Squeezed States and Hermite polynomials in a Complex Variable

Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].Comment: 15 page

Exact and explicit probability densities for one-sided Levy stable distributions

We study functions g_{\alpha}(x) which are one-sided, heavy-tailed Levy stable probability distributions of index \alpha, 0< \alpha <1, of fundamental importance in random systems, for anomalous diffusion and fractional kinetics. We furnish exact and explicit expression for g_{\alpha}(x), 0 \leq x < \infty, satisfying \int_{0}^{\infty} exp(-p x) g_{\alpha}(x) dx = exp(-p^{\alpha}), p>0, for all \alpha = l/k < 1, with k and l positive integers. We reproduce all the known results given by k\leq 4 and present many new exact solutions for k > 4, all expressed in terms of known functions. This will allow a 'fine-tuning' of \alpha in order to adapt g_{\alpha}(x) to a given experimental situation.Comment: 4 pages, 3 figures and 1 tabl

Commensurate anisotropic oscillator, SU(2) coherent states and the classical limit

We demonstrate a formally exact quantum-classical correspondence between the stationary coherent states associated with the commensurate anisotropic two-dimensional harmonic oscillator and the classical Lissajous orbits. Our derivation draws upon earlier work of Louck et al [1973 \textit {J. Math. Phys.} \textbf {14} 692] wherein they have provided a non-bijective canonical transformation that maps, within a degenerate eigenspace, the commensurate anisotropic oscillator on to the isotropic oscillator. This mapping leads, in a natural manner, to a Schwinger realization of SU(2) in terms of the canonically transformed creation and annihilation operators. Through the corresponding coherent states built over a degenerate eigenspace, we directly effect the classical limit via the expectation values of the underlying generators. Our work completely accounts for the fact that the SU(2) coherent state in general corresponds to an ensemble of Lissajous orbits.Comment: 11 pages, Latex2e, iopart.cls, replaced with published versio

Levy stable distributions via associated integral transform

We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x < \infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a distribution g_{\alpha}(x) suffices to obtain exactly g_{\alpha^{p}}(x), p=2, 3,... Similarly, from known g_{\alpha}(x) and g_{\beta}(x), 0 < \alpha, \beta < 1, we obtain g_{\alpha \beta}(x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For \alpha rational, \alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g_{l/k}(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration.Comment: 12 pages, typos removed, references adde

Miniature radiocarbon measurements (< 150 μg C) from sediments of Lake Żabińskie, Poland: effect of precision and dating density on age-depth models

The recent development of the MIni CArbon DAting System (MICADAS) allows researchers to obtain radiocarbon (14C) ages from a variety of samples with miniature amounts of carbon (<150 µg C) by using a gas ion source input that bypasses the graphitization step used for conventional 14C dating with accelerator mass spectrometry (AMS). The ability to measure smaller samples, at reduced cost compared with graphitized samples, allows for greater dating density of sediments with low macrofossil concentrations. In this study, we use a section of varved sediments from Lake Żabińskie, NE Poland, as a case study to assess the usefulness of miniature samples from terrestrial plant macrofossils for dating lake sediments. Radiocarbon samples analyzed using gas-source techniques were measured from the same depths as larger graphitized samples to compare the reliability and precision of the two techniques directly. We find that the analytical precision of gas-source measurements decreases as sample mass decreases but is comparable with graphitized samples of a similar size (approximately 150 µg C). For samples larger than 40 µg C and younger than 6000 BP, the uncalibrated 1σ age uncertainty is consistently less than 150 years (±0.010 F14C). The reliability of 14C ages from both techniques is assessed via comparison with a best-age estimate for the sediment sequence, which is the result of an OxCal V sequence that integrates varve counts with 14C ages. No bias is evident in the ages produced by either gas-source input or graphitization. None of the 14C ages in our dataset are clear outliers; the 95 % confidence intervals of all 48 calibrated 14C ages overlap with the median best-age estimate. The effects of sample mass (which defines the expected analytical age uncertainty) and dating density on age–depth models are evaluated via simulated sets of 14C ages that are used as inputs for OxCal P-sequence age–depth models. Nine different sampling scenarios were simulated in which the mass of 14C samples and the number of samples were manipulated. The simulated age–depth models suggest that the lower analytical precision associated with miniature samples can be compensated for by increased dating density. The data presented in this paper can improve sampling strategies and can inform expectations of age uncertainty from miniature radiocarbon samples as well as age–depth model outcomes for lacustrine sediments

Integrating Concepts of Artificial Intelligence in the EO4GEO Body of Knowledge

Ponència del XXIV ISPRS Congress (2022 edition), 6–11 June 2022, Nice, FranceThe EO4GEO Body of Knowledge (BoK) forms a structure of concepts and relationships between them, describing the domain of Earth Observation and Geo-Information (EO/GI). Each concept carries a short description, a list of key literature references and a set of associated skills which are used for job profiling and curriculum building. As the EO/GI domain is evolving continuously, the BoK needs regular updates with new concepts embodying new trends, and deprecating concepts which are not relevant anymore. This paper presents the inclusion of BoK concepts related to Artificial Intelligence. This broad field of knowledge has links to several applications in EO/GI. Its connection to concepts, already existing in the BoK, needs special attention. To perform a clean and structural integration of the cross-cutting domain of AI, first a separate cluster of AI concepts was created, which was then merged with the existing BoK. The paper provides examples of this integration with specific concepts and examples of training resources in which AI-related concepts are used. Although the presented structure already provides a good starting point, the positioning of AI within the EO/GI-focussed BoK needs to be further enhanced with the help of expert calls as part of the BoK update cycle