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The coincidence rank, introduced by Barge and Kwapisz, measures the regularity of the maximal equicontinuous factor of minimal dynamical systems. We provide a characterization of the finiteness of coincidence rank using a multivariate notion of equicontinuity.

We establish a connection between percolation on the Cayley graphs of a group and the dynamical diversity of cellular automata on that group. Specifically, we demonstrate that Gilman's dichotomy between equicontinuity and sensitivity with respect to Bernoulli measures holds on a finitely generated group if and only if the group has a trivial percolation threshold. Consequently, we show that a countable group satisfies Gilman's dichotomy if and only if it is locally virtually cyclic., Comment: 23 pages, 1 cute picture, minor fixes

We investigate the Extended Lipkin Model (ELM), whose phase diagram mirrors that of the Interacting Boson Approximation model (IBA). Unlike the standard Lipkin model, the ELM (as the IBA) features both first- and second-order quantum shape phase transitions depending on the model parameters. Our goal is to implement the ELM on a quantum platform, leveraging Machine Learning techniques to identify its quantum phase transitions and critical lines. To achieve this, we offer: i) ground state energy calculations using a variational quantum eigensolver; ii) a detailed formulation for ELM dynamics within quantum computing, facilitating experimental exploration of the IBA phase diagram; and iii) a phase diagram determination using various Machine Learning methods. We successfully replicate the ELM ground-state energy using the Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) algorithm across the entire phase space. Our framework ensures ELM implementation on quantum platforms with controlled errors. Lastly, our ML predictions yield a meaningful phase diagram for the model. Keywords: Quantum Platforms Nuclear Models ADAPT-VQE Quantum Shape Phase Transitions Interacting Boson Approximation Extended Lipkin Model Machine Learning, Comment: 23 pages, 14 figures

Using a local perspective, we introduce \textit{mean dimension pairs} and give sufficient conditions of when every non-trivial factor of a continuous group action of a sofic group $G$ has positive mean dimension. In addition we show that the mean dimension map is Borel, and that the set of subshifts with completely positive mean dimension of $[0,1]^G$, the full $G$-shift on the interval, is a complete coanalytic set in the set of all subshifts (hence not Borel). Our results are new even when the acting group is $\Z$., Comment: to appear in GGD

In this contribution, the shape coexistence phenomenon near the proton sub-shell closure at Z=40 is analyzed. Particular emphasis is placed on extracting the nuclear deformation values by examining experimental B(E2) transition rates and observing how the kinematic moment of inertia evolves in these nuclei. Based on the analysis of these two observables, we arrive at the conclusion that the notable effects of shape coexistence at approximately Z=40 are largely diminished in Mo isotopes and are scarcely detectable in Ru isotopes., Comment: To appear in the CGS-17 2023 proceedings, 3 pages

We study the topological, dynamical, and descriptive set theoretic properties of Hurwitz continued fractions. Hurwitz continued fractions associate an infinite sequence of Gaussian integers to every complex number which is not a Gaussian rational. The resulting space of sequences of Gaussian integers $\Omega$ is not closed. By means of an algorithm, we show that $\Omega$ contains a natural subset whose closure $\overline{\mathsf{R}}$ encodes continued fraction expansions of complex numbers which are not Gaussian rationals. We prove that $(\overline{\mathsf{R}}, \sigma)$ is a subshift with a feeble specification property. As an application, we determine the rank in the Borel hierarchy of the set of Hurwitz normal numbers with respect to the complex Gauss measure. We also construct a family of complex transcendental numbers with bounded partial quotients., Comment: Several typos were fixed. Aiming towards clarity, additional details were added in the proofs and some paragraphs were rephrased. Figures 1, 2, and 3 were added. The title was changed

The empirical spectra and $E2$ decay rates in $^{110,112,114,116}$Cd are shown to be consistent with a vibrational interpretation for low-lying normal states, coexisting with a single deformed $\gamma$-soft band of intruder states. The observed deviations from this paradigm show up in particular non-yrast states, which are properly described by a Hamiltonian with U(5) partial dynamical symmetry. The latter is characterized by a good (broken) symmetry in most (in selected) normal states, weakly coupled to intruder states., Comment: 5 pages, 3 figures, 2 tables, accepted for publication as a Letter in Phys. Rev. C

Background Even-even isotopes of Mo ($Z=42$) and Ru ($Z=44$) are nuclei close to the subshell closure at $Z=40$, where shape coexistence plays a significant role. As a result, their spectroscopic properties are expected to resemble those of Sr ($Z=38$) and Zr ($Z=40$). Exploring the evolution of these properties as they move away from the subshell closure is of great interest. Purpose The purpose of this study is to reproduce the spectroscopic properties of even-even $^{96-110}_{\phantom{961-}42}$Mo and $^{98-114}_{\phantom{961-}44}$Ru isotopes and to determine the influence of shape coexistence. Method We have employed the interacting boson model with configuration mixing as the framework to calculate all the observables for Mo and Ru isotopes. We have considered two types of configurations: 0-particle-0-hole and 2-particle-2-hole excitations. The model parameters have been determined using a least-squares fitting to match the excitation energies and the $B(E2)$ transition rates. Results We have obtained the excitation energies, $B(E2)$ values, two-neutron separation energies, nuclear radii, and isotope shifts for the entire chain of isotopes. Our theoretical results have shown good agreement with experimental data. Furthermore, we have conducted a detailed analysis of the wave functions and obtained the mean-field energy surfaces and the nuclear deformation parameter, $\beta$, for all considered isotopes. Conclusions Our findings reveal that shape coexistence plays a significant role in Mo isotopes, with the crossing of intruder and regular configurations occurring at neutron number $60$ ($A=102$), which induces a quantum phase transition. In contrast, in Ru isotopes, the intruder states have minimal influence, remaining at higher energies. However, at neutron number $60$, also a quantum phase transition occurs in Ru isotopes., Comment: Accepted for publication in Physical Review C. arXiv admin note: text overlap with arXiv:2203.05324

