Closed and open superconducting microwave waveguide networks as a model for quantum graphs.

We report on high-precision measurements that were performed with superconducting waveguide networks with the geometry of a tetrahedral and a honeycomb graph. They consist of junctions of valency three that connect straight rectangular waveguides of equal width but incommensurable lengths. The experiments were performed in the frequency range of a single transversal mode, where the associated Helmholtz equation is effectively one-dimensional and waveguide networks may serve as models of quantum graphs with the joints and waveguides corresponding to the vertices and bonds. The tetrahedral network comprises T junctions, while the honeycomb network exclusively consists of Y junctions, that join waveguides with relative angles 90^{∘} and 120^{∘}, respectively. We demonstrate that the vertex scattering matrix, which describes the propagation of the modes through the junctions, strongly depends on frequency and is nonsymmetric at a T junction and thus differs from that of a quantum graph with Neumann boundary conditions at the vertices. On the other hand, at a Y junction, similarity can be achieved in a certain frequency range. We investigate the spectral properties of closed waveguide networks and fluctuation properties of the scattering matrix of open ones and find good agreement with random matrix theory predictions for the honeycomb waveguide graph.

Spirituality in Oncology: Relations between Spirituality, Its Facets, and Psychological and Demographic Factors in Cancer Patients in Germany.

INTRODUCTION: Cancer diagnoses are constantly increasing in clinical practice. Therefore, more and more patients are interested in how they can actively participate in the process of treatment. Spirituality represents a hidden issue of the population, which counts as a branch of complementary and alternative treatment. Therefore, the aim of our study was to investigate whether there are associations between spirituality and demographic and psychosocial factors, as well as religious beliefs, in cancer patients. METHODS: We conducted a survey with 451 participants in 10 oncology centers between March and July 2021. A composition of the following 9 different questionnaires was used to collect data on spirituality, demographics, resilience, self-efficiency, life satisfaction, and sense of coherence: Functional Assessment of Chronic Illness Therapy-Spiritual Well-Being (FACIT-Sp12), General Life Satisfaction Short Scale (L-1), Resilienzskala Kurzform (RS-13), Sense of Coherence Scale - Leipziger Kurzform (SOC-L9), Allgemeine Selbstwirksamkeit Kurzskala (AKSU), Adolescent Food Habits Checklist, Likert-Scale of daily activities, questionnaire of the Working group Prävention und Integrative Onkologie (PRiO), and personal opinion on the cause of the disease. Calculated data and analyzed group differences using ANOVA Bonferroni were used to test associations between spirituality and the variables studied. For more detailed examination of spirituality, we took a closer look at the different components of spirituality - peace, meaning, and faith - and their relation to each other (three-factor spirituality analyses). RESULTS: Higher spirituality scores in total as well as meaning, peace, and faith were each associated with higher levels of resilience and life satisfaction. Higher religious belief was found to be associated with higher spiritual attitudes. High personal self-efficiency was found in people with higher spiritual beliefs in general as well as higher meaning and peace. Meaning and peace emerge as essential components of spiritual well-being and show a stronger association with expressions of general spirituality than faith. CONCLUSION: Spirituality takes a crucial role among the resources of life-threatening diseases. As such, further research is needed to expand and integrate patient options into a modernized concept of care. Our data indicate that higher spiritual well-being is associated with a more tolerant approach to illness. Thus, addressing spiritual needs in therapy is associated with better psychological adjustment to the individual situation and reduces negative distress. To promote spiritual needs in the future, cognitive as well as affective components of spirituality should be emphasized.

Usage of Complementary and Alternative Methods, Lifestyle, and Psychological Variables in Cancer Care.

BACKGROUND/AIM: People who are undergoing cancer treatment often ask themselves what they can do in addition to conventional medical therapy with regard to nutrition, activity, and complementary methods. However, we know little about the motivation why people opt for one or the other measure. The aim of this study was therefore to examine the extent of physical activity (PA), healthy nutrition, and the use of complementary methods in relation to both demographic and psychological data. MATERIALS AND METHODS: A questionnaire was used to collect data on demographic data, resilience, coherence, self-efficacy, spirituality, satisfaction, and complementary and alternative medicine (CAM) behavior, PA, and diet. Between March and July 2021, data from 446 patients were collected. Regression models and correlation analyzes were used to examine the associations between CAM use, diet and PA with the other variables surveyed. RESULTS: CAM usage could only be predicted based on the patient's spirituality. Women used CAM more often and ate more healthily. Healthy eating was also related to younger age, shorter medical history, resilience, satisfaction, and coherence. In addition, the results showed that daily PA was related to the level of resilience, spirituality, and self-efficacy. CONCLUSION: Which people or why patients use CAM remains a question to be further investigated. Our data suggest that CAM seeks to address similar needs that others find in spirituality. In order to promote a healthy diet and PA in cancer patients in the future, various psychological variables seem conceivable. Resilience stands out, which is related to an overall healthier lifestyle.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison.

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

Cross-section fluctuations in chaotic scattering systems.

Exact analytical expressions for the cross-section correlation functions of chaotic scattering systems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering (S)-matrix correlation functions accurately. Our results are given in the energy and in the time representations and apply in the whole range from isolated to overlapping resonances. The S-matrix contributions to the cross-section correlations are obtained in terms of explicit irreducible and reducible correlation functions. Consequently, the model can be used for a detailed exploration of the key features of the cross-section correlations and the underlying physical mechanisms. In the region of isolated resonances, the cross-section correlations contain a dominant contribution from the self-correlation term. For narrow states the self-correlations originate predominantly from widely spaced states with exceptionally large partial width. In the asymptotic region of well-overlapping resonances, the cross-section autocorrelation functions are given in terms of the S-matrix autocorrelation functions. For inelastic correlations, in particular, the Ericson fluctuations rapidly dominate in that region. Agreement with known analytical and experimental results is excellent.

Avoided-level-crossing statistics in open chaotic billiards.

We investigate a two-level model with a large number of open decay channels in order to describe avoided level crossing statistics in open chaotic billiards. This model allows us to describe the fundamental changes in the probability distribution of the avoided level crossings compared with the closed case. Explicit expressions are derived for systems with preserved and broken time-reversal symmetry. We find that the decay process induces a modification at small spacings of the probability distribution of the avoided level crossings due to an attraction of the resonances. The theoretical predictions are in complete agreement with the recent experimental results of Dietz [Phys. Rev. E 73, 035201 (2006)].