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GUT phase transition during inflation solves the GUT monopole problem on one hand. On the other hand, gravitational waves (GWs) from such a phase transition, if it is first-order, are redshifted and deformed, and might be observed today in GW observatories. We review the formalism of inflated GWs and derive the general deformation function between inflated and uninflated GW spectra in the instant-source application. It is valid for any e-folding number of instant source. Applying the formalism to GUT phase transition, we find that the e-folding number at 15 or 25 can shift the GWs to 10 Hz or mHz hands, respectively, which might be tested in the future ground-based or space-based interferometers. We further generalise the discussion to inflated GWs via phase transition below the GUT scale. It is worth mentioning that, due to the deformation of the spectrum, the peak of inflated GWs is not simply a redshift of the peak of uninflated GWs., Comment: 22 pages, 7 figures

Past ontology requirements engineering (ORE) has primarily relied on manual methods, such as interviews and collaborative forums, to gather user requirements from domain experts, especially in large projects. Current OntoChat offers a framework for ORE that utilises large language models (LLMs) to streamline the process through four key functions: user story creation, competency question (CQ) extraction, CQ filtration and analysis, and ontology testing support. In OntoChat, users are expected to prompt the chatbot to generate user stories. However, preliminary evaluations revealed that they struggle to do this effectively. To address this issue, we experimented with a research method called participatory prompting, which involves researcher-mediated interactions to help users without deep knowledge of LLMs use the chatbot more effectively. This participatory prompting user study produces pre-defined prompt templates based on user queries, focusing on creating and refining personas, goals, scenarios, sample data, and data resources for user stories. These refined user stories will subsequently be converted into CQs.

Dual-unitary quantum circuits can provide analytic spatiotemporal correlation functions of local operators from transfer matrices, enriching our understanding of quantum dynamics with exact solutions. Nevertheless, a full understanding is still lacking as the case of a non-diagonalizable transfer matrix with exceptional points has less been investigated. In this paper, we give an inverse approach for constructing dual-unitary quantum circuits with exceptional points in the transfer matrices, by establishing relations between transfer matrices and local unitary gates. As a consequence of the coalesce of eigenvectors, the correlation functions exhibit a polynomial modified exponential decay, which is significantly different from pure exponential decay, especially at early stages. Moreover, we point out that the Hamiltonian evolution of a kicked XXZ spin chain can be approximately mapped to a dual-unitary circuit with exceptional points by Trotter decomposition. Finally, we investigate the dynamics approaching and at exceptional points, showing that behaviors of correlation functions are distinct by Laplace transformation., Comment: 11 pages, 6 figures, references added

In this paper, we establish a Minkowski-type inequality for weak Lebesgue space, which allows us to obtain a characterization of relative compactness in these spaces. Furthermore, we are the first to investigate the compactness results of commutators at the endpoint. The paper provides a comprehensive study of the compactness properties of commutators of Calder\'{o}n-Zygmund operators in Hardy and $L^{1}(\mathbb{R}^n)$ type spaces. Additionally, we provide factorization theorems for Hardy spaces in terms of singular integral operators in the $L^1(\mathbb{R}^n)$ space., Comment: 36 pages

We investigate the dynamical properties of quasiparticles in graphene superlattices with three typical Kekul\'{e} distortions (i.e., Kekul\'{e}-O, Kekul\'{e}-Y and Kekul\'{e}-M). On the one hand, we numerically show the visualized evolution process of Kekul\'{e} quasiparticles; while on the other hand, we analytically obtain the centroid trajectory of the quasiparticles, and both of them agree well with each other. The results reveal that the relativistic Zitterbewegung (ZB) phenomenon occurs in the Kekul\'{e} systems. Furthermore, through analyzing the frequency of ZB, we unveil the one-to-one relationship between ZB and Kekul\'{e} textures, i.e., the ZB frequenies of Kekul\'{e}-O, Kekul\'{e}-Y and Kekul\'{e}-M quasiparticles feature single, double and six frequencies, respectively. Finally, we propose a scheme to distinguish among different Kekul\'{e} textures from the dynamical perspective. The predictions in this paper are expected to be experimentally verified in the near future, so as to facilitate further research of Kekul\'{e} structures in solid materials or artificial systems.

