1,320 research outputs found
On the distribution of the total energy of a system on non-interacting fermions: random matrix and semiclassical estimates
We consider a single particle spectrum as given by the eigenvalues of the
Wigner-Dyson ensembles of random matrices, and fill consecutive single particle
levels with n fermions. Assuming that the fermions are non-interacting, we show
that the distribution of the total energy is Gaussian and its variance grows as
n^2 log n in the large-n limit. Next to leading order corrections are computed.
Some related quantities are discussed, in particular the nearest neighbor
spacing autocorrelation function. Canonical and gran canonical approaches are
considered and compared in detail. A semiclassical formula describing, as a
function of n, a non-universal behavior of the variance of the total energy
starting at a critical number of particles is also obtained. It is illustrated
with the particular case of single particle energies given by the imaginary
part of the zeros of the Riemann zeta function on the critical line.Comment: 28 pages in Latex format, 5 figures, submitted for publication to
Physica
Semiclassical Theory of Bardeen-Cooper-Schrieffer Pairing-Gap Fluctuations
Superfluidity and superconductivity are genuine many-body manifestations of
quantum coherence. For finite-size systems the associated pairing gap
fluctuates as a function of size or shape. We provide a parameter free
theoretical description of pairing fluctuations in mesoscopic systems
characterized by order/chaos dynamics. The theory accurately describes
experimental observations of nuclear superfluidity (regular system), predicts
universal fluctuations of superconductivity in small chaotic metallic grains,
and provides a global analysis in ultracold Fermi gases.Comment: 4 pages, 2 figure
Spectral spacing correlations for chaotic and disordered systems
New aspects of spectral fluctuations of (quantum) chaotic and diffusive
systems are considered, namely autocorrelations of the spacing between
consecutive levels or spacing autocovariances. They can be viewed as a
discretized two point correlation function. Their behavior results from two
different contributions. One corresponds to (universal) random matrix
eigenvalue fluctuations, the other to diffusive or chaotic characteristics of
the corresponding classical motion. A closed formula expressing spacing
autocovariances in terms of classical dynamical zeta functions, including the
Perron-Frobenius operator, is derived. It leads to a simple interpretation in
terms of classical resonances. The theory is applied to zeros of the Riemann
zeta function. A striking correspondence between the associated classical
dynamical zeta functions and the Riemann zeta itself is found. This induces a
resurgence phenomenon where the lowest Riemann zeros appear replicated an
infinite number of times as resonances and sub-resonances in the spacing
autocovariances. The theoretical results are confirmed by existing ``data''.
The present work further extends the already well known semiclassical
interpretation of properties of Riemann zeros.Comment: 28 pages, 6 figures, 1 table, To appear in the Gutzwiller
Festschrift, a special Issue of Foundations of Physic
On the ground--state energy of finite Fermi systems
We study the ground--state shell correction energy of a fermionic gas in a
mean--field approximation.
