Numerical Evidence that the Perturbation Expansion for a Non-Hermitian PT\mathcal{PT}-Symmetric Hamiltonian is Stieltjes

Recently, several studies of non-Hermitian Hamiltonians having $\mathcal{PT}$ symmetry have been conducted. Most striking about these complex Hamiltonians is how closely their properties resemble those of conventional Hermitian Hamiltonians. This paper presents further evidence of the similarity of these Hamiltonians to Hermitian Hamiltonians by examining the summation of the divergent weak-coupling perturbation series for the ground-state energy of the $\mathcal{PT}$-symmetric Hamiltonian $H=p^2+{1/4}x^2+i\lambda x^3$ recently studied by Bender and Dunne. For this purpose the first 193 (nonzero) coefficients of the Rayleigh-Schr\"odinger perturbation series in powers of $\lambda^2$ for the ground-state energy were calculated. Pad\'e-summation and Pad\'e-prediction techniques recently described by Weniger are applied to this perturbation series. The qualitative features of the results obtained in this way are indistinguishable from those obtained in the case of the perturbation series for the quartic anharmonic oscillator, which is known to be a Stieltjes series.Comment: 20 pages, 0 figure

Regge trajectories and quarkonium spectrum from a first principle Salpeter equation

We compute the heavy-heavy, light-light and light-heavy quarkonium spectrum starting from a first principle Salpeter equation obtained in a preceding paper. We neglect spin-orbit structures and exclude from our treatment the light pseudoscalar states which in principle would require the use of the full Bethe-Salpeter equation due to the chiral symmetry breaking problem. For the rest we find an overall good agreement with the experimental data. In particular for the light-light case we find straight Regge trajectories with the right slope and intercepts. The strong coupling constant $\alpha_s$, the string tension $\sigma$ occurring in the potential and the heavy quark masses are taken from the heavy quarkonium semirelativistic fit with only a small rearrangement. The light quark masses are set equal to baricentral value of the current quark masses as reported by the particle data group. For what concerns the light-light and the light-heavy systems the calculation is essentially parameter free.Comment: 18 pages, 3 figures, revtex.st

Relativistic bound-state calculations in Light Front Dynamics

We calculated bound states in the quantum field theoretical approach. Using the Wick-Cutkosky model and an extended version of this model (in which a particle with finite mass is exchanged) we have calculated the bound states in the scalar case.Comment: 3 pages, proceedings of the Light Cone Meeting Trento 2001, to be published in Nucl. Phys. B - Proceedings Supplement

A Unique Multi-Messenger Signal of QCD Axion Dark Matter

We propose a multi-messenger probe of QCD axion Dark Matter based on observations of black hole-neutron star binary inspirals. It is suggested that a dense Dark Matter spike may grow around intermediate mass black holes ($10^{3}-10^{5} \mathrm{\,M_{\odot}}$). The presence of such a spike produces two unique effects: a distinct phase shift in the gravitational wave strain during the inspiral and an enhancement of the radio emission due to the resonant axion-photon conversion occurring in the neutron star magnetosphere throughout the inspiral and merger. Remarkably, the observation of the gravitational wave signal can be used to infer the Dark Matter density and, consequently, to predict the radio emission. We study the projected reach of the LISA interferometer and next-generation radio telescopes such as the Square Kilometre Array. Given a sufficiently nearby system, such observations will potentially allow for the detection of QCD axion Dark Matter in the mass range $10^{-7}\,\mathrm{eV}$ to $10^{-5}\,\mathrm{eV}$.Comment: 5 pages, 3 figures. Appendix added with additional figures. Updated to published versio

Albatross:a scalable simulation-based inference pipeline for analysing stellar streams in the Milky Way

Stellar streams are potentially a very sensitive observational probe of galactic astrophysics, as well as the dark matter population in the Milky Way. On the other hand, performing a detailed, high-fidelity statistical analysis of these objects is challenging for a number of key reasons. First, the modelling of streams across their (potentially billions of years old) dynamical age is complex and computationally costly. Secondly, their detection and classification in large surveys such as Gaia renders a robust statistical description regarding e.g. the stellar membership probabilities, challenging. As a result, the majority of current analyses must resort to simplified models that use only subsets or summaries of the high quality data. In this work, we develop a new analysis framework that takes advantage of advances in simulation-based inference techniques to perform complete analysis on complex stream models. To facilitate this, we develop a new, modular dynamical modelling code sstrax for stellar streams that is highly accelerated using jax. We test our analysis pipeline on a mock observation that resembles the GD1 stream, and demonstrate that we can perform robust inference on all relevant parts of the stream model simultaneously. Finally, we present some outlook as to how this approach can be developed further to perform more complete and accurate statistical analyses of current and future data

Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory

\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation which uses as input data not only the elements of a sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates $\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit incorporation of the information contained in the truncation error estimates makes this and related transformations potentially much more powerful than for instance Pad\'{e} approximants. Special cases of the new transformation are sequence transformations introduced by Levin [Int. J. Comput. Math. B \textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189 - 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A \textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations - explicit expressions, recurrence formulas, explicit expressions in the case of special remainder estimates, and asymptotic order estimates satisfied by rational approximants to power series - is formulated in terms of hitherto unknown mathematical properties of the new transformation introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of Mathematical Physic

Disentangling Instrumental Features of the 130 GeV Fermi Line

We study the instrumental features of photons from the peak observed at $E_\gamma=130$ GeV in the spectrum of Fermi-LAT data. We use the {\sc sPlots} algorithm to reconstruct -- seperately for the photons in the peak and for background photons -- the distributions of incident angles, the recorded time, features of the spacecraft position, the zenith angles, the conversion type and details of the energy and direction reconstruction. The presence of a striking feature or cluster in such a variable would suggest an instrumental cause for the peak. In the publically available data, we find several suggestive features which may inform further studies by instrumental experts, though the size of the signal sample is too small to draw statistically significant conclusions.Comment: 9 pages, 22 figures; this version includes additional variables, study of stat sensitivity, and modification to the chi-sq calculatio

The Use of the Health of the Nation Outcome Scales for Assessing Functional Change in Treatment Outcome Monitoring of Patients with Chronic Schizophrenia.

Schizophrenia is a severe mental disorder that is characterized not only by symptomatic severity but also by high levels of functional impairment. An evaluation of clinical outcome in treatment of schizophrenia should therefore target not only assessing symptom change but also alterations in functioning. This study aimed to investigate whether there is an agreement between functional- and symptom-based outcomes in a clinical sample of admissions with chronic forms of schizophrenia. A full 3-year cohort of consecutive inpatient admissions for schizophrenia (N = 205) was clinically rated with the Positive and Negative Symptom Scale (PANSS) and the Health of the Nation Outcome Scales (HoNOS) as measures of functioning at the time of admission and discharge. The sample was stratified twofold: first, according to the degree of PANSS symptom improvement during treatment with the sample being divided into three treatment response groups: non-response, low response, and high response. Second, achievement of remission was defined using the Remission in Schizophrenia Working Group criteria based on selected PANSS symptoms. Repeated measures analyses were used to compare the change of HoNOS scores over time across groups. More than a half of all admissions achieved a symptom reduction of at least 20% during treatment and around one quarter achieved remission at discharge. Similarly, HoNOS scores improved significantly between admission and discharge. Interaction analyses indicated higher functional improvements to be associated with increasing levels of treatment response. Functional improvement in individuals treated for schizophrenia was linked to a better clinical outcome, which implies a functional association. Thus, improvement of functioning represents an important therapeutic target in the treatment of schizophrenia

The performance of the Health of the Nation Outcome Scales as measures of clinical severity.

The aim of this study was to examine the performance of the Health of the Nation Outcome Scales (HoNOS) against other measures of functioning and mental health in a full three-year cohort of admissions to a psychiatric hospital. A sample of N=1719 patients (35.3% females, aged 17-78 years) was assessed using observer-rated measures and self-reports of psychopathology at admission. Self-reports were available from 51.7% of the sample (34.4% females, aged 17-76 years). Functioning and psychopathology were compared across five ICD-10 diagnostic groups: substance use disorders, schizophrenia and psychotic disorders, affective disorders, anxiety/somatoform disorders and personality disorders. Associations between the measures were examined, stratifying by diagnostic subgroup. The HoNOS were strongly linked to other measures primarily in psychotic disorders (except for the behavioral subscale), while those with substance use disorders showed rather poor links. Those with anxiety/somatoform disorders showed null or only small associations. This study raises questions about the overall validity of the HoNOS. It seems to entail different levels of validity when applied to different diagnostic groups. In clinical practice the HoNOS should not be used as a stand-alone instrument to assess outcome but rather as part of a more comprehensive battery including diagnosis-specific measures