Long-distance asymptotic behaviour of multi-point correlation functions in massless quantum models

We provide a microscopic model setting that allows us to readily access to the large-distance asymptotic behaviour of multi-point correlation functions in massless, one-dimensional, quantum models. The method of analysis we propose is based on the form factor expansion of the correlation functions and does not build on any field theory reasonings. It constitutes an extension of the restricted sum techniques leading to the large-distance asymptotic behaviour of two-point correlation functions obtained previously.Comment: 25 page

Teacher perspectives of challenges within the Norwegian Educational system

This research examines teacher perspectives’ of educational challenges in Norway. Norway is one of the most well-resourced, prosperous, social welfare states in the world, yet the OECD (2011) recognized students’ weak basic skills and insufficient teacher ability in content and pedagogy, along with engagement and imbalanced resources as points for educational improvement. An open-ended questionnaire was administered to 138 teachers practicing in Norway to explore challenges from their perspective. Teachers reported the following challenges: completing government paperwork with competing pedagogical demands, adapting teaching to each student due to large class sizes, motivating students, managing social and emotional problems of students, and meeting society’s increasingly unrealistic expectations. Teachers perceived their challenges to be a result of a poorly built educational system, not from deficits in their teaching skills. We concluded from this study that teacher voice and participation in improvement decisions are needed, given some discrepancy in perceived challenges among these findings, international surveys, and policy-related reports

On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain

We consider the problem of computing form factors of the massless XXZ Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit where the size M of the chain becomes large. For that purpose, we take the particular example of the matrix element of the third component of spin between the ground state and an excited state with one particle and one hole located at the opposite ends of the Fermi interval (umklapp-type term). We exhibit its power-law decrease in terms of the size of the chain M, and compute the corresponding exponent and amplitude. As a consequence, we show that this form factor is directly related to the amplitude of the leading oscillating term in the long-distance asymptotic expansion of the two-point correlation function of the third component of spin.Comment: 28 page

Domain wall partition functions and KP

We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an overall normalization).Comment: 16 pages, LaTeX2

Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions

We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin correlation function of the XXZ Heisenberg spin-1/2 chain (with magnetic field) in the disordered regime as well as to the density-density correlation func- tion of the interacting one-dimensional Bose gas. At leading order, the results confirm the Luttinger liquid and conformal field theory predictions.Comment: 78 page

Some families of density matrices for which separability is easily tested

We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree condition") to test separability of density matrices of graphs. The condition is directly related to the PPT-criterion. We prove that the degree condition is necessary for separability and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest point graphs and perfect matchings. We observe that the degree condition appears to have value beyond density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. The paper isolates a number of problems and delineates further generalizations.Comment: 14 pages, 4 figure

Riemann-Hilbert approach to a generalized sine kernel and applications

We investigate the asymptotic behavior of a generalized sine kernel acting on a finite size interval [-q,q]. We determine its asymptotic resolvent as well as the first terms in the asymptotic expansion of its Fredholm determinant. Further, we apply our results to build the resolvent of truncated Wiener--Hopf operators generated by holomorphic symbols. Finally, the leading asymptotics of the Fredholm determinant allows us to establish the asymptotic estimates of certain oscillatory multidimensional coupled integrals that appear in the study of correlation functions of quantum integrable models.Comment: 74 page

Crypto collectibles, museum funding and openGLAM: Challenges, opportunities and the potential of non-fungible tokens (NFTs)

Non-fungible tokens (NFTs) make it technically possible for digital assets to be owned and traded, introducing the concept of scarcity in the digital realm for the first time. Resulting from this technical development, this paper asks the question, do they provide an opportunity for fundraising for galleries, libraries, archives and museums (GLAM), by selling ownership of digital copies of their collections? Although NFTs in their current format were first invented in 2017 as a means for game players to trade virtual goods, they reached the mainstream in 2021, when the auction house Christie’s held their first-ever sale exclusively for an NFT of a digital image, that was eventually sold for a record 69 million USD. The potential of NFTs to generate significant revenue for artists and museums by selling effectively a cryptographically signed copy of a digital image (similar to real-world limited editions, which are signed and numbered copies of a given artwork), has sparked the interest of the financially deprived museum and heritage sector with world-renowned institutions such as the Uffizi Gallery and the Hermitage Museum, having already employed NFTs in order to raise funds. Concerns surrounding the environmental impact of blockchain technology and the rise of malicious projects, exploiting previously digitised heritage content made available through OpenGLAM licensing, have attracted criticism over the speculative use of the technology. In this paper, we present the current state of affairs in relation to NFTs and the cultural heritage sector, identifying challenges, whilst highlighting opportunities that they create for revenue generation, in order to help address the ever-increasing financial challenges of galleries and museums

Interactive Exploration and Flattening of Deformed Historical Documents

We present an interactive application for browsing severely damaged documents and other cultural artefacts. Such documents often contain strong geometric distortions such as wrinkling, buckling, and shrinking and cannot be flattened physically due to the high risk of causing further damage. Previous methods for virtual restoration involve globally flattening a 3D reconstruction of the document to produce a static image. We show how this global approach can fail in cases of severe geometric distortion, and instead propose an interactive viewer which allows a user to browse a document while dynamically flattening only the local region under inspection. Our application also records the provenance of the reconstruction by displaying the reconstruction side by side with the original image data

Classicality in discrete Wigner functions

Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that the only pure states having non-negative W for all such functions are stabilizer states, as conjectured by one of us [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of W for all definitions of W form a subgroup of the Clifford group. This means pure states with non-negative W and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.Comment: 10 pages, 1 figur