Spectral statistics in chaotic systems with a point interaction

We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown for order tau^2 and tau^3 that off-diagonal contributions to the form factor which involve diffractive orbits cancel exactly the diagonal contributions from diffractive orbits, implying that the perturbation by the scatterer does not change the spectral statistic. We further show that parametric spectral statistics for these systems are universal for small changes of the strength of the scatterer.Comment: LaTeX, 21 pages, 7 figures, small corrections, new references adde

Correlations between spectra with different symmetry: any chance to be observed?

A standard assumption in quantum chaology is the absence of correlation between spectra pertaining to different symmetries. Doubts were raised about this statement for several reasons, in particular, because in semiclassics spectra of different symmetry are expressed in terms of the same set of periodic orbits. We reexamine this question and find absence of correlation in the universal regime. In the case of continuous symmetry the problem is reduced to parametric correlation, and we expect correlations to be present up to a certain time which is essentially classical but larger than the ballistic time

The Dirichlet-to-Robin Transform

A simple transformation converts a solution of a partial differential equation with a Dirichlet boundary condition to a function satisfying a Robin (generalized Neumann) condition. In the simplest cases this observation enables the exact construction of the Green functions for the wave, heat, and Schrodinger problems with a Robin boundary condition. The resulting physical picture is that the field can exchange energy with the boundary, and a delayed reflection from the boundary results. In more general situations the method allows at least approximate and local construction of the appropriate reflected solutions, and hence a "classical path" analysis of the Green functions and the associated spectral information. By this method we solve the wave equation on an interval with one Robin and one Dirichlet endpoint, and thence derive several variants of a Gutzwiller-type expansion for the density of eigenvalues. The variants are consistent except for an interesting subtlety of distributional convergence that affects only the neighborhood of zero in the frequency variable.Comment: 31 pages, 5 figures; RevTe

From quantum graphs to quantum random walks

We give a short overview over recent developments on quantum graphs and outline the connection between general quantum graphs and so-called quantum random walks.Comment: 14 pages, 6 figure

Leading off-diagonal contribution to the spectral form factor of chaotic quantum systems

We semiclassically derive the leading off-diagonal correction to the spectral form factor of quantum systems with a chaotic classical counterpart. To this end we present a phase space generalization of a recent approach for uniformly hyperbolic systems (M. Sieber and K. Richter, Phys. Scr. T90, 128 (2001); M. Sieber, J. Phys. A: Math. Gen. 35, L613 (2002)). Our results coincide with corresponding random matrix predictions. Furthermore, we study the transition from the Gaussian orthogonal to the Gaussian unitary ensemble.Comment: 8 pages, 2 figures; J. Phys. A: Math. Gen. (accepted for publication

Evaluating climate change adaptation options in the agriculture sector: a PROMETHEE-GAIA analysis

Mitigating maladaptation and effectively managing climate risks are crucial components of strategic planning in agriculture amidst climate change. Evaluation serves as a pivotal element in this process, facilitating the identification of effective adaptation strategies tailored to local contexts. Consequently, it's imperative to thoroughly evaluate these strategies to ensure their success and resilience. The current study evaluated adaptation methods tailored to the local context in southwest Iran across three categories-crop, farm, and water management-employing Multi-Criteria Decision-Making (MCDM) and the PROMETHEE-GAIA. Sensitivity analysis was performed during the AHP (Analytical Hierarchy Process) stage to confirm the criteria weights and in the PROMETHEE to confirm the ranking. A set of eight criteria, including effectiveness/importance, affordability, institutional feasibility, technical feasibility, social feasibility, traditional acceptance, flexibility, and environment side effects (positive) were applied to evaluate the adaptation measures. Our results indicated the three highest rankings in each set of measures, as follows: i) crop management—relay intercropping, change of crop type, and mixed intercropping; ii) farm management—pest and disease management, weed control, and crop rotation; iii) water management—lining water canals or covering their earth floors with nylon, using pipes rather than open canals to transfer water to the field, and increasing the time intervals between irrigations to deal with water shortages. The outcomes underscore the urgency of formulating region-specific adaptation policies that align with local expertise and contextual needs. By prioritizing the identified effective strategies, policymakers can enhance resilience against water scarcity in southwest Iran. Moreover, the study highlights the importance of ongoing evaluation and adaptation, emphasizing the dynamic nature of climate challenges and the need for continuous refinement of adaptive policies

