strategic approach to mediating between the claims of different stakeholder groups, institutional investors are prepared to take a long-term view of their holdings, and strong and independent trade unions are in a position to facilitate organisational change