On the statistics of resonances and non-orthogonal eigenfunctions in a model for single-channel chaotic scattering

We describe analytical and numerical results on the statistical properties of complex eigenvalues and the corresponding non-orthogonal eigenvectors for non-Hermitian random matrices modeling one-channel quantum-chaotic scattering in systems with broken time-reversal invariance.Comment: 4 pages, 2 figure

Wavefunction statistics in open chaotic billiards

We study the statistical properties of wavefunctions in a chaotic billiard that is opened up to the outside world. Upon increasing the openings, the billiard wavefunctions cross over from real to complex. Each wavefunction is characterized by a phase rigidity, which is itself a fluctuating quantity. We calculate the probability distribution of the phase rigidity and discuss how phase rigidity fluctuations cause long-range correlations of intensity and current density. We also find that phase rigidities for wavefunctions with different incoming wave boundary conditions are statistically correlated.Comment: 4 pages, RevTeX; 1 figur

Conductance of Open Quantum Billiards and Classical Trajectories

We analyse the transport phenomena of 2D quantum billiards with convex boundary of different shape. The quantum mechanical analysis is performed by means of the poles of the S-matrix while the classical analysis is based on the motion of a free particle inside the cavity along trajectories with a different number of bounces at the boundary. The value of the conductance depends on the manner the leads are attached to the cavity. The Fourier transform of the transmission amplitudes is compared with the length of the classical paths. There is good agreement between classical and quantum mechanical results when the conductance is achieved mainly by special short-lived states such as whispering gallery modes (WGM) and bouncing ball modes (BBM). In these cases, also the localization of the wave functions agrees with the picture of the classical paths. The S-matrix is calculated classically and compared with the transmission coefficients of the quantum mechanical calculations for five modes in each lead. The number of modes coupled to the special states is effectively reduced.Comment: 19 pages, 6 figures (jpg), 2 table

Study of electron anti-neutrinos associated with gamma-ray bursts using KamLAND

We search for electron anti-neutrinos ($\overline{\nu}_e$) from long and short-duration gamma-ray bursts~(GRBs) using data taken by the KamLAND detector from August 2002 to June 2013. No statistically significant excess over the background level is found. We place the tightest upper limits on $\overline{\nu}_e$ fluence from GRBs below 7 MeV and place first constraints on the relation between $\overline{\nu}_e$ luminosity and effective temperature.Comment: 16 pages and 5 figure

KamLAND Sensitivity to Neutrinos from Pre-Supernova Stars

In the late stages of nuclear burning for massive stars (M>8~M_{\sun}), the production of neutrino-antineutrino pairs through various processes becomes the dominant stellar cooling mechanism. As the star evolves, the energy of these neutrinos increases and in the days preceding the supernova a significant fraction of emitted electron anti-neutrinos exceeds the energy threshold for inverse beta decay on free hydrogen. This is the golden channel for liquid scintillator detectors because the coincidence signature allows for significant reductions in background signals. We find that the kiloton-scale liquid scintillator detector KamLAND can detect these pre-supernova neutrinos from a star with a mass of 25~M_{\sun} at a distance less than 690~pc with 3$\sigma$ significance before the supernova. This limit is dependent on the neutrino mass ordering and background levels. KamLAND takes data continuously and can provide a supernova alert to the community.Comment: 19 pages, 6 figures, 1 tabl

Distribution of nearest distances between nodal points for the Berry function in two dimensions

According to Berry a wave-chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes. Here we consider the distribution of nodal points associated with this state. Using the property that both the real and imaginary parts of the wave function are random Gaussian fields we analyze the correlation function and densities of the nodal points. Using two approaches (the Poisson and Bernoulli) we derive the distribution of nearest neighbor separations. Furthermore the distribution functions for nodal points with specific chirality are found. Comparison is made with results from from numerical calculations for the Berry wave function.Comment: 11 pages, 7 figure

Giving Back: Contributions Congruent to Library Dependency Changes in a Software Ecosystem

The widespread adoption of third-party libraries for contemporary software development has led to the creation of large inter-dependency networks, where sustainability issues of a single library can have widespread network effects. Maintainers of these libraries are often overworked, relying on the contributions of volunteers to sustain these libraries. To understand these contributions, in this work, we leverage socio-technical techniques to introduce and formalise dependency-contribution congruence (DC congruence) at both ecosystem and library level, i.e., to understand the degree and origins of contributions congruent to dependency changes, analyze whether they contribute to library dormancy (i.e., a lack of activity), and investigate similarities between these congruent contributions compared to typical contributions. We conduct a large-scale empirical study to measure the DC congruence for the npm ecosystem using 1.7 million issues, 970 thousand pull requests (PRs), and over 5.3 million commits belonging to 107,242 npm libraries. We find that the most congruent contributions originate from contributors who can only submit (not commit) to both a client and a library. At the project level, we find that DC congruence shares an inverse relationship with the likelihood that a library becomes dormant. Specifically, a library is less likely to become dormant if the contributions are congruent with upgrading dependencies. Finally, by comparing the source code of contributions, we find statistical differences in the file path and added lines in the source code of congruent contributions when compared to typical contributions. Our work has implications to encourage dependency contributions, especially to support library maintainers in sustaining their projects.Supatsara Wattanakriengkrai, Dong Wang, Raula Gaikovina Kula, Christoph Treude, Patanamon Thongtanunam, Takashi Ishio, and Kenichi Matsumot

Effective Hamiltonian and unitarity of the S matrix

The properties of open quantum systems are described well by an effective Hamiltonian ${\cal H}$ that consists of two parts: the Hamiltonian $H$ of the closed system with discrete eigenstates and the coupling matrix $W$ between discrete states and continuum. The eigenvalues of ${\cal H}$ determine the poles of the $S$ matrix. The coupling matrix elements $\tilde W_k^{cc'}$ between the eigenstates $k$ of ${\cal H}$ and the continuum may be very different from the coupling matrix elements $W_k^{cc'}$ between the eigenstates of $H$ and the continuum. Due to the unitarity of the $S$ matrix, the \TW_k^{cc'} depend on energy in a non-trivial manner, that conflicts with the assumptions of some approaches to reactions in the overlapping regime. Explicit expressions for the wave functions of the resonance states and for their phases in the neighbourhood of, respectively, avoided level crossings in the complex plane and double poles of the $S$ matrix are given.Comment: 17 pages, 7 figure

Negative length orbits in normal-superconductor billiard systems

The Path-Length Spectra of mesoscopic systems including diffractive scatterers and connected to superconductor is studied theoretically. We show that the spectra differs fundamentally from that of normal systems due to the presence of Andreev reflection. It is shown that negative path-lengths should arise in the spectra as opposed to normal system. To highlight this effect we carried out both quantum mechanical and semiclassical calculations for the simplest possible diffractive scatterer. The most pronounced peaks in the Path-Length Spectra of the reflection amplitude are identified by the routes that the electron and/or hole travels.Comment: 4 pages, 4 figures include