arXiv subjects

Declan Mulhall

Publications and source records attributed to Declan Mulhall.

7 recordsLinked to original sources

arXiv2025

Order, Collectivity, Structured Yrast Lines, and Correlated Energies in Random Bosonic Systems

Signatures of order and collectivity appear in a broad range of one and two level boson systems. Toy systems of $N$ particles on a single $j=3,\,4\dots 7$ level, and on 2 levels $(j_1,\,j_2)$ with $j_1+j_2 \leq 6$ were studied. Surprising novel features in the yrast lines were consistent with boson condensates. Strong signatures of order and collectivity were the norm. These included the usual energy ratios and quadrupole transition strengths for vibrational and rotational bands. There were pronounced correlations in energy ratios, sharp peaks in the Alga ratios and fractional collectivity across all the 1-level systems, as well as signatures of triaxiality

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arXiv2022

Are the ground states of randomly interacting bosons random?

Bosonic degrees of freedom and their emergence as a part of complex quantum many-body dynamics, symmetries, collective behavior, clustering and phase transitions play an important role in modern studies of quantum systems. In this work we present a systematic study of many-boson systems governed by random interactions. Our findings show that ground states of randomly interacting bosons are not random, being dominated by a few collective configurations containing condensates of clusters.

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arXiv2015

Open quantum systems and Random Matrix Theory

A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the $Δ_3(L)$ statistic, width distribution and level spacing are examined as a function of the strength of this coupling. A super-radiant transition is observed, and it is seen that as it is formed, the level spacing and $Δ_3(L)$ statistic exhibit the signatures of missed levels.

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arXiv2014

Calculating and visualizing the density of states for simple quantum mechanical systems

We present a graphical approach to understanding the degeneracy, density of states, and cumulative state number for some simple quantum systems. By taking advantage of basic computing operations we define a straightforward procedure for determining the relationship between discrete quantum energy levels and the corresponding density of states and cumulative level number. The density of states for a particle in a rigid box of various shapes and dimensions is examined and graphed. It is seen that the dimension of the box, rather than its shape, is the most important feature. In addition, we look at the density of states for a multi-particle system of identical bosons built on the single-particle spectra of those boxes. A simple model is used to explain how the $N$-particle density of states arises from the single particle system it is based on.

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arXiv2011

Ergodicity of the $Δ_3$ statistic and purity of neutron resonance data

The $Δ_3(L)$ statistic characterizes the fluctuations of the number of levels as a function of the length of the spectral interval. It is studied as a possible tool to indicate the regular or chaotic nature of underlying dynamics, detect missing levels and the mixing of sequences of levels of different symmetry, particularly in neutron resonance data. The relation between the ensemble average and the average over different fragments of a given realization of spectra is considered. A useful expression for the variance of $Δ_3(L)$ which accounts for finite sample size is discussed. An analysis of neutron resonance data presents the results consistent with a maximum likelihood method applied to the level spacing distribution.

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arXiv2011

A maximum likelihood method to correct for missed levels based on the $Δ_3(L)$ statistic

The $Δ_3(L)$ statistic of Random Matrix Theory is defined as the average of a set of random numbers $\{δ\}$, derived from a spectrum. The distribution $p(δ)$ of these random numbers is used as the basis of a maximum likelihood method to gauge the fraction $x$ of levels missed in an experimental spectrum. The method is tested on an ensemble of depleted spectra from the gaussian orthogonal ensemble (GOE), and accurately returned the correct fraction of missed levels. Neutron resonance data and acoustic spectra of an aluminum block were analyzed. All results were compared with an analysis based on an established expression for $Δ_3(L)$ for a depleted GOE spectrum. The effects of intruder levels is examined, and seen to be very similar to that of missed levels. Shell model spectra were seen to give the same $p(δ)$ as the GOE.

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arXiv2009

Using the $Δ_3$ statistic to test for missed levels in mixed sequence neutron resonance data

The $Δ_3(L)$ statistic is studied as a tool to detect missing levels in the neutron resonance data where 2 sequences are present. These systems are problematic because there is no level repulsion, and the resonances can be too close to resolve. $Δ_3(L)$ is a measure of the fluctuations in the number of levels in an interval of length $L$ on the energy axis. The method used is tested on ensembles of mixed Gaussian Orthogonal Ensemble (GOE) spectra, with a known fraction of levels ($x%$) randomly depleted, and can accurately return $x$. The accuracy of the method as a function of spectrum size is established. The method is used on neutron resonance data for 11 isotopes with either s-wave neutrons on odd-A, or p-wave neutrons on even-A. The method compares favorably with a maximum likelihood method applied to the level spacing distribution. Nuclear Data Ensembles were made from 20 isotopes in total, and their $Δ_3(L)$ statistic are discussed in the context of Random Matrix Theory.

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