Related papers: Microscopic definitions of anyon data
The anyon exciton model is generalized to the case of a neutral exciton consisting of a valence hole and an arbitrary number N of fractionally-charged quasielectrons (anyons). A complete set of exciton basis functions is obtained and these…
A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of…
In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for $so(2p+1)_2$. These categories describe non-abelian anyons dubbed `metaplectic anyons'. We…
Lagrangian and Hamiltonian formulations of a free spinning particle in 2+1-dimensions or {\it anyon} are established, following closely the analysis of Hanson and Regge. Two viable (and inequivalent) Lagrangians are derived. It is also…
Symbolic regression (SR) aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, is a powerful paradigm for scientific discovery. Recent advances have expanded SR to describe related phenomena using a…
In this paper we propose and lay the foundations of a functorial framework for representing signals. By incorporating additional category-theoretic relative and generative perspective alongside the classic set-theoretic measure theory the…
The early time expansion of the space-time, namely inflation, is introduced to solve some cosmological problems. $F(R)$ gravity is a simple extension of the general relativity to induce the inflationary expansion. The precise observation of…
Flame graphs are a popular way of representing profiling data. In this paper we propose a possible mathematical definition of flame graphs. In doing so, we gain some interesting algebraic properties almost for free, which in turn allow us…
The R\'enyi entropy is a mathematical generalization of the concept of entropy and it encodes the total information of a system as a funtion of its order parameter $\alpha$. The meaning of the R\'enyi entropy in physics is not completely…
We propose a simple model for a free relativistic particle of fractional spin in 2+1 dimensions which satisfies all the necessary conditions. The canonical quantization of the system leads to the description of one- particle states of the…
We establish sensitivity analysis on the sphere. We present formulas that allow us to decompose a function $f\colon \mathbb S^d\rightarrow \mathbb R$ into a sum of terms $f_{\boldsymbol u,\boldsymbol \xi}$. The index $\boldsymbol u$ is a…
Identifying experimental signatures of anyons, which exhibit fractional exchange statistics, remains a central challenge in the study of two-dimensional topologically ordered systems. Previous theoretical work has shown that the threshold…
Studies of free particles in low-dimensional quantum systems such as two-leg ladders provide insight into the influence of statistics on collective behaviour. The behaviours of bosons and fermions are well understood, but two-dimensional…
This paper gives an introduction to the theory of orthogonal projection of functions or signals. Several kinds of decomposition are explored: Fourier, Fourier-Legendre, Fourier-Bessel series for 1D signals, and Spherical Harmonic series for…
Diagrammatic, analogical or iconic representations are often contrasted with linguistic or logical representations, in which the shape of the symbols is arbitrary. The aim of this paper is to make a case for the usefulness of diagrams in…
We introduce a simple initial working system in which relations (such as part-whole) are directly represented via an architecture with operating and learning rules fundamentally distinct from standard artificial neural network methods.…
The statistical distribution function of anyon is used to find the eighth viral coefficient in the high-temperature limit and the equation of state in the low-temperature limit. The perturbative results indicate that the thermodynamic…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
We study relativistic anyon field theory in 1+1 dimensions. While (2+1)-dimensional anyon fields are equivalent to boson or fermion fields coupled with the Chern-Simons gauge fields, (1+1)-dimensional anyon fields are equivalent to boson or…
We show that the presence of anyons in the excitation spectrum of a two-dimensional system can be inferred from nonlinear spectroscopic quantities. In particular, we consider pump-probe spectroscopy, where a sample is irradiated by two…