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We analyze the spectral properties of the Heisenberg spin-1/2 chain with random fields in light of recent works of the renormalization-group flow of the Anderson model in infinite dimension. We reconstruct the beta function of the order parameter from the numerical data, and show that it does not admit a one-parameter scaling form and a simple Wilson-Fisher fixed point. Rather, it is compatible with a two-parameter, Berezinskii-Kosterlitz-Thouless-like flow with a line of fixed points (the many-body localized phase), which terminates into the localization transition critical point. Therefore, we argue that previous studies, which assumed the existence of an isolated Wilson- Fisher fixed point and performed one-parameter finite-size scaling analysis, could not explain the numerical data in a coherent way., Comment: 15 pages, 12 figures

We investigate the efficiency of approximate counterdiabatic driving (CD) in accelerating adiabatic passage through a first-order quantum phase transition. Specifically, we analyze a minimal spin-glass bottleneck model that is analytically tractable and exhibits both an exponentially small gap at the transition point and a change in the ground state that involves a macroscopic rearrangement of spins. Using the variational Floquet-Krylov expansion to construct CD terms, we find that while the formation of excitations is significantly suppressed, achieving fully adiabatic evolution remains challenging, necessitating high-order nonlocal terms in the expansion. Our results demonstrate that local CD strategies have limited effectiveness when crossing the extremely small gaps characteristic of NP-hard Ising problems. To address this limitation, we propose an alternative method, termed quantum brachistochrone counterdiabatic driving (QBCD), which significantly increases the fidelity to the target state over the expansion method by directly addressing the gap-closing point and the associated edge states.

Open quantum systems have complex energy eigenvalues which are expected to follow non-Hermitian random matrix statistics when chaotic, or 2-dimensional (2d) Poisson statistics when integrable. We investigate the spectral properties of a many-body quantum spin chain, the Hermitian XXZ Heisenberg model with imaginary disorder. Its rich complex eigenvalue statistics is found to separately break both Hermiticity and integrability at different scales of the disorder strength. With no disorder, the system is integrable and Hermitian, with spectral statistics corresponding to 1d Poisson. At very small disorder, we find a transition from 1d Poisson statistics to an effective $D$-dimensional Poisson point process, showing Hermiticity breaking. At intermediate disorder we find integrability breaking, and the statistics agrees with that of non-Hermitian complex symmetric random matrices in class AI$^\dag$. For large disorder, we recover the expected 2d Poisson statistics. Our analysis uses numerically generated nearest and next-to-nearest neighbour spacing distributions of an effective 2d Coulomb gas description at inverse temperature $\beta$, fitting them to the spin chain data. We confirm such an effective description of random matrices in class AI$^\dag$ and AII$^\dag$ up to next-to-nearest neighbour spacings., Comment: 12+3 pages, 13+2 figures. comments welcome

In this paper we study existence and regularity of solutions to Dirichlet problems as $$ \begin{cases} - {\rm div}\left(|u|^m\frac{D u}{|D u|}\right) = f & \text{in}\;\Omega,\\ \newline u=0 & \text{on}\;\partial\Omega, \end{cases} $$ where $\Omega$ is an open bounded subset of $\mathbb{R}^N$ ($N\geq 2$) with Lipschitz boundary, $m>0$, and $f$ belongs to the Lorentz space $L^{N,\infty}(\Omega)$. In particular, we explore the regularizing effect given by the degenerate coefficient $|u|^m$ in order to get non-trivial and bounded solutions with no smallness assumptions on the size of the data.

We consider the optimal driving of the ground state of a many-body quantum system across a quantum phase transition in finite time. In this context, excitations caused by the breakdown of adiabaticity can be minimized by adjusting the schedule of the control parameter that drives the transition. Drawing inspiration from the Kibble-Zurek mechanism, we characterize the timescale of onset of adiabaticity for several optimal control procedures. Our analysis reveals that schedules relying on local adiabaticity, such as Roland-Cerf's local adiabatic driving and the quantum adiabatic brachistochrone, fail to provide a significant speedup over the adiabatic evolution in the transverse-field Ising and long-range Kitaev models. As an alternative, we introduce a novel framework, Non-Adiabatic Quantum Optimization (NAQO), that, by exploiting the Landau-Zener formula and taking into account the role of higher-excited states, outperforms schedules obtained via both local adiabaticity and state-of-the-art numerical optimization. NAQO is not restricted to exactly solvable models, and we further confirm its superior performance in a disordered non-integrable model., Comment: 24 pages, 15 figures, comments welcome