Considering the particular case of 3D harmonic trapping potentials, we show
the rich variety of different behaviors (erratic, regular, supershells) that
appear when the number--theoretic properties of the frequency ratios are
varied. For self--bound systems, where the shape of the trapping potential is
determined by energy minimization, we obtain accurate analytic formulas for the
deformation and the shell correction energy as a function of the particle
number . Special attention is devoted to the average of the shell correction
energy. We explain why in self--bound systems it is a decreasing (and negative)
function of .Comment: 10 pages, 5 figures, 2 table
Dipole Oscillations of a Bose-Einstein Condensate in Presence of Defects and Disorder
We consider dipole oscillations of a trapped dilute Bose-Einstein condensate
in the presence of a scattering potential consisting either in a localized
defect or in an extended disordered potential. In both cases the breaking of
superfluidity and the damping of the oscillations are shown to be related to
the appearance of a nonlinear dissipative flow. At supersonic velocities the
flow becomes asymptotically dissipationless.Comment: 4 pages, 4 figure
Impact of knee marker misplacement on gait kinematics of children with cerebral palsy using the Conventional Gait Model — a sensitivity study
Clinical gait analysis is widely used in clinical routine to assess the function of patients with motor disorders. The proper assessment of the patient’s function relies greatly on the repeatability between the measurements. Marker misplacement has been reported as the largest source of variability between measurements and its impact on kinematics is not fully understood. Thus, the purpose of this study was: 1) to evaluate the impact of the misplacement of the lateral femoral epicondyle marker on lower limb kinematics, and 2) evaluate if such impact can be predicted. The kinematic data of 10 children with cerebral palsy and 10 aged-match typical developing children were included. The lateral femoral epicondyle marker was virtually misplaced around its measured position at different magnitudes and directions. The outcome to represent the impact of each marker misplacement on the lower limb was the root mean square deviations between the resultant kinematics from each simulated misplacement and the originally calculated kinematics. Correlation and regression equations were estimated between the root mean square deviation and the magnitude of the misplacement expressed in percentage of leg length. Results indicated that the lower-limb kinematics is highly sensitive to the lateral femoral epicondyle marker misplacement in the anterior-posterior direction. The joint angles most impacted by the anterior-posterior misplacement were the hip internal-external rotation (5.3° per 10 mm), the ankle internal-external rotation (4.4° per 10 mm) and the knee flexion-extension (4.2° per 10 mm). Finally, it was observed that the lower the leg length, the higher the impact of misplacement on kinematics. This impact was predicted by regression equations using the magnitude of misplacement expressed in percentage of leg length. An error below 5° on all joints requires a marker placement repeatability under 1.2% of the leg length. In conclusion, the placement of the lateral femoral epicondyle marker in the antero-posterior direction plays a crucial role on the reliability of gait measurements with the Conventional Gait Model
Quantitative analysis of microstructures produced by creep of Ti-48Al-2Cr-2Nb-1B: Thermal and athermal mechanisms
A γ-based TiAl alloy with equiaxed microstructure and fine grain size has been studied to analyze the deformation mechanisms responsible for the creep behavior. The microstructures produced by creep and high temperature deformation have been examined by TEM to obtain information about the different aspects characterizing the primary and secondary stages of creep. Mechanical twinning has been confirmed to occur in a fraction of the grains that never exceeds 50% while 1/2 ‹110› dislocations are active within all the γ grains. The twins are only responsible for a small amount of strain, but they lead to a subdivision of the microstructure and determine (directly or indirectly) the hardening process observed during the primary stage of creep. We have proposed that during the secondary stage the creep rate is determined by the unblocking of pinned dislocations by processes such as a pipe diffusion or cross slip that allow thermally activated glide of 1/2‹110› dislocations on (001) plane
Overview of SERI's high efficiency solar cell research
The bulk of the research efforts supported by the Solar Energy Research Institute (SERI) High Efficiency Concepts area has been directed towards establishing the feasibility of achieving very high efficiencies, 30% for concentrator and more than 20% for thin film flat plate, in solar cell designs which could possibly be produced competitively. The research has accomplished a great deal during the past two years. Even though the desired performance levels have not yet been demonstrated, based on the recent progress, a greater portion of the terrestrial photovoltaics community believes that these efficiencies are attainable. The program will now allocate a larger portion of resources to low cost, large area deposition technology. The program is currently shifting greater emphasis on to the study of crystal growth in order to provide the understanding and tools needed to design a large area process
Finite size corrections to the blackbody radiation laws
We investigate the radiation of a blackbody in a cavity of finite size. For a
given geometry, we use semiclassical techniques to obtain explicit expressions
of the modified Planck's and Stefan-Boltzmann's blackbody radiation laws as a
function of the size and shape of the cavity. We determine the range of
parameters (temperature, size and shape of the cavity) for which these effects
are accessible to experimental verification. Finally we discuss potential
applications of our findings in the physics of the cosmic microwave background
and sonoluminescence.Comment: 5 pages, 1 figure, journal versio
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
- …