Ehrenfest times for classically chaotic systems

We describe the quantum mechanical spreading of a Gaussian wave packet by means of the semiclassical WKB approximation of Berry and Balazs. We find that the time scale $\tau$ on which this approximation breaks down in a chaotic system is larger than the Ehrenfest times considered previously. In one dimension \tau=\fr{7}{6}\lambda^{-1}\ln(A/\hbar), with $\lambda$ the Lyapunov exponent and $A$ a typical classical action.Comment: 4 page

Universality of Parametric Spectral Correlations: Local versus Extended Perturbing Potentials

We explore the influence of an arbitrary external potential perturbation V on the spectral properties of a weakly disordered conductor. In the framework of a statistical field theory of a nonlinear sigma-model type we find, depending on the range and the profile of the external perturbation, two qualitatively different universal regimes of parametric spectral statistics (i.e. cross-correlations between the spectra of Hamiltonians H and H+V). We identify the translational invariance of the correlations in the space of Hamiltonians as the key indicator of universality, and find the connection between the coordinate system in this space which makes the translational invariance manifest, and the physically measurable properties of the system. In particular, in the case of localized perturbations, the latter turn out to be the eigenphases of the scattering matrix for scattering off the perturbing potential V. They also have a purely statistical interpretation in terms of the moments of the level velocity distribution. Finally, on the basis of this analysis, a set of results obtained recently by the authors using random matrix theory methods is shown to be applicable to a much wider class of disordered and chaotic structures.Comment: 16 pages, 7 eps figures (minor changes and reference [17] added

Nearest-neighbor distribution for singular billiards

The exact computation of the nearest-neighbor spacing distribution P(s) is performed for a rectangular billiard with point-like scatterer inside for periodic and Dirichlet boundary conditions and it is demonstrated that for large s this function decreases exponentially. Together with the results of [Bogomolny et al., Phys. Rev. E 63, 036206 (2001)] it proves that spectral statistics of such systems is of intermediate type characterized by level repulsion at small distances and exponential fall-off of the nearest-neighbor distribution at large distances. The calculation of the n-th nearest-neighbor spacing distribution and its asymptotics is performed as well for any boundary conditions.Comment: 38 pages, 10 figure

Conductance Peak Height Correlations for a Coulomb-Blockaded Quantum Dot in a Weak Magnetic Field

We consider statistical correlations between the heights of conductance peaks corresponding to two different levels in a Coulomb-blockaded quantum dot. Correlations exist for two peaks at the same magnetic field if the field does not fully break time-reversal symmetry as well as for peaks at different values of a magnetic field that fully breaks time-reversal symmetry. Our results are also relevant to Coulomb-blockade conductance peak height statistics in the presence of weak spin-orbit coupling in a chaotic quantum dot.Comment: 5 pages, 3 figures, REVTeX 4, accepted for publication in Phys. Rev.

A Bayesian elicitation of veterinary beliefs regarding systemic dry cow therapy: variation and importance for clinical trial design

The two key aims of this research were: (i) to conduct a probabilistic elicitation to quantify the variation in veterinarians’ beliefs regarding the efficacy of systemic antibiotics when used as an adjunct to intra-mammary dry cow therapy and (ii) to investigate (in a Bayesian statistical framework) the strength of future research evidence required (in theory) to change the beliefs of practising veterinary surgeons regarding the efficacy of systemic antibiotics, given their current clinical beliefs. The beliefs of 24 veterinarians in 5 practices in England were quantified as probability density functions. Classic multidimensional scaling revealed major variations in beliefs both within and between veterinary practices which included: confident optimism, confident pessimism and considerable uncertainty. Of the 9 veterinarians interviewed holding further cattle qualifications, 6 shared a confidently pessimistic belief in the efficacy of systemic therapy and whilst 2 were more optimistic, they were also more uncertain. A Bayesian model based on a synthetic dataset from a randomised clinical trial (showing no benefit with systemic therapy) predicted how each of the 24 veterinarians’ prior beliefs would alter as the size of the clinical trial increased, assuming that practitioners would update their beliefs rationally in accordance with Bayes’ theorem. The study demonstrated the usefulness of probabilistic elicitation for evaluating the diversity and strength of practitioners’ beliefs. The major variation in beliefs observed raises interest in the veterinary profession's approach to prescribing essential medicines. Results illustrate the importance of eliciting prior beliefs when designing clinical trials in order to increase the chance that trial data are of sufficient strength to alter the clinical beliefs of practitioners and do not merely serve to satisfy researchers