Modeling open hole failure of composites is a complex task, consisting in a highly nonlinear response with interacting failure modes. Numerical modeling of this phenomenon has traditionally been based on the finite element method, but requires to tradeoff between high fidelity and computational cost. To mitigate this shortcoming, recent work has leveraged machine learning to predict the strength of open hole composite specimens. Here, we also propose using data-based models but to tackle open hole composite failure from a classification point of view. More specifically, we show how to train surrogate models to learn the ultimate failure envelope of an open hole composite plate under in-plane loading. To achieve this, we solve the classification problem via support vector machine (SVM) and test different classifiers by changing the SVM kernel function. The flexibility of kernel-based SVM also allows us to integrate the recently developed quantum kernels in our algorithm and compare them with the standard radial basis function (RBF) kernel. Finally, thanks to kernel-target alignment optimization, we tune the free parameters of all kernels to best separate safe and failure-inducing loading states. The results show classification accuracies higher than 90% for RBF, especially after alignment, followed closely by the quantum kernel classifiers.

The wide adoption of composite structures in the aerospace industry requires reliable numerical methods to account for the effects of various damage mechanisms, including delamination. Cohesive elements are a versatile and physically representative way of modelling delamination. However, using their standard form which conforms to solid substrate elements, multiple elements are required in the narrow cohesive zone, thereby requiring an excessively fine mesh and hindering the applicability in practical scenarios. The present work focuses on the implementation and testing of triangular thin plate substrate elements and compatible cohesive elements, which satisfy C1-continuity in the domain. The improved regularity meets the continuity requirement coming from the Kirchhoff Plate Theory and the triangular shape allows for conformity to complex geometries. The overall model is validated for mode I delamination, the case with the smallest cohesive zone. Very accurate predictions of the limit load and crack propagation phase are achieved, using elements as large as 11 times the cohesive zone.

Alzheimer's disease (AD), a debilitating neurodegenerative disorder, remains one of the foremost public health challenges of our time. Despite decades of research, its etiology largely remains enigmatic. Recently, attention has turned to the gut-brain axis, a complex network of communication between the gastrointestinal tract and the brain, as a potential player in the pathogenesis of AD. Here we exploited X-ray Phase Contrast Tomography to provide an in-depth analysis of the link between the gut condition and AD, exploring gut anatomy and structure in murine models. We conducted a comprehensive analysis by comparing the outcomes in various mouse models of cognitive impairment, including AD, frail mice, and frontotemporal dementia (FTD) affected mice. We discovered an association between substantial changes in the gut structure and the presence of amyloid-beta (A\b{eta}) in the brain. We found that the most important gut alterations are related to A\b{eta} occurrence in the brain. In particular, we investigated the gut morphology, the distribution of enteric micro-processes and neurons in the ileum. Understanding the intricate interplay between gut condition and dementia may open new avenues for early AD diagnosis and treatment offering hope for a future where these diseases may be more effectively addressed., Comment: 14 pages and 7 figures

Strong local disorder in interacting quantum spin chains can turn delocalized eigenmodes into localized eigenstates, giving rise to many-body localized (MBL) phases. This is accompanied by distinct spectral statistics: chaotic for the delocalized phase and integrable for the localized phase. In isolated systems, localization and chaos are defined through a web of relations among eigenvalues, eigenvectors, and real-time dynamics. These may change as the system is made open. We ask whether random dissipation (without random disorder) can induce chaotic or localized behavior in an otherwise integrable system. The dissipation is described using non-Hermitian Hamiltonians, which can effectively be obtained from Markovian dynamics conditioned on null measurement. Through the use of the singular value decomposition and the introduction of new diagnostic tools complementing the singular-value statistics, namely, the singular form factor, the inverse participation ratio, and entanglement entropy for singular vectors, we provide a positive answer. Our method is illustrated in an XXZ Hamiltonian with random local dissipation., Comment: 5+6 pages, 2+6 figures

