Regular-to-chaotic tunneling rates using a fictitious integrable system

We derive a formula predicting dynamical tunneling rates from regular states to the chaotic sea in systems with a mixed phase space. Our approach is based on the introduction of a fictitious integrable system that resembles the regular dynamics within the island. For the standard map and other kicked systems we find agreement with numerical results for all regular states in a regime where resonance-assisted tunneling is not relevant.Comment: 4 pages, 4 figure

Observing the emergence of chaos in a many-particle quantum system

Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincar\'e-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics.Comment: 5+2 pages, 4 figure

Dynamical tunneling in mushroom billiards

We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling rates. Experimentally, we use microwave spectra to investigate a mushroom billiard with adjustable foot height. Numerically, we obtain tunneling rates from high precision eigenvalues using the improved method of particular solutions. Analytically, a prediction is given by extending an approach using a fictitious integrable system to billiards. In contrast to previous approaches for billiards, we find agreement with experimental and numerical data without any free parameter.Comment: 4 pages, 4 figure

Complex paths for regular-to-chaotic tunneling rates

In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical approach based on complex paths for the prediction of dynamical tunneling rates from regular tori to the chaotic region. This approach is demonstrated for the standard map giving excellent agreement with numerically determined tunneling rates.Comment: 5 pages, 4 figure

Quality factors and dynamical tunneling in annular microcavities

The key characteristic of an optical mode in a microcavity is its quality factor describing the optical losses. The numerical computation of this quantity can be very demanding for present-day devices. Here we show for a certain class of whispering-gallery cavities that the quality factor is related to dynamical tunneling, a phenomenon studied in the field of quantum chaos. We extend a recently developed approach for determining dynamical tunneling rates to open cavities. This allows us to derive an analytical formula for the quality factor which is in very good agreement with full solutions of Maxwell's equations.Comment: 7 pages, 5 figure

Open Mushrooms: Stickiness revisited

We investigate mushroom billiards, a class of dynamical systems with sharply divided phase space. For typical values of the control parameter of the system $\rho$, an infinite number of marginally unstable periodic orbits (MUPOs) exist making the system sticky in the sense that unstable orbits approach regular regions in phase space and thus exhibit regular behaviour for long periods of time. The problem of finding these MUPOs is expressed as the well known problem of finding optimal rational approximations of a real number, subject to some system-specific constraints. By introducing a generalized mushroom and using properties of continued fractions, we describe a zero measure set of control parameter values $\rho\in(0,1)$ for which all MUPOs are destroyed and therefore the system is less sticky. The open mushroom (billiard with a hole) is then considered in order to quantify the stickiness exhibited and exact leading order expressions for the algebraic decay of the survival probability function $P(t)$ are calculated for mushrooms with triangular and rectangular stems.Comment: 21 pages, 11 figures. Includes discussion of a three-dimensional mushroo

The prevalence of extramedullary acute myeloid leukemia detected by 18FDG-PET/CT: final results from the prospective PETAML trial

Extramedullary (EM) disease in patients with acute myeloid leukemia (AML) is a known phenomenon. Since the prevalence of EM AML has so far only been clinically determined on examination, we performed a prospective study in patients with AML. The aim of the study was to determine the prevalence of metabolically active EM AML using total body 18Fluorodesoxy-glucose positron emission tomography/computed tomography (18FDG-PET/CT) imaging at diagnosis prior to initiation of therapy. In order to define the dynamics of EM AML throughout treatment, PET-positive patients underwent a second 18FDG-PET/CT imaging series during follow up by the time of remission assessment. A total of 93 patients with AML underwent 18FDG-PET/CT scans at diagnosis. The prevalence of PET-positive EM AML was 19% with a total of 65 EM AML manifestations and a median number of two EM manifestations per patient (range, 1-12), with a median maximum standardized uptake value of 6.1 (range, 2-51.4). When adding those three patients with histologically confirmed EM AML who were 18FDG-PET/CT negative in the 18FDG-PET/CT at diagnosis, the combined prevalence for EM AML was 22%, resulting in 77% sensitivity and 97% specificity. Importantly, 60% (6 of 10) patients with histologically confirmed EM AML still had active EM disease in their follow up 18FDG-PET/CT. 18FDG-PET/CT reveals a high prevalence of metabolically active EM disease in AML patients. Metabolic activity in EM AML may persist even beyond the time point of hematologic remission, a finding that merits further prospective investigation to explore its prognostic relevance. (Trial registered at clinicaltrials.gov identifier: 01278069.

The image biomarker standardization initiative: Standardized convolutional filters for reproducible radiomics and enhanced clinical insights

Standardizing convolutional filters that enhance specific structures and patterns in medical imaging enables reproducible radiomics analyses, improving consistency and reliability for enhanced clinical insights. Filters are commonly used to enhance specific structures and patterns in images, such as vessels or peritumoral regions, to enable clinical insights beyond the visible image using radiomics. However, their lack of standardization restricts reproducibility and clinical translation of radiomics decision support tools. In this special report, teams of researchers who developed radiomics software participated in a three-phase study (September 2020 to December 2022) to establish a standardized set of filters. The first two phases focused on finding reference filtered images and reference feature values for commonly used convolutional filters: mean, Laplacian of Gaussian, Laws and Gabor kernels, separable and nonseparable wavelets (including decomposed forms), and Riesz transformations. In the first phase, 15 teams used digital phantoms to establish 33 reference filtered images of 36 filter configurations. In phase 2, 11 teams used a chest CT image to derive reference values for 323 of 396 features computed from filtered images using 22 filter and image processing configurations. Reference filtered images and feature values for Riesz transformations were not established. Reproducibility of standardized convolutional filters was validated on a public data set of multimodal imaging (CT, fluorodeoxyglucose PET, and T1-weighted MRI) in 51 patients with soft-tissue sarcoma. At validation, reproducibility of 486 features computed from filtered images using nine configurations × three imaging modalities was assessed using the lower bounds of 95% CIs of intraclass correlation coefficients. Out of 486 features, 458 were found to be reproducible across nine teams with lower bounds of 95% CIs of intraclass correlation coefficients greater than 0.75. In conclusion, eight filter types were standardized with reference filtered images and reference feature values for verifying and calibrating radiomics software packages. A web-based tool is available for compliance checking

Integrable approximation of regular islands : The iterative canonical transformation method

Generic Hamiltonian systems have a mixed phase space, where classically disjoint regions of regular and chaotic motion coexist. We present an iterative method to construct an integrable approximation, which resembles the regular dynamics of a given mixed system and extends it into the chaotic region. The method is based on the construction of an integrable approximation in action representation which is then improved in phase space by iterative applications of canonical transformations. This method works for strongly perturbed systems and arbitrary degrees of freedom. We apply it to the standard map and the cosine billiard.Comment: 13 pages, 12 figure