10,000 research outputs found
Nonlinear dynamical systems and classical orthogonal polynomials
It is demonstrated that nonlinear dynamical systems with analytic
nonlinearities can be brought down to the abstract Schr\"odinger equation in
Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion
of solutions to the Schr\"odinger equation in the particular occupation number
representation are expressed by means of the classical orthogonal polynomials.
The introduced formalism amounts a generalization of the classical methods for
linearization of nonlinear differential equations such as the Carleman
embedding technique and Koopman approach.Comment: 21 pages latex, uses revte
Quantum particle on hyperboloid
We present quantization of particle dynamics on one-sheet hyperboloid
embedded in three dimensional Minkowski space. Taking account of all global
symmetries enables unique quantization. Making use of topology of canonical
variables not only simplifies calculations but also gives proper framework for
analysis.Comment: 7 pages, no figures, revtex
A Comparative Law Analysis of the Retained Rights of Artists
This Article presents an analytical and theoretical discussion of how an artist\u27s artwork should be treated once it enters the global marketplace. Considering only the visual arts, the answer is short and simple: this Author believes that all, or at least the better-known legal systems, uphold the rights granted to the artist when the work was created. Consequently, the artist retains some rights not only as the artist\u27s intellectual property, but also in its tangible manifestation, for example, sculpture or painting--traditionally called corpus mechanicum--even though he does not own this particular sculpture or painting anymore. This, however, is only a simple explanation: the remainder of the problem is decidedly more complex. Transfer of ownership of the art object to a third party results in the imposition of the artist\u27s rights on the property rights of the new owner of the work. In law this phenomenon is not anything new or special: similar examples exist in other areas. For example, when there are adjoining pieces of real estate, property law differentiates between certain competing neighbors\u27 rights. As is easily seen, not all rights are created equal; on the contrary, some rights are mutually exclusive, thus creating areas of potential conflict. The problem does not exist as long as the artist retains the ownership of his work and its material embodiment because he is the only owner of both aspects of the work. The moment of sale is the beginning of a hypothetical conflict with the new owner. Sometimes the hypothetical conflict becomes very real and requires application to a court for resolution. The judgment in such a case depends on the legal system in question, but regardless of the jurisdiction, it is often very difficult to gauge the outcome of such a conflict. Courts are not uniform in their decisions and the legal systems vary widely--even in the increasingly global world. This diversity results from, on one hand, a different appraisal of interests which come into play, and on the other hand, the enduring nature of some philosophies about artists\u27 work and the work\u27s purposes. Understanding these differences is fundamental to understanding the status of an artist versus the status of his work. Therefore, it is appropriate to start with some historical background. It will be necessary to concentrate on so called moral and moral-like rights; only these rights can be retained by the artist after the art object has been sold or disposed in another way
Bubble statistics and positioning in superhelically stressed DNA
We present a general framework to study the thermodynamic denaturation of
double-stranded DNA under superhelical stress. We report calculations of
position- and size-dependent opening probabilities for bubbles along the
sequence. Our results are obtained from transfer-matrix solutions of the
Zimm-Bragg model for unconstrained DNA and of a self-consistent linearization
of the Benham model for superhelical DNA. The numerical efficiency of our
method allows for the analysis of entire genomes and of random sequences of
corresponding length ( base pairs). We show that, at physiological
conditions, opening in superhelical DNA is strongly cooperative with average
bubble sizes of base pairs (bp), and orders of magnitude higher
than in unconstrained DNA. In heterogeneous sequences, the average degree of
base-pair opening is self-averaging, while bubble localization and statistics
are dominated by sequence disorder. Compared to random sequences with identical
GC-content, genomic DNA has a significantly increased probability to open large
bubbles under superhelical stress. These bubbles are frequently located
directly upstream of transcription start sites.Comment: to be appeared in Physical Review
Astrophysical neutrinos flavored with Beyond the Standard Model physics
We systematically study the allowed parameter space for the flavor
composition of astrophysical neutrinos measured at Earth, including beyond the
Standard Model theories at production, during propagation, and at detection.