In this paper, we prove Wiener's criterion for parabolic equations with singular and degenerate coefficients. To be precise, we study the problem of the regularity of boundary points for the Dirichlet problem for degenerate parabolic equations, and give a geometric characterization of those boundary points that are regular., Comment: 65pages

We prove the existence of a critical Fujita exponent for a non-homogeneous semilinear heat equation which involves degenerate coefficients. More precisely, in order to give a rather complete theory, we focus on two types of weights $w(x)=|x_1|^a$ or $w(x)=|x|^b$ where $a, b>0$ in a suitable range. The coefficients under consideration admit either a singularity at the origin or a line of singularities. In the latter case, the problem is related to the fractional Laplacian., Comment: 24pages. arXiv admin note: substantial text overlap with arXiv:1711.11187 by other authors

Operator size growth describes the scrambling of operators in quantum dynamics and stands out as an essential physical concept for characterizing quantum chaos. Important as it is, a scheme for direct measuring operator size on a quantum computer is still absent. Here, we propose a quantum algorithm for direct measuring the operator size and its distribution based on Bell measurement. The algorithm is verified with spin chains and meanwhile, the effects of Trotterization error and quantum noise are analyzed. It is revealed that saturation of operator size growth can be due to quantum chaos itself or be a consequence of quantum noises, which make a distinction between quantum integrable and chaotic systems difficulty on noisy quantum processors. Nevertheless, it is found that the error mitigation will effectively reduce the influence of noise, so as to restore the distinguishability of quantum chaotic systems. Our work provides a feasible protocol for investigating quantum chaos on noisy quantum computers by measuring operator size growth., Comment: 7 pages, 4 figures

We study a cluster Ising model with non-Hermitian external field which can be exactly solved in the language of free fermions. By investigating the second derivative of energy density and fidelity, the possible new critical points are tentatively located. String order parameter and staggered magnetization are then detected to reveal emergent phases of brand new characteristics. To categorize the exotic phases and phase transitions induced by non-Hermiticity, we calculate the variation mode of spin correlation function as well as string parameter, which characterize the emergent phases and critical points with different patterns of decay and critical exponents. With the help of string order parameter and staggered magnetization, we find that there are four phases after introducing the non-Hermiticity -- the cluster phase, the gapless phase, the paramagnetic (PM) phase and the antiferromagnetic (AF) phase. A phase diagram is then presented to graphically illustrate, based on two "KT-like" phase transitions and an Ising phase transition, respectively, the generation of three critical lines as non-Hermitian strength increases. Our theoretical work is expected to be realized in the experiment of ultra-cold atoms, pushing for progress in exploring novel phases and phase transitions., Comment: published version

In the intention of minimizing excessive X-ray radiation administration to patients, low-dose computed tomography (LDCT) has become a distinct trend in radiology. However, while lowering the radiation dose reduces the risk to the patient, it also increases noise and artifacts, compromising image quality and clinical diagnosis. In most supervised learning methods, paired CT images are required, but such images are unlikely to be available in the clinic. We present a self-supervised learning model (Noise2Projection) that fully exploits the raw projection images to reduce noise and improve the quality of reconstructed LDCT images. Unlike existing self-supervised algorithms, the proposed method only requires noisy CT projection images and reduces noise by exploiting the correlation between nearby projection images. We trained and tested the model using clinical data and the quantitative and qualitative results suggest that our model can effectively reduce LDCT image noise while also drastically removing artifacts in LDCT images.

We study the regularity of the viscosity solution to the fully nonlinear parabolic thin obstacle problem. In particular, we prove that the solution is local $H^{1+\alpha}$ on each side of the smooth obstacle, for some small $\alpha>0.$ Following the method which was first introduced for the harmonic case by Caffarelli in 1979, we extend the results of Fern\'{a}ndez-Real (2016) who treated the fully nonlinear elliptic case. Our results also extend those of Chatzigeorgiou (2019) in two ways. First, we do not assume solutions nor operators to be symmetric. Second, our estimates are local, in the sense that do not rely on the boundary data., Comment: arXiv admin note: substantial text overlap with arXiv:1603.04185 by other authors