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We develop a stochastic description of the topological properties in an interacting Chern insulator. We confirm the Mott transition's first-order nature in the interacting Haldane model on the honeycomb geometry, from a mean-field…
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a…
Colored tensor models (CTM) is a random geometrical approach to quantum gravity. We scrutinize the structure of the connected correlation functions of general CTM-interactions and organize them by boundaries of Feynman graphs. For rank-$D$…
We propose an index of non-invertible symmetry operators in 1+1 dimensions and discuss its relation to the realizability of non-invertible symmetries on the tensor product of finite dimensional on-site Hilbert spaces on the lattice. Our…
This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping…
In the context of the coloured stochastic vertex model in a quadrant, we identify a family of observables whose averages are given by explicit contour integrals. The observables are certain linear combinations of $q$-moments of the coloured…
The space of inflationary models is vast, containing wide varieties of mechanisms, symmetries, and spectra of particles. Consequently, the space of observational signatures is similarly complex. Hence, it is natural to look for boundaries…
A study of the slow-roll inflation for an exponential potential in the frame of the scalar-tensor theory is performed, where non-minimal kinetic coupling to curvature and non-minimal coupling of the scalar field to the Gauss-Bonnet…
Bumblebee models, a class of vector-tensor theories in which a vector field acquires a nonzero vacuum expectation value that spontaneously breaks spacetime symmetries, are ubiquitous in the literature. By constructing the most general…
In this paper, we address the open problem (stated in Pennisi and Trovato, 1987. Int. J. Engng Sci., 25(8), 1059-1065) associated with the irreducibility of representations for isotropic functions. In particular, we prove that for isotropic…
We compute the four-loop beta functions of short and long-range multi scalar models with general sextic interactions and complex fields. We then specialize the beta functions to a $U(N)^3$ symmetry and study the renormalization group at…
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams…
Colloidal systems find important applications ranging from fabrication of photonic crystals to direct probing of phenomena typically encountered in atomic crystals and glasses. New applications - such as nanoantennas, plasmonic sensors, and…
We identify universal signatures in the bispectrum arising from a transient tachyonic instability of entropic fluctuations during inflation, a phenomenon that naturally arises in hyperbolic field-space geometries. We perform exact numerical…
A novel definition of holographic correlation functions on the celestial sphere of Minkowski space was recently introduced in arXiv:2301.01810 as the extrapolation of bulk time-ordered correlation functions to the celestial sphere. In this…
This thesis is centered on three main subjects within the theory of inflation and cosmological perturbations: loop corrections to the power spectrum of curvature fluctuations generated during inflation; evolution of cosmological…
The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…
This work identifies a solvable (in the sense that spectral correlation functions can be expressed in terms of orthogonal polynomials), rotationally invariant random matrix ensemble with a logarithmic weakly confining potential. The…
We introduce a set of generic conditions for the slow contracting Universe and for a narrowed-down category of models called fast-roll models. We present general conditions for super horizon freeze-out of scalar and tensor perturbations and…
We study cosmological tensor perturbations induced by second-order scalar perturbations in the presence of anisotropic non-Gaussianity. This class of induced tensor modes arises on superhorizon scales through the intrinsic quadrupole…