相关论文: Hardy and Lieb-Thirring inequalities for anyons
The topology of two-dimensional movement allows for existing of anyons -- particles obeying statistics intermediate between that of bosons and fermions. In this article, the functional form of the occupation numbers of free anyons is…
We obtain sharp Hardy inequalities on antisymmetric functions where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the previously published paper \cite{HL}, where Hardy's inequalities were…
In this article we prove both norm and modular Hardy inequalities for a class functions in one-dimensional fractional Orlicz-Sobolev spaces.
Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a…
Traditional statistical mechanics is constrained by the binary paradigms of identical/distinguishable and bosonic/fermionic particle statistics, leading to a fundamental logical gap in describing systems with partial distinguishability. We…
In the present paper we shall establish n-dimensional Hardy's inequalities with non-doubling weight functions of the distance to the boundary, where the boundary is a $C^2$ class bounded domain of $R^N$. This work is essentially based on…
The behavior of a collection of identical particles is intimately linked to the symmetries of their wavefunction under particle exchange. Topological anyons, arising as quasiparticles in low-dimensional systems, interpolate between bosons…
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 calculate the anomalous magnetic moment of anyons in three dimensional $CP^{N-1}$ model with a Chern-Simons term in various limits in $1/N$ expansion. We have found