This paper explores the potential application of quantum and hybrid quantum-classical neural networks in power flow analysis. Experiments are conducted using two datasets based on 4-bus and 33-bus test systems. A systematic performance comparison is also conducted among quantum, hybrid quantum-classical, and classical neural networks. The comparison is based on (i) generalization ability, (ii) robustness, (iii) training dataset size needed, (iv) training error, and (v) training process stability. The results show that the developed hybrid quantum-classical neural network outperforms both quantum and classical neural networks, and hence can improve deep learning-based power flow analysis in the noisy-intermediate-scale quantum (NISQ) and fault-tolerant quantum (FTQ) era., Comment: 8 pages, 13 figures

Prior to the deep learning era, shape was commonly used to describe the objects. Nowadays, state-of-the-art (SOTA) algorithms in medical imaging are predominantly diverging from computer vision, where voxel grids, meshes, point clouds, and implicit surface models are used. This is seen from numerous shape-related publications in premier vision conferences as well as the growing popularity of ShapeNet (about 51,300 models) and Princeton ModelNet (127,915 models). For the medical domain, we present a large collection of anatomical shapes (e.g., bones, organs, vessels) and 3D models of surgical instrument, called MedShapeNet, created to facilitate the translation of data-driven vision algorithms to medical applications and to adapt SOTA vision algorithms to medical problems. As a unique feature, we directly model the majority of shapes on the imaging data of real patients. As of today, MedShapeNet includes 23 dataset with more than 100,000 shapes that are paired with annotations (ground truth). Our data is freely accessible via a web interface and a Python application programming interface (API) and can be used for discriminative, reconstructive, and variational benchmarks as well as various applications in virtual, augmented, or mixed reality, and 3D printing. Exemplary, we present use cases in the fields of classification of brain tumors, facial and skull reconstructions, multi-class anatomy completion, education, and 3D printing. In future, we will extend the data and improve the interfaces. The project pages are: https://medshapenet.ikim.nrw/ and https://github.com/Jianningli/medshapenet-feedback, Comment: 16 pages

In this paper we deal with the following boundary value problem \begin{equation*} \begin{cases} -\Delta_{p}u + g(u) | \nabla u|^{p} = h(u)f & \text{in $\Omega$,} \newline u\geq 0 & \text{in $\Omega$,} \newline u=0 & \text{on $\partial \Omega$,} \ \end{cases} \end{equation*} in a domain $\Omega \subset \mathbb{R}^{N}$ $(N \geq 2)$, where $1\leq p

The Kibble-Zurek mechanism (KZM) predicts that the average number of topological defects generated upon crossing a continuous or quantum phase transition obeys a universal scaling law with the quench time. Fluctuations in the defect number near equilibrium are approximately of Gaussian form, in agreement with the central limit theorem. Using large deviations theory, we characterize the universality of fluctuations beyond the KZM and report the exact form of the rate function in the transverse-field quantum Ising model. In addition, we characterize the scaling of large deviations in an arbitrary continuous phase transition, building on recent evidence establishing the universality of the defect number distribution., Comment: 6+6 pages, 1+2 figures

Alzheimer's is a neurodegenerative disease that is the most common form of dementia, but there is still no definitive cure for this disease. The noninvasive X-ray Phase Contrast Tomography (XPCT) imaging technique was used to study brain tissues in mouse models of Alzheimer's disease, AP-PS1 and APP23. The XPCT technique enabled high-resolution imaging of brain tissues, distinguishing between different brain structures, such as amyloid deposits and neuronal cells. In addition, the XPCT technique provided detailed information on the distribution and morphology of amyloid deposits in AP-PS1 and APP23 mice putting in evidence the differences between these two models. This work demonstrates the effectiveness of this technique in supporting Alzheimer's studies and evaluating new therapeutic strategies., Comment: 14 pages, 8 figures