Decoherence as Decay of the Loschmidt Echo in a Lorentz Gas

Classical chaotic dynamics is characterized by the exponential sensitivity to initial conditions. Quantum mechanics, however, does not show this feature. We consider instead the sensitivity of quantum evolution to perturbations in the Hamiltonian. This is observed as an atenuation of the Loschmidt Echo, $M(t)$, i.e. the amount of the original state (wave packet of width $\sigma$) which is recovered after a time reversed evolution, in presence of a classically weak perturbation. By considering a Lorentz gas of size $L$, which for large $L$ is a model for an {\it unbounded} classically chaotic system, we find numerical evidence that, if the perturbation is within a certain range, $M(t)$ decays exponentially with a rate $1/\tau_{\phi}$ determined by the Lyapunov exponent $\lambda$ of the corresponding classical dynamics. This exponential decay extends much beyond the Eherenfest time $t_{E}$ and saturates at a time $t_{s}\simeq \lambda^{-1}\ln (\widetilde{N})$, where $\widetilde{N}\simeq (L/\sigma)^2$ is the effective dimensionality of the Hilbert space. Since $\tau _{\phi}$ quantifies the increasing uncontrollability of the quantum phase (decoherence) its characterization and control has fundamental interest.Comment: 3 ps figures, uses Revtex and epsfig. Major revision to the text, now including discussion and references on averaging and Ehrenfest time. Figures 2 and 3 content and order change

Holonomic quantum gates: A semiconductor-based implementation

We propose an implementation of holonomic (geometrical) quantum gates by means of semiconductor nanostructures. Our quantum hardware consists of semiconductor macroatoms driven by sequences of ultrafast laser pulses ({\it all optical control}). Our logical bits are Coulomb-correlated electron-hole pairs (excitons) in a four-level scheme selectively addressed by laser pulses with different polarization. A universal set of single and two-qubit gates is generated by adiabatic change of the Rabi frequencies of the lasers and by exploiting the dipole coupling between excitons.Comment: 10 Pages LaTeX, 10 Figures include

Gravitational Geometric Phase in the Presence of Torsion

We investigate the relativistic and non-relativistic quantum dynamics of a neutral spin-1/2 particle submitted an external electromagnetic field in the presence of a cosmic dislocation. We analyze the explicit contribution of the torsion in the geometric phase acquired in the dynamic of this neutral spinorial particle. We discuss the influence of the torsion in the relativistic geometric phase. Using the Foldy-Wouthuysen approximation, the non-relativistic quantum dynamics are studied and the influence of the torsion in the Aharonov-Casher and He-McKellar-Wilkens effects are discussed.Comment: 14 pages, no figur

Quantum Effects in Coulomb Blockade

We review the quantum interference effects in a system of interacting electrons confined to a quantum dot. The review starts with a description of an isolated quantum dot. We discuss the status of the Random Matrix theory (RMT) of the one-electron states in the dot, present the universal form of the interaction Hamiltonian compatible with the RMT, and derive the leading corrections to the universal interaction Hamiltonian. Next, we discuss a theoretical description of a dot connected to leads via point contacts. Having established the theoretical framework to describe such an open system, we discuss its transport and thermodynamic properties. We review the evolution of the transport properties with the increase of the contact conductances from small values to values $\sim e^2/\pi\hbar$. In the discussion of transport, the emphasis is put on mesoscopic fluctuations and the Kondo effect in the conductance.Comment: 169 pages, 28 figures; several references and footnotes are added, and noticed typos correcte

A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade

We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi surface distortion), but smeared and pinned by disorder. At finite $g$, the two phases and critical point evolve into three regimes in the $u_m-1/g$ plane -- weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum critical point. In the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $\Delta$ within a few $\Delta$'s of the Fermi energy due to coupling to collective excitations. In the strong coupling regime if $m$ is odd, the dot will (if isolated) cross over from the orthogonal to unitary ensemble for an exponentially small external flux, or will (if strongly coupled to leads) break time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we are treating charge-channel instabilities in spinful systems, leaving spin-channel instabilities for future work. No substantive results are change