18,520 research outputs found
Regularity of Bound States
We study regularity of bound states pertaining to embedded eigenvalues of a
self-adjoint operator , with respect to an auxiliary operator that is
conjugate to in the sense of Mourre. We work within the framework of
singular Mourre theory which enables us to deal with confined massless
Pauli-Fierz models, our primary example, and many-body AC-Stark Hamiltonians.
In the simpler context of regular Mourre theory our results boils down to an
improvement of results obtained recently in \cite{CGH}.Comment: 70 page
Asymptotically Universal Crossover in Perturbation Theory with a Field Cutoff
We discuss the crossover between the small and large field cutoff (denoted
x_{max}) limits of the perturbative coefficients for a simple integral and the
anharmonic oscillator. We show that in the limit where the order k of the
perturbative coefficient a_k(x_{max}) becomes large and for x_{max} in the
crossover region, a_k(x_{max}) is proportional to the integral from -infinity
to x_{max} of e^{-A(x-x_0(k))^2}dx. The constant A and the function x_0(k) are
determined empirically and compared with exact (for the integral) and
approximate (for the anharmonic oscillator) calculations. We discuss how this
approach could be relevant for the question of interpolation between
renormalization group fixed points.Comment: 15 pages, 11 figs., improved and expanded version of hep-th/050304
Ab initio study of single molecular transistor modulated by gate-bias
We use a self-consistent method to study the current of the single molecular
transistor modulated by the transverse gate-bias in the level of the
first-principles calculations. The numerical results show that both the
polyacene-dithiol molecules and the fused-ring oligothiophene molecules are the
potential high-frequency molecular transistor controlled by the transverse
field. The long molecules of the polyacene-dithiol or the fused-ring thiophene
are in favor of realizing the gate-bias controlled molecular transistor. The
theoretical results suggest the related experiments.Comment: 14 pages, 7 figure
Perturbation theory of von Neumann Entropy
In quantum information theory, von Neumann entropy plays an important role.
The entropies can be obtained analytically only for a few states. In continuous
variable system, even evaluating entropy numerically is not an easy task since
the dimension is infinite. We develop the perturbation theory systematically
for calculating von Neumann entropy of non-degenerate systems as well as
degenerate systems. The result turns out to be a practical way of the expansion
calculation of von Neumann entropy.Comment: 7 page
The problem of deficiency indices for discrete Schr\"odinger operators on locally finite graphs
The number of self-adjoint extensions of a symmetric operator acting on a
complex Hilbert space is characterized by its deficiency indices. Given a
locally finite unoriented simple tree, we prove that the deficiency indices of
any discrete Schr\"odinger operator are either null or infinite. We also prove
that almost surely, there is a tree such that all discrete Schr\"odinger
operators are essentially self-adjoint. Furthermore, we provide several
criteria of essential self-adjointness. We also adress some importance to the
case of the adjacency matrix and conjecture that, given a locally finite
unoriented simple graph, its the deficiency indices are either null or
infinite. Besides that, we consider some generalizations of trees and weighted
graphs.Comment: Typos corrected. References and ToC added. Paper slightly
reorganized. Section 3.2, about the diagonalization has been much improved.
The older section about the stability of the deficiency indices in now in
appendix. To appear in Journal of Mathematical Physic
Collective synchronization in populations of globally coupled phase oscillators with drifting frequencies
We generalize the Kuramoto model for coupled phase oscillators by allowing
the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such
drifting frequencies were recently measured in cellular populations of
circadian oscillator and inspired our work. Linear stability analysis of the
Fokker-Planck equation for an infinite population is amenable to exact solution
and we show that the incoherent state is unstable passed a critical coupling
strength K_c(\ga, \sigf), where \ga is the inverse characteristic drifting
time and \sigf the asymptotic frequency dispersion. Expectedly agrees
with the noisy Kuramoto model in the large \ga (Schmolukowski) limit but
increases slower as \ga decreases. Asymptotic expansion of the solution for
\ga\to 0 shows that the noiseless Kuramoto model with Gaussian frequency
distribution is recovered in that limit. Thus varying a single parameter allows
to interpolate smoothly between two regimes: one dominated by the frequency
dispersion and the other by phase diffusion.Comment: 5 pages, 5 figures, accepted in Phys. Rev.
