930 research outputs found
Limitations on the Use of Appropriations Riders by Congress to Effectuate Substantive Policy Changes
Parametric statistics of zeros of Husimi representations of quantum chaotic eigenstates and random polynomials
Local parametric statistics of zeros of Husimi representations of quantum
eigenstates are introduced. It is conjectured that for a classically fully
chaotic systems one should use the model of parametric statistics of complex
roots of Gaussian random polynomials which is exactly solvable as demonstrated
below. For example, the velocities (derivatives of zeros of Husimi function
with respect to an external parameter) are predicted to obey a universal
(non-Maxwellian) distribution where is the mean square velocity. The
conjecture is demonstrated numerically in a generic chaotic system with two
degrees of freedom. Dynamical formulation of the ``zero-flow'' in terms of an
integrable many-body dynamical system is given as well.Comment: 13 pages in plain Latex (1 figure available upon request
Superfluidity versus Anderson localization in a dilute Bose gas
We consider the motion of a quasi one dimensional beam of Bose-Einstein
condensed particles in a disordered region of finite extent. Interaction
effects lead to the appearance of two distinct regions of stationary flow. One
is subsonic and corresponds to superfluid motion. The other one is supersonic,
dissipative and shows Anderson localization. We compute analytically the
interaction-dependent localization length. We also explain the disappearance of
the supersonic stationary flow for large disordered samples.Comment: 4 pages, 3 figures, final published versio
Level density of a Fermi gas: average growth and fluctuations
We compute the level density of a two--component Fermi gas as a function of
the number of particles, angular momentum and excitation energy. The result
includes smooth low--energy corrections to the leading Bethe term (connected to
a generalization of the partition problem and Hardy--Ramanujan formula) plus
oscillatory corrections that describe shell effects. When applied to nuclear
level densities, the theory provides a unified formulation valid from
low--lying states up to levels entering the continuum. The comparison with
experimental data from neutron resonances gives excellent results.Comment: 4 pages, 1 figur
Average ground-state energy of finite Fermi systems
Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give
a good description of the smooth average part of the total energy of a Fermi
gas in some external potential when the chemical potential is varied. However,
in systems with a fixed number of particles N, these methods overbind the
actual average of the quantum energy as N is varied. We describe a theory that
accounts for this effect. Numerical illustrations are discussed for fermions
trapped in a harmonic oscillator potential and in a hard wall cavity, and for
self-consistent calculations of atomic nuclei. In the latter case, the
influence of deformations on the average behavior of the energy is also
considered.Comment: 10 pages, 8 figure
Crystal properties of eigenstates for quantum cat maps
Using the Bargmann-Husimi representation of quantum mechanics on a torus
phase space, we study analytically eigenstates of quantized cat maps. The
linearity of these maps implies a close relationship between classically
invariant sublattices on the one hand, and the patterns (or `constellations')
of Husimi zeros of certain quantum eigenstates on the other hand. For these
states, the zero patterns are crystals on the torus. As a consequence, we can
compute explicit families of eigenstates for which the zero patterns become
uniformly distributed on the torus phase space in the limit . This
result constitutes a first rigorous example of semi-classical equidistribution
for Husimi zeros of eigenstates in quantized one-dimensional chaotic systems.Comment: 43 pages, LaTeX, including 7 eps figures Some amendments were made in
order to clarify the text, mainly in the 4 first sections. Figures are
unchanged. To be published in: Nonlinearit
Reliability of walking and stair climbing kinematics in a young obese population using a standard kinematic and the CGM2 model
Background:
Recently, the successor of the Conventional Gait Model, the CGM2 was introduced. Even though achievable reliability of gait kinematics is a well-assessed topic in gait analysis for several models, information about reliability in difficult study samples with high amount of subcutaneous fat is scarce and to date, not available for the CGM2. Therefore, this study evaluated the test–retest reliability of the CGM2 model for difficult data with high amount of soft tissue artifacts.
Research question:
What is the test–retest reliability of the CGM2 during level walking and stair climbing in a young obese population? Is there a clinically relevant difference in reliability between a standard direct kinematic model and the CGM2?
Methods:
A retrospective test–retest dataset from eight male and two female volunteers was used. It comprised standard 3D gait analysis data of three walking conditions: level walking, stair ascent and descent. To quantify test–retest reliability the Standard Error of Measurement (SEM) was calculated for each kinematic waveform for a direct kinematic model (Cleveland clinic marker set) and the CGM2.
Results:
Both models showed an acceptable level of test–retest reliability in all three walking conditions. However, SEM ranged between two and five degrees () for both models and, thus, needs consideration during interpretation. The choice of model did not affect reliability considerably. Differences in SEM between stair climbing and level walking were small and not clinically relevant (1°).
Significance:
Results showed an acceptable level of reliability and only small differences between the models. It is noteworthy, that the SEM was increased during the first half of swing in all walking conditions. This might be attributed to increased variability resulting for example from inaccurate knee and ankle axis definitions or increased variability in the gait pattern and needs to be considered during data interpretation
Band Distributions for Quantum Chaos on the Torus
Band distributions (BDs) are introduced describing quantization in a toral
phase space. A BD is the uniform average of an eigenstate phase-space
probability distribution over a band of toral boundary conditions. A general
explicit expression for the Wigner BD is obtained. It is shown that the Wigner
functions for {\em all} of the band eigenstates can be reproduced from the
Wigner BD. Also, BDs are shown to be closer to classical distributions than
eigenstate distributions. Generalized BDs, associated with sets of adjacent
bands, are used to extend in a natural way the Chern-index characterization of
the classical-quantum correspondence on the torus to arbitrary rational values
of the scaled Planck constant.Comment: 12 REVTEX page
Correlations and fluctuations of a confined electron gas
The grand potential and the response of a phase-coherent confined noninteracting electron gas depend
sensitively on chemical potential or external parameter . We compute
their autocorrelation as a function of , and temperature. The result
is related to the short-time dynamics of the corresponding classical system,
implying in general the absence of a universal regime. Chaotic, diffusive and
integrable motions are investigated, and illustrated numerically. The
autocorrelation of the persistent current of a disordered mesoscopic ring is
also computed.Comment: 12 pages, 1 figure, to appear in Phys. Rev.
Quantum Chaotic Dynamics and Random Polynomials
We investigate the distribution of roots of polynomials of high degree with
random coefficients which, among others, appear naturally in the context of
"quantum chaotic dynamics". It is shown that under quite general conditions
their roots tend to concentrate near the unit circle in the complex plane. In
order to further increase this tendency, we study in detail the particular case
of self-inversive random polynomials and show that for them a finite portion of
all roots lies exactly on the unit circle. Correlation functions of these roots
are also computed analytically, and compared to the correlations of eigenvalues
of random matrices. The problem of ergodicity of chaotic wave-functions is also
considered. For that purpose we introduce a family of random polynomials whose
roots spread uniformly over phase space. While these results are consistent
with random matrix theory predictions, they provide a new and different insight
into the problem of quantum ergodicity. Special attention is devoted all over
the paper to the role of symmetries in the distribution of roots of random
polynomials.Comment: 33 pages, Latex, 6 Figures not included (a copy of them can be
requested at [email protected]); to appear in Journal of Statistical
Physic
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