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 $\sim 1/\hbar$ 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