462 research outputs found
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 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 the Lyapunov
exponent and 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, ,
i.e. the amount of the original state (wave packet of width ) which is
recovered after a time reversed evolution, in presence of a classically weak
perturbation. By considering a Lorentz gas of size , which for large is
a model for an {\it unbounded} classically chaotic system, we find numerical
evidence that, if the perturbation is within a certain range, decays
exponentially with a rate determined by the Lyapunov exponent
of the corresponding classical dynamics. This exponential decay
extends much beyond the Eherenfest time and saturates at a time
, where is the effective dimensionality of the Hilbert space. Since 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 . 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
(the Thouless energy) of the Fermi energy. Within this window we show that the
interactions can be characterized by Landau Fermi liquid parameters. When ,
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 (as in a large-N theory). The infinite 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 , the two phases and critical point evolve into three
regimes in the 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
within a few 's of the Fermi energy due to coupling to collective
excitations. In the strong coupling regime if 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
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