Rotation Measure Synthesis of Galactic Polarized Emission with the DRAO 26-m Telescope

Radio polarimetry at decimetre wavelengths is the principal source of information on the Galactic magnetic field. The diffuse polarized emission is strongly influenced by Faraday rotation in the magneto-ionic medium and rotation measure is the prime quantity of interest, implying that all Stokes parameters must be measured over wide frequency bands with many frequency channels. The DRAO 26-m Telescope has been equipped with a wideband feed, a polarization transducer to deliver both hands of circular polarization, and a receiver, all operating from 1277 to 1762 MHz. Half-power beamwidth is between 40 and 30 arcminutes. A digital FPGA spectrometer, based on commercially available components, produces all Stokes parameters in 2048 frequency channels over a 485-MHz bandwidth. Signals are digitized to 8 bits and a Fast Fourier Transform is applied to each data stream. Stokes parameters are then generated in each frequency channel. This instrument is in use at DRAO for a Northern sky polarization survey. Observations consist of scans up and down the Meridian at a drive rate of 0.9 degree per minute to give complete coverage of the sky between declinations -30 degree and 90 degree. This paper presents a complete description of the receiver and data acquisition system. Only a small fraction of the frequency band of operation is allocated for radio astronomy, and about 20 percent of the data are lost to interference. The first 8 percent of data from the survey are used for a proof-of-concept study, which has led to the first application of Rotation Measure Synthesis to the diffuse Galactic emission obtained with a single-antenna telescope. We find rotation measure values for the diffuse emission as high as approximately 100 rad per square metre, much higher than recorded in earlier work.Comment: Accepted for publication in The Astronomical Journa

Semiclassical Inequivalence of Polygonalized Billiards

Polygonalization of any smooth billiard boundary can be carried out in several ways. We show here that the semiclassical description depends on the polygonalization process and the results can be inequivalent. We also establish that generalized tangent-polygons are closest to the corresponding smooth billiard and for de Broglie wavelengths larger than the average length of the edges, the two are semiclassically equivalent.Comment: revtex, 4 ps figure

The Two Active X Chromosomes in Female ESCs Block Exit from the Pluripotent State by Modulating the ESC Signaling Network

During early development of female mouse embryos, both X chromosomes are transiently active. X gene dosage is then equalized between the sexes through the process of X chromosome inactivation (XCI). Whether the double dose of X-linked genes in females compared with males leads to sex-specific developmental differences has remained unclear. Using embryonic stem cells with distinct sex chromosome compositions as a model system, we show that two X chromosomes stabilize the naive pluripotent state by inhibiting MAPK and Gsk3 signaling and stimulating the Akt pathway. Since MAPK signaling is required to exit the pluripotent state, differentiation is paused in female cells as long as both X chromosomes are active. By preventing XCI or triggering it precociously, we demonstrate that this differentiation block is released once XX cells have undergone X inactivation. We propose that double X dosage interferes with differentiation, thus ensuring a tight coupling between X chromosome dosage compensation and development

The Partition Function and Level Density for Yang-Mills-Higgs Quantum Mechanics

We calculate the partition function $Z(t)$ and the asymptotic integrated level density $N(E)$ for Yang-Mills-Higgs Quantum Mechanics for two and three dimensions ($n = 2, 3$). Due to the infinite volume of the phase space $\Gamma$ on energy shell for $n= 2$, it is not possible to disentangle completely the coupled oscillators ($x^2 y^2$-model) from the Higgs sector. The situation is different for $n = 3$ for which $\Gamma$ is finite. The transition from order to chaos in these systems is expressed by the corresponding transitions in $Z(t)$ and $N(E)$, analogous to the transitions in adjacent level spacing distribution from Poisson distribution to Wigner-Dyson distribution. We also discuss a related system with quartic coupled oscillators and two dimensional quartic free oscillators for which, contrary to YMHQM, both coupling constants are dimensionless.Comment: 10 pages, LaTeX; minor changes; version accepted for publication as a Letter in J. Phys.