Covariant Affine Integral Quantization(s)
Covariant affine integral quantization of the half-plane is studied and
applied to the motion of a particle on the half-line. We examine the
consequences of different quantizer operators built from weight functions on
the half-plane. To illustrate the procedure, we examine two particular choices
of the weight function, yielding thermal density operators and affine inversion
respectively. The former gives rise to a temperature-dependent probability
distribution on the half-plane whereas the later yields the usual canonical
quantization and a quasi-probability distribution (affine Wigner function)
which is real, marginal in both momentum p and position q.Comment: 36 pages, 10 figure
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Frequency-Domain Streak Camera And Tomography For Ultrafast Imaging Of Evolving And Channeled Plasma Accelerator Structures
We demonstrate a prototype Frequency Domain Streak Camera (FDSC) that can capture the picosecond time evolution of the plasma accelerator structure in a single shot. In our prototype Frequency-Domain Streak Camera, a probe pulse propagates obliquely to a sub-picosecond pump pulse that creates an evolving nonlinear index >bubble> in fused silica glass, supplementing a conventional Frequency Domain Holographic (FDH) probe-reference pair that co-propagates with the >bubble>. Frequency Domain Tomography (FDT) generalizes Frequency-Domain Streak Camera by probing the >bubble> from multiple angles and reconstructing its morphology and evolution using algorithms similar to those used in medical CAT scans. Multiplexing methods (Temporal Multiplexing and Angular Multiplexing) improve data storage and processing capability, demonstrating a compact Frequency Domain Tomography system with a single spectrometer.Physic
Resolving the pulsations of subdwarf B stars: HS 0039+4302, HS 0444+0458, and an examination of the group properties of resolved pulsators
We continue our program of single-site observations of pulsating subdwarf B
(sdB) stars and present the results of extensive time series photometry of HS
0039+4302 and HS 0444+0458. Both were observed at MDM Observatory during the
fall of 2005. We extend the number of known frequencies for HS 0039+4302 from 4
to 14 and discover one additional frequency for HS 0444+0458, bringing the
total to three. We perform standard tests to search for multiplet structure,
measure amplitude variations, and examine the frequency density to constrain
the mode degree .
Including the two stars in this paper, 23 pulsating sdB stars have received
follow-up observations designed to decipher their pulsation spectra. It is
worth an examination of what has been detected. We compare and contrast the
frequency content in terms of richness and range and the amplitudes with
regards to variability and diversity. We use this information to examine
observational correlations with the proposed pulsation mechanism as
well as alternative theories.Comment: 32 pages, 18 figures, 7 tables. Accepted for publication in MNRA
How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration?
International audienceThis study provides a comprehensive assessment of state-of-the-art evolutionary multiobjective optimization (EMO) tools' relative effectiveness in calibrating hydrologic models. The relative computational efficiency, accuracy, and ease-of-use of the following EMO algorithms are tested: Epsilon Dominance Nondominated Sorted Genetic Algorithm-II (?-NSGAII), the Multiobjective Shuffled Complex Evolution Metropolis algorithm (MOSCEM-UA), and the Strength Pareto Evolutionary Algorithm 2 (SPEA2). This study uses three test cases to compare the algorithms' performances: (1) a standardized test function suite from the computer science literature, (2) a benchmark hydrologic calibration test case for the Leaf River near Collins, Mississippi, and (3) a computationally intensive integrated surface-subsurface model application in the Shale Hills watershed in Pennsylvania. One challenge and contribution of this work is the development of a methodology for comprehensively comparing EMO algorithms that have different search operators and randomization techniques. Overall, SPEA2 attained competitive to superior results for most of the problems tested in this study. The primary strengths of the SPEA2 algorithm lie in its search reliability and its diversity preservation operator. The biggest challenge in maximizing the performance of SPEA2 lies in specifying an effective archive size without a priori knowledge of the Pareto set. In practice, this would require significant trial-and-error analysis, which is problematic for more complex, computationally intensive calibration applications. ?-NSGAII appears to be superior to MOSCEM-UA and competitive with SPEA2 for hydrologic model calibration. ?-NSGAII's primary strength lies in its ease-of-use due to its dynamic population sizing and archiving which lead to rapid convergence to very high quality solutions with minimal user input. MOSCEM-UA is best suited for hydrologic model calibration applications that have small parameter sets and small model evaluation times. In general, it would be expected that MOSCEM-UA's performance would be met or exceeded by either SPEA2 or ?-NSGAII
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