In this paper, the application of quantum simulations and quantum machine learning to solve low-energy nuclear physics problems is explored. The use of quantum computing to deal with nuclear physics problems is, in general, in its infancy and, in particular, the use of quantum machine learning in the realm of nuclear physics at low energy is almost nonexistent. We present here three specific examples where the use of quantum computing and quantum machine learning provides, or could provide in the future, a possible computational advantage: i) the determination of the phase/shape in schematic nuclear models, ii) the calculation of the ground state energy of a nuclear shell model-type Hamiltonian and iii) the identification of particles or the determination of trajectories in nuclear physics experiments., Comment: Submitted to the special issue "Quantum Machine Learning" of the journal Advanced Quantum Technologies

Background: The mercury isotopes around $N=104$ are a well-known example of nuclei exhibiting shape coexistence. Mixing of configurations can be studied by measuring the monopole strength $\rho^2(E0)$, however, currently the experimental information is scarce and lacks precision, especially for the $I^\pi \rightarrow I^\pi$ ($I \neq 0$) transitions. Purpose: The goals of this study were to increase the precision of the known branching ratios and internal conversion coefficients, to increase the amount of available information regarding excited states in $^{182,184,186}$Hg and to interpret the results in the framework of shape coexistence using different models. Method: The low-energy structures in $^{182,184,186}$Hg were populated in the $\beta$ decay of $^{182,184,186}$Tl, produced at ISOLDE and purified by laser ionization and mass separation. The $\gamma$-ray and internal conversion electron events were detected by five germanium clover detectors and a segmented silicon detector, respectively, and correlated in time to build decay schemes. Results: In total, 193, 178 and 156 transitions, including 144, 140 and 108 observed for the first time in a $\beta$-decay experiment, were assigned to $^{182,184,186}$Hg, respectively. Internal conversion coefficients were determined for 23 transitions, out of which 12 had an $E0$ component. Extracted branching ratios allowed the sign of the interference term in $^{182}$Hg as well as $\rho^2(E0;0^+_2\rightarrow 0^+_1)$ and $B(E2;0^+_2\rightarrow 2^+_1)$ in $^{184}$Hg to be determined. By means of electron-electron coincidences, the $0^+_3$ state was identified in $^{184}$Hg. The experimental results were qualitatively reproduced by five theoretical approaches, the IBM with configuration mixing with two different parametrizations, the General Bohr Hamiltonian, the BMF model and the SCCM model. However, a quantitative description is lacking., Comment: 21 pages, 30 figures, accepted for publication in Physical Review C

This file is composed of questions that emerged or were of interest during the workshop "Interactions between Descriptive Set Theory and Smooth Dynamics" that took place in Banff, Canada on 2022.

In this contribution we study the even-even Sr isotopes considering the influence of particle-hole intruder states. We find that the rapid onset of deformation at A $=98$ and onwards can be explained by the crossing of regular and intruder states. We compare the systematics of Sr with the ones of Zr, Pt, and Hg nuclei, Comment: To appear in the EUNPC 2022 proceedings

We find sufficient conditions for bounded density shifts to have a unique measure of maximal entropy. We also prove that every measure of maximal entropy of a bounded density shift is fully supported. As a consequence of this, we obtain that bounded density shifts are surjunctive., Comment: 19 pages

We characterize measure-theoretic sequence entropy pairs of continuous abelian group actions using mean sensitivity. This solves an open question mentioned by Li and Yu. As a consequence of our results we provide a simpler characterization of Kerr and Li's independence sequence entropy pairs ($\mu$-IN-pairs) when the measure is ergodic and the group is abelian., Comment: 12 pages

A digital quantum simulation for the extended Agassi model is proposed using a quantum platform with eight trapped ions. The extended Agassi model is an analytically solvable model including both short range pairing and long range monopole-monopole interactions with applications in nuclear physics and in other many-body systems. In addition, it owns a rich phase diagram with different phases and the corresponding phase transition surfaces. The aim of this work is twofold: on one hand, to propose a quantum simulation of the model at the present limits of the trapped ions facilities and, on the other hand, to show how to use a machine learning algorithm on top of the quantum simulation to accurately determine the phase of the system. Concerning the quantum simulation, this proposal is scalable with polynomial resources to larger Agassi systems. Digital quantum simulations of nuclear physics models assisted by machine learning may enable one to outperform the fastest classical computers in determining fundamental aspects of nuclear matter., Comment: 15 pages, 11 figures. New title and minor changes. Published in PRC