One motivation is to illustrate the discrimination power of the next-generation
neutrino telescopes such as IceCube-Gen2. We identify several examples that
lead to potential deviations from the standard neutrino mixing expectation such
as significant sterile neutrino production at the source, effective operators
modifying the neutrino propagation at high energies, dark matter interactions
in neutrino propagation, or non-standard interactions in Earth matter.
IceCube-Gen2 can exclude about 90% of the allowed parameter space in these
cases, and hence will allow to efficiently test and discriminate models. More
detailed information can be obtained from additional observables such as the
energy-dependence of the effect, fraction of electron antineutrinos at the
Glashow resonance, or number of tau neutrino events.Comment: 21 pages, 9 figures, 3 tables, v2: references added, typos corrected,
conclusion unchanged, matches final version in PR
Moving Difference (MDIFF) Non-adiabatic Rapid Sweep (NARS) EPR of Copper(II)
Non-adiabatic rapid sweep (NARS) EPR spectroscopy has been introduced for application to nitroxide-labeled biological samples (Kittell et al., 2011). Displays are pure absorption, and are built up by acquiring data in spectral segments that are concatenated. In this paper we extend the method to frozen solutions of copper-imidazole, a square planar copper complex with four in-plane nitrogen ligands. Pure absorption spectra are created from concatenation of 170 5-gauss segments spanning 850 G at 1.9 GHz. These spectra, however, are not directly useful since nitrogen superhyperfine couplings are barely visible. Application of the moving difference (MDIFF) algorithm to the digitized NARS pure absorption spectrum is used to produce spectra that are analogous to the first harmonic EPR. The signal intensity is about four times higher than when using conventional 100 kHz field modulation, depending on line shape. MDIFF not only filters the spectrum, but also the noise, resulting in further improvement of the SNR for the same signal acquisition time. The MDIFF amplitude can be optimized retrospectively, different spectral regions can be examined at different amplitudes, and an amplitude can be used that is substantially greater than the upper limit of the field modulation amplitude of a conventional EPR spectrometer, which improves the signal-to-noise ratio of broad lines
Coulomb matrix elements for the impact ionization process in nanocrystals: the envelope function approach
We propose a method for calculating Coulomb matrix elements between exciton
and biexciton states in semiconductor nanocrystals based on the envelope
function formalism. We show that such a calculation requires proper treatment
of the Bloch parts of the carrier wave functions which, in the leading order,
leads to spin selection rules identical to those holding for optical interband
transitions. Compared to the usual (intraband) Coulomb couplings, the resulting
matrix elements are additionally scaled by the ratio of the lattice constant to
the nanocrystal radius. As a result, the Coulomb coupling between exciton and
biexciton states scale as 1/R^2. We present also some statistical estimates of
the distribution of the coupling magnitudes and energies of the coupled states
The number of biexciton states coupled to exciton states form a certain energy
range shows a power-law scaling with the ratio of the coupling magnitude to the
energy separation. We estimate also the degree of mixing between exciton and
biexciton states. The amount of biexciton admixture to exciton states at least
1 eV above the multiple exciton generation threshold can reach 80% but varies
strongly with the nanocrystal size.Comment: 11 page
Physics of Quantum Relativity through a Linear Realization
The idea of quantum relativity as a generalized, or rather deformed, version
of Einstein (special) relativity has been taking shape in recent years.
Following the perspective of deformations, while staying within the framework
of Lie algebra, we implement explicitly a simple linear realization of the
relativity symmetry, and explore systematically the resulting physical
interpretations. Some suggestions we make may sound radical, but are arguably
natural within the context of our formulation. Our work may provide a new
perspective on the subject matter, complementary to the previous approach(es),
and may lead to a better understanding of the physics.Comment: 27 pages in Revtex, no figure; proof-edited version to appear in
Phys.Rev.
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