We study the transport and equilibration properties of a classical Heisenberg chain, whose couplings are random variables drawn from a one-parameter family of power-law distributions. The absence of a scale in the couplings makes the system deviate substantially from the usual paradigm of diffusive spin hydrodynamics, and exhibit a regime of subdiffusive transport with an exponent changing continuously with the parameter of the distribution. We propose a solvable phenomenological model that correctly yields the subdiffusive exponent, thereby linking local fluctuations in the coupling strengths to the long-time, large-distance behaviour. It also yields the finite-time corrections to the asymptotic scaling, which can be important in fitting the numerical data. We show how such exponents undergo transitions as the distribution of the coupling gets wider, marking the passage from diffusion to a regime of slow diffusion, and finally to subdiffusion., Comment: 10+3 pages, 5+4 figures

In a recent paper [Phys. Rev. Lett. 129, 120601] we have shown that the dynamics of interfaces, in the symmetry-broken phase of the two-dimensional ferromagnetic quantum Ising model, displays a robust form of ergodicity breaking. In this paper, we elaborate more on the issue. First, we discuss two classes of initial states on the square lattice, the dynamics of which is driven by complementary terms in the effective Hamiltonian and may be solved exactly: (a) strips of consecutive neighbouring spins aligned in the opposite direction of the surrounding spins, and (b) a large class of initial states, characterized by the presence of a well-defined "smooth" interface separating two infinitely extended regions with oppositely aligned spins. The evolution of the latter states can be mapped onto that of an effective one-dimensional fermionic chain, which is integrable in the infinite-coupling limit. In this case, deep connections with noteworthy results in mathematics emerge, as well as with similar problems in classical statistical physics. We present a detailed analysis of the evolution of these interfaces both on the lattice and in a suitable continuum limit, including the interface fluctuations and the dynamics of entanglement entropy. Second, we provide analytical and numerical evidence supporting the conclusion that the observed non-ergodicity -- arising from Stark localization of the effective fermionic excitations -- persists away from the infinite-Ising-coupling limit, and we highlight the presence of a timescale $T\sim e^{c L\ln L}$ for the decay of a region of large linear size $L$. The implications of our work for the classic problem of the decay of a false vacuum are also discussed., Comment: 33 pages, 12 figures

The melting of the corner of a crystal is a classical, real-world, non-equilibrium statistical mechanics problem which has shown several connections with other branches of physics and mathematics. For a perfect, classical crystal in two and three dimensions the solution is known: the crystal melts reaching a certain asymptotic shape, which keeps expanding ballistically. In this paper, we move onto the quantum realm and show that the presence of quenched disorder slows down severely the melting process. Nevertheless, we show that there is no many-body localization transition, which could impede the crystal to be completely eroded. We prove such claim both by a perturbative argument, using the forward approximation, and via numerical simulations. At the same time we show how, despite the lack of localization, the erosion dynamics is slowed from ballistic to logarithmic, therefore pushing the complete melting of the crystal to extremely long timescales., Comment: 16 pages, 10 figures

We present a novel approach which produces Dark Matter jets along the rotation axis of Kerr black holes utilizing the Penrose process. The properties of these jets are investigated, as well as their potential to create Dark Matter overdensities in the solar system and in the vicinity of the black hole. We discover a highly collimated and long-range Dark Matter jet with a density that is most sensitive to the mass and distance to the black hole., Comment: 5 pages, 3 figures

We study the non-equilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model -- a setup relevant in several contexts, from quantum nucleation dynamics and false-vacuum decay scenarios to recent experiments with Rydberg-atom arrays. We demonstrate that the quantum-fluctuating interface delimiting a large bubble can be studied as an effective one-dimensional system through a "holographic" mapping. For the considered model, the emergent interface excitations map to an integrable chain of fermionic particles. We discuss how this integrability is broken by geometric features of the bubbles and by corrections in inverse powers of the ferromagnetic coupling, and provide a lower bound to the timescale after which the bubble is ultimately expected to melt. Remarkably, we demonstrate that a symmetry-breaking longitudinal field gives rise to a robust ergodicity breaking in two dimensions, a phenomenon underpinned by Stark many-body localization of the emergent fermionic excitations of the interface., Comment: 7+1 pages, 4 figures