Related papers: Real-space representation of the second Chern numb…
We apply ideas of Dijkgraaf and Witten on three-dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define classical…
This is the first of a series of two papers devoted to the partition function realization of Wilson surfaces in strict higher gauge theory. A higher version of the Kirillov-Kostant-Souriau theory of coadjoint orbits is presented based on…
Topological order can be found in a wide range of physical systems, from crystalline solids, photonic meta-materials and even atmospheric waves to optomechanic, acoustic and atomic systems. Topological systems are a robust foundation for…
We introduce "state space persistence analysis" for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent…
We develop representation theoretic techniques to construct three dimensional non-semisimple topological quantum field theories which model homologically truncated topological B-twists of abelian Gaiotto-Witten theory with linear matter.…
We conduct computer-assisted analysis of the two-dimensional model of a neuron introduced by Chialvo in 1995 (Chaos, Solitons & Fractals 5, 461-479). We apply the method for rigorous analysis of global dynamics based on a set-oriented…
We revisit and clarify some aspects of perturbative renormalization in pure Chern-Simons theory by means of a localization principle associated with an underlying supersymmetry. This perspective allows the otherwise perturbative one-loop…
In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic…
In this paper the hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane is performed. We use the techniques of geometric quantization to show that the classical reduced phase space of the theory has nontrivial…
Subspace representation is a fundamental technique in various fields of machine learning. Analyzing a geometrical relationship among multiple subspaces is essential for understanding subspace series' temporal and/or spatial dynamics. This…
The use of the physical variables in the fashion of Dirac in the three-dimensional Chern-Simons theories is presented. Our previous results are reinterpreted in a new aspect.
We construct a one-dimensional (1D) topological SSH-like model with chiral symmetry and a superimposed hopping modulation, which we call the chiral Aubry-Andr\'e model. We show that its topological properties can be described in terms of a…
When aiming to apply mathematical results of non-commutative geometry to physical problems the question arises how they translate to a context in which only a part of the spectrum is known. In this article we aim to detect when a…
We discuss methods for calculating Chern numbers of two-dimensional lattice systems using spiral boundary conditions, which sweep all lattice sites in one-dimensional order. Specifically, we establish the one-dimensional representation of…
We present a finite dimensional matrix model associated to the noncommutative Chern-Simons theory, obtained by inserting a Wilson line. For a specific choice of the representation of the Wilson line the model is equivalent to the minimal…
We consider the representation of real numbers by alternating Perron series ($P^-$-representation), which is a generalization of representations of real numbers by Ostrogradsky-Sierpi\'nski-Pierce series (Pierce series), alternating…
We quantize a generalized electromagnetism in 2 + 1 dimensions which contains a higher-order derivative term by using Dirac's method. By introducing auxiliary fields we transform the original theory in a lower-order derivative one which can…
The Kitaev spin liquid, stabilized as the ground state of the Kitaev honeycomb model, is a paradigmatic example of a topological $\mathbb{Z}_2$ quantum spin liquid. The fate of the Kitaev spin liquid in presence of an external magnetic…
Models of discrete space and space-time that exhibit continuum-like behavior at large lengths could have profound implications for physics. They may tame the infinities that arise from quantizing gravity, and dispense with the machinery of…
A bilinear estimate in terms of Bourgain spaces associated with a linearised Kadomtsev-Petviashvili-type equation on the three-dimensional torus is shown. As a consequence, time localized linear and bilinear space time estimates for this…