On the discrete spectrum of spin-orbit Hamiltonians with singular interactions

We give a variational proof of the existence of infinitely many bound states below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba and Dresselhaus cases) perturbed by measure potentials thus extending the results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007) F113--F117.Comment: 10 pages; to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler). Results improved in this versio

Spin Gap in the Single Spin-1/2 Chain Cuprate Sr1.9_{1.9}Ca0.1_{0.1}CuO3_3

We report $^{63}$Cu nuclear magnetic resonance and muon spin rotation measurements on the S=1/2 antiferromagnetic Heisenberg spin chain compound Sr$_{1.9}$Ca$_{0.1}$CuO$_3$. An exponentially decreasing spin-lattice relaxation rate 1/T$_1$ indicates the opening of a spin gap. This behavior is very similar to what has been observed for the cognate zigzag spin chain compound Sr$_{0.9}$Ca$_{0.1}$CuO$_2$, and confirms that the occurrence of a spin gap upon Ca doping is independent of the interchain exchange coupling $J'$. Our results therefore generally prove the appearance of a spin gap in an antiferromagnetic Heisenberg spin chain induced by a local bond disorder of the intrachain exchange coupling $J$. A low temperature upturn of 1/T$_1$ evidences growing magnetic correlations. However, zero field muon spin rotation measurements down to 1.5 K confirm the absence of magnetic order in this compound which is most likely suppressed by the opening of the spin gap.Comment: 5 pages, 4 figure

On the Nodal Count Statistics for Separable Systems in any Dimension

We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in arbitrary dimension. We give an explicit expression for the limiting distribution of normalised nodal counts and analyse some of its universal properties. Our results are illustrated by detailed discussion of simple examples and numerical nodal count distributions.Comment: 21 pages, 4 figure

Detecting chaos in particle accelerators through the frequency map analysis method

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.Comment: Submitted for publication in Chaos, Focus Issue: Chaos Detection Methods and Predictabilit

Spectral properties of a short-range impurity in a quantum dot

The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit form. In the case of a spherically symmetric quantum dot, the dependence of the spectrum on the impurity position and the strength of the impurity potential is analyzed in detail. It is proven that the confinement potential of the dot can be recovered from the spectroscopy data. The consequences of the hidden symmetry breaking by the impurity are considered. The effect of the positional disorder is studied.Comment: 30 pages, 6 figures, Late

CeRuPO: A rare example of a Ferromagnetic Kondo lattice

We have determined the physical ground state properties of the compounds CeRuPO and CeOsPO by means of magnetic susceptibility chi(T), specific heat C(T), electrical resistivity rho(T), and thermopower S(T) measurements. chi(T) reveals a trivalent 4f1 cerium state in both compounds. For CeRuPO a pronounced decrease of rho(T) below 50K indicates the onset of coherent Kondo scattering which is confirmed by enhanced S(T). The temperature and magnetic field dependence of chi(T) and C(T) evidence ferromagnetic (FM) order at TC=15K. Thus, CeRuPO seems to be one of the rare example of a FM Kondo lattice. In contrast, CeOsPO shows antiferromagnetic order at TN=4.4K despite only minor changes in lattice parameters and electronic configuration. Additional 31P NMR results support these scenarios. LSDA+U calculations evidence a quasi two dimensional electronic band structure, reflecting a strong covalent bonding within the CeO and RuP layers and a weak ionic like bonding between the layers.Comment: accepted in Phys. Rev. B, high quality figures: http://www.cpfs.mpg.de/~krellner

AI Models for Supporting SI Analysis on PCB Net Structures: Comparing Linear and Non-Linear Data Sources

Signal integrity (SI) is an essential part in assuring the functionality of microelectronic components on a printed circuit board (PCB). Depending on the complexity of the designed interconnect structure, even the experienced PCB developer might be reliant on multiple design cycles to optimally configure the PCB parameters, which eventually results in a very complex, time-consuming and costly process. Under these aggravating conditions, artificial intelligence (AI) models may have the potential to support and simplify the SI-aware PCB design process by building predictive models and proposing design solutions to streamline the existing workflows and unburden the PCB designer. In this paper, the AI approach is divided into two separate stages consisting of neural network (NN) regression in the first step and parameterization of the PCB net structure in the second step. First, the NN models are applied to learn the relationship between the electrical parameters and the resulting signal quality captured by domain-oriented signal features in the time domain. Second, based on the trained NN models, on the one hand, the k-nearest neighbor (kNN) method is utilized to select solution candidates within the feature space, while on the other hand, genetic algorithms (GA) are applied to directly optimize the parameters of the interconnect structure. Moreover, the influence of the simulation abstraction level is investigated by comparing simulation data originating from linear and I/O buffer information specification (IBIS)-based non-linear modeling of the integrated circuit (IC) characteristics concerning the prediction accuracy and direct transferability. Finally, transfer learning concepts are evaluated to exchange learned knowledge representations between the different modeling of the IC characteristics to improve data efficiency and reduce computational complexity.</p

Common effect of chemical and external pressures on the magnetic properties of RECoPO (RE = La, Pr)

We report a detailed investigation of RECoPO (RE = La, Pr) and LaCoAsO materials performed by means of muon spin spectroscopy. Zero-field measurements show that the electrons localized on the Pr$^{3+}$ ions do not play any role in the static magnetic properties of the compounds. Magnetism at the local level is indeed fully dominated by the weakly-itinerant ferromagnetism from the Co sublattice only. The increase of the chemical pressure triggered by the different ionic radii of La$^{3+}$ and Pr$^{3+}$, on the other hand, plays a crucial role in enhancing the value of the magnetic critical temperature and can be mimicked by the application of external hydrostatic pressure up to 24 kbar. A sharp discontinuity in the local magnetic field at the muon site in LaCoPO at around 5 kbar suggests a sizeable modification in the band structure of the material upon increasing pressure. This scenario is qualitatively supported by \emph{ab-initio} density-functional theory calculations.Comment: 13 pages, 10 figure

Transition rate of the Unruh-DeWitt detector in curved spacetime

We examine the Unruh-DeWitt particle detector coupled to a scalar field in an arbitrary Hadamard state in four-dimensional curved spacetime. Using smooth switching functions to turn on and off the interaction, we obtain a regulator-free integral formula for the total excitation probability, and we show that an instantaneous transition rate can be recovered in a suitable limit. Previous results in Minkowski space are recovered as a special case. As applications, we consider an inertial detector in the Rindler vacuum and a detector at rest in a static Newtonian gravitational field. Gravitational corrections to decay rates in atomic physics laboratory experiments on the surface of the Earth are estimated to be suppressed by 42 orders of magnitude.Comment: 27 pages, 1 figure. v3: Typos corrected. Published versio