Related papers: Cyclic Statistics In Three Dimensions
We introduce the concept of cyclicity and hypercyclicity in self-similar groups as an analogue of cyclic and hypercyclic vectors for an operator on a Banach space. We derive a sufficient condition for cyclicity of non-finitary automorphisms…
Quantum fluctuations generate in three-dimensional gauge theories not only radiative corrections to the Chern-Simons coupling but also non-analytic terms in the effective action. We review the role of those terms in gauge theories with…
We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in $[0,\frac{1}{3}]$, answering a question of Cameron, and that the number of those…
The Hermiticity axiom of quantum mechanics guarantees that the energy spectrum is real and the time evolution is unitary (probability-preserving). Nevertheless, non-Hermitian but $\mathcal{PT}$-symmetric Hamiltonians may also have real…
In this paper we study different restrictions imposed over the set of permutations of size $n$, $S_n$, and for specific classes of restrictions study the cycle structure of corresponding permutations. More specifically, we prove that for…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
Certain models with rank-$3$ tensor degrees of freedom have been shown by Gurau and collaborators to possess a novel large $N$ limit, where $g^2 N^3$ is held fixed. In this limit the perturbative expansion in the quartic coupling constant,…
The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory. Their integrability is not…
This paper defines, on the Galilean space-time, the group of asymptotically Euclidean transformations (AET), which are equivalent to Euclidean transformations at space-time infinity, and proposes a formulation of nonrelativistic quantum…
There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states $\mathbf{P}$ -- i.e., the set of one-dimensional projections on a complex Hilbert space $H$ -- and the…
I present in detail the case for regarding black hole thermodynamics as having a statistical-mechanical explanation in exact parallel with the statistical-mechanical explanation believed to underly the thermodynamics of other systems. (Here…
If we treat the symmetric group $S_n$ as a probability measure space where each element has measure $1/n!$, then the number of cycles in a permutation becomes a random variable. The Cycle Length Lemma describes the expected values of…
A necessary and sufficient condition for Pauli's spin-statistics relation is given for nonrelativistic anyons, bosons, and fermions in two and three spatial dimensions. For any point particle species in two spatial dimensions, denote by J…
We develop a first-principle approach to compute the counting statistics in the ground-state of $N$ noninteracting spinless fermions in a general potential in arbitrary dimensions $d$ (central for $d>1$). In a confining potential, the Fermi…
Rydberg-atom quantum simulators are of keen interest because of their possibilities towards high-dimensional qubit architectures. Here we report three-dimensional conformation spectra of quantum-Ising Hamiltonian systems with programmed…
In this work we explore the structure of the branching graph of the unitary group using Schur transitions. We find that these transitions suggest a new combinatorial expression for counting paths in the branching graph. This formula, which…
The concept of space group has long served as the fundamental framework to describe the physical properties of crystalline materials, from electronic bands to photonic dispersions. The recent progress of spatiotemporal control, such as…
The three dimensional Chern-Simons theory on $\rr^2_{\theta}\times \rr$ is studied. Considering the gauge transformations under the group elements which are going to one at infinity, we show that under arbitrary (finite) gauge…
Algebraic cycles on complex projective space P(V) are known to have beautiful and surprising properties. Therefore, when V carries a real or quaternionic structure, it is natural to ask for the properties of the groups of real or…
An overview of the mathematical structure of the three-dimensional (3D) Ising model is given, from the viewpoints of topologic, algebraic and geometric aspects. By analyzing the relations among transfer matrices of the 3D Ising model,…