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 ($10^6-10^9$ base pairs). We show that, at physiological conditions, opening in superhelical DNA is strongly cooperative with average bubble sizes of $10^2-10^3$ 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.