The Effects of Inlet Flow Modification on Cavitating Inducer Performance

This paper explores the effect of inlet flow modification on the cavitating and noncavitating performance of two cavitating inducers, one of simple helical design and the other a model of the low-pressure LOX pump in the Space Shuttle Main Engine. The modifications were generated by sections of honeycomb, both uniform and nonuniform. Significant improvement in the performance over a wide range of flow coefficients resulted from the use of either honeycomb section. Measurements of the axial and swirl velocity profiles of the flows entering the inducers were made in order to try to understand the nature of the inlet flow and the manner in which it is modified by the honeycomb sections

Solving the One-Dimensional Time-Independent Schr\"odinger Equation with High Accuracy: The LagrangeMesh Mathematica Package

In order to find the spectrum associated with the one-dimensional Schr\"oodinger equation, we discuss the Lagrange Mesh method (LMM) and its numerical implementation for bound states. After presenting a general overview of the theory behind the LMM, we introduce the LagrangeMesh package: the numerical implementation of the LMM in Mathematica. Using few lines of code, the package enables a quick home-computer computation of the spectrum and provides a practical tool to study a large class of systems in quantum mechanics. The main properties of the package are (i) the input is basically the potential function and the interval on which is defined; and (ii) the accuracy in calculations and final results is controllable by the user. As illustration, a highly accurate spectrum of some relevant quantum systems is obtained by employing the commands that the package offers. In fact, the present work can be regarded as a user guide based on worked examples.Comment: File LagrangeMesh.wl can be provided to the interested reader, just contact the author via email. Alternatively, it can be found at https://github.com/JuanCarlosdelValle/LagrangeMesh-Packag

Production and decays of supersymmetric Higgs bosons in spontaneously broken R-parity

We study the mass spectra, production and decay properties of the lightest supersymmetric CP-even and CP-odd Higgs bosons in models with spontaneously broken R-parity (SBRP). We compare the resulting mass spectra with expectations of the Minimal Supersymmetric Standard Model (MSSM), stressing that the model obeys the upper bound on the lightest CP-even Higgs boson mass. We discuss how the presence of the additional scalar singlet states affects the Higgs production cross sections, both for the Bjorken process and the "associated production". The main phenomenological novelty with respect to the MSSM comes from the fact that the spontaneous breaking of lepton number leads to the existence of the majoron, denoted J, which opens new decay channels for supersymmetric Higgs bosons. We find that the invisible decays of CP-even Higgses can be dominant, while those of the CP-odd bosons may also be sizeable.Comment: 21 pages, 8 figures; minor changes, final version for publicatio

Spontaneous, collective coherence in driven, dissipative cavity arrays

We study an array of dissipative tunnel-coupled cavities, each interacting with an incoherently pumped two-level emitter. For cavities in the lasing regime, we find correlations between the light fields of distant cavities, despite the dissipation and the incoherent nature of the pumping mechanism. These correlations decay exponentially with distance for arrays in any dimension but become increasingly long ranged with increasing photon tunneling between adjacent cavities. The interaction-dominated and the tunneling-dominated regimes show markedly different scaling of the correlation length which always remains finite due to the finite photon trapping time. We propose a series of observables to characterize the spontaneous build-up of collective coherence in the system.Comment: 9 pages, 4 figures, including supplemental material (with 4 pages, 1 figure). This is a shorter version with some modifications in the supplemental material (a gap in the proof was closed and calculations significantly generalized and improved

Exciting polaritons with quantum light

We discuss the excitation of polaritons---strongly-coupled states of light and matter---by quantum light, instead of the usual laser or thermal excitation. As one illustration of the new horizons thus opened, we introduce Mollow spectroscopy, a theoretical concept for a spectroscopic technique that consists in scanning the output of resonance fluorescence onto an optical target, from which weak nonlinearities can be read with high precision even in strongly dissipative environments.Comment: 5 pages, 3 figure

