296 research outputs found
Level velocity statistics of hyperbolic chaos
A generalized version of standard map is quantized as a model of quantum
chaos. It is shown that, in hyperbolic chaotic regime, second moment of quantum
level velocity is as predicted by the random matrix theory.Comment: 11 pages, 4 figure
Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map
We rationalize the somewhat surprising efficacy of the Hadamard transform in
simplifying the eigenstates of the quantum baker's map, a paradigmatic model of
quantum chaos. This allows us to construct closely related, but new, transforms
that do significantly better, thus nearly solving for many states of the
quantum baker's map. These new transforms, which combine the standard Fourier
and Hadamard transforms in an interesting manner, are constructed from
eigenvectors of the shift permutation operator that are also simultaneous
eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal)
symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title;
corrected minor error
Recurrence of fidelity in near integrable systems
Within the framework of simple perturbation theory, recurrence time of
quantum fidelity is related to the period of the classical motion. This
indicates the possibility of recurrence in near integrable systems. We have
studied such possibility in detail with the kicked rotor as an example. In
accordance with the correspondence principle, recurrence is observed when the
underlying classical dynamics is well approximated by the harmonic oscillator.
Quantum revivals of fidelity is noted in the interior of resonances, while
classical-quantum correspondence of fidelity is seen to be very short for
states initially in the rotational KAM region.Comment: 13 pages, 6 figure
Chaos in a well : Effects of competing length scales
A discontinuous generalization of the standard map, which arises naturally as
the dynamics of a periodically kicked particle in a one dimensional infinite
square well potential, is examined. Existence of competing length scales,
namely the width of the well and the wavelength of the external field,
introduce novel dynamical behaviour. Deterministic chaos induced diffusion is
observed for weak field strengths as the length scales do not match. This is
related to an abrupt breakdown of rotationally invariant curves and in
particular KAM tori. An approximate stability theory is derived wherein the
usual standard map is a point of ``bifurcation''.Comment: 15 pages, 5 figure
Multifractal eigenstates of quantum chaos and the Thue-Morse sequence
We analyze certain eigenstates of the quantum baker's map and demonstrate,
using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse
sequence, a simple sequence that is at the border between quasi-periodicity and
chaos, and hence is a good paradigm for quantum chaotic states. We show a
family of states that are also simply related to Thue-Morse sequence, and are
strongly scarred by short periodic orbits and their homoclinic excursions. We
give approximate expressions for these states and provide evidence that these
and other generic states are multifractal.Comment: Substantially modified from the original, worth a second download. To
appear in Phys. Rev. E as a Rapid Communicatio
Interpreting sources of variation in clinical gait analysis: A case study
© 2016 Objective To illustrate and discuss sources of gait deviations (experimental, genuine and intentional) during a gait analysis and how these deviations inform clinical decision making. Methods A case study of a 24-year old male diagnosed with Alkaptonuria undergoing a routine gait analysis. A 3D motion capture with the Helen-Hayes marker set was used to quantify lower-limb joint kinematics during barefoot walking along a 10 m walkway at a self-selected pace. Additional 2D video data were recorded in the sagittal and frontal plane. The patient reported no aches or pains in any joint and described his lifestyle as active. Results Temporal-spatial parameters were within normal ranges for his age and sex. Three sources of gait deviations were identified; the posteriorly rotated pelvis was due to an experimental error and marker misplacement, the increased rotation of the pelvis in the horizontal plane was genuine and observed in both 3D gait curves and in 2D video analysis, finally the inconsistency in knee flexion/extension combined with a seemingly innocuous interest in the consequences of abnormal gait suggested an intentional gait deviation. Conclusions Gait analysis is an important analytical tool in the management of a variety of conditions that negatively impact on movement. Experienced gait analysts have the ability to recognise genuine gait adaptations that forms part of the decision-making process for that patient. However, their role also necessitates the ability to identify and correct for experimental errors and critically evaluate when a deviation may not be genuine
What does the arthropathy of alkaptonuria teach us about disease mechanisms in osteoarthritis and ageing of joints? Lessons from a rare disease
AKU Society, the Rosetrees Foundation, the Childwick Trust, the Big Lottery and EUFP
Record statistics in random vectors and quantum chaos
The record statistics of complex random states are analytically calculated,
and shown that the probability of a record intensity is a Bernoulli process.
The correlation due to normalization leads to a probability distribution of the
records that is non-universal but tends to the Gumbel distribution
asymptotically. The quantum standard map is used to study these statistics for
the effect of correlations apart from normalization. It is seen that in the
mixed phase space regime the number of intensity records is a power law in the
dimensionality of the state as opposed to the logarithmic growth for random
states.Comment: figures redrawn, discussion adde
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