Degenerate neutrinos from a supersymmetric A_4 model

We investigate the supersymmetric A_4 model recently proposed by Babu, Ma and Valle. The model naturally gives quasi-degenerate neutrinos that are bi-largely mixed, in agreement with observations. Furthermore, the mixings in the quark sector are constrained to be small, making it a complete model of the flavor structure. Moreover, it has the interesting property that CP-violation in the leptonic sector is maximal (unless vanishing). The model exhibit a close relation between the slepton and lepton sectors and we derive the slepton spectra that are compatible with neutrino data and the present bounds on flavor-violating charged lepton decays. The prediction for the branching ratio of the decay tau -> mu gamma has a lower limit of 10^{-9}. In addition, the overall neutrino mass scale is constrained to be larger than 0.3 eV. Thus, the model will be tested in the very near future.Comment: 11 pages, 6 figures. Talk given at the International Workshop on Astroparticle and High Energy Physics (AHEP), Valencia, Spain, 14-18 Oct. 200

Radial power-like potentials: from the Bohr-Sommerfeld SS-state energies to the exact ones

Following our previous study of the Bohr-Sommerfeld (B-S) quantization condition for one-dimensional case (del Valle \& Turbiner (2021) \cite{First}), we extend it to $d$-dimensional power-like radial potentials. The B-S quantization condition for $S$-states of the $d$-dimensional radial Schr\"odinger equation is proposed. Based on numerical results obtained for the spectra of power-like potentials, $V(r)=r^m$ with $m \in [-1, \infty)$, the correctness of the proposed B-S quantization condition is established for various dimensions $d$. It is demonstrated that by introducing the {\it WKB correction} $\gamma$ (supposedly coming from the higher order WKB terms) into the r.h.s. of the B-S quantization condition leads to the so-called {\it exact WKB quantization condition}, which reproduces the exact energies, while $\gamma$ remains always very small. For $m=2$ (any integer $d$) and for $m=-1$ (at $d=2$) the WKB correction $\gamma=0$: for $S$ states the B-S spectra coincides with the exact ones. Concrete calculations for physically important cases of linear, cubic, quartic, and sextic oscillators, as well as Coulomb and logarithmic potentials in dimensions $d=2,3,6$ are presented. Radial quartic anharmonic oscillator is considered briefly.Comment: 15 pages, 4 figures, 4 tables; extended, some typos fixed, to be published in IJMP

Radial Anharmonic Oscillator: Perturbation Theory, New Semiclassical Expansion, Approximating Eigenfunctions. II. Quartic and Sextic Anharmonicity Cases

In our previous paper I (del Valle--Turbiner, Int. J. Mod. Phys. A34, 1950143, 2019) it was developed the formalism to study the general $D$-dimensional radial anharmonic oscillator with potential $V(r)= \frac{1}{g^2}\,\hat{V}(gr)$. It was based on the Perturbation Theory (PT) in powers of $g$ (weak coupling regime) and in inverse, fractional powers of $g$ (strong coupling regime) in both $r$-space and in $(gr)$-space, respectively. As the result it was introduced - the Approximant - a locally-accurate uniform compact approximation of a wave function. If taken as a trial function in variational calculations it has led to variational energies of unprecedented accuracy for cubic anharmonic oscillator. In this paper the formalism is applied to both quartic and sextic, spherically-symmetric radial anharmonic oscillators with two term potentials $V(r)= r^2 + g^{2(m-1)}\, r^{2m}, m=2,3$, respectively. It is shown that a two-parametric Approximant for quartic oscillator and a five-parametric one for sextic oscillator for the first four eigenstates used to calculate the variational energy are accurate in 8-12 figures for any $D=1,2,3\ldots$ and $g \geq 0$, while the relative deviation of the Approximant from the exact eigenfunction is less than $10^{-6}$ for any $r \geq 0$.Comment: 52 pages, 17 figures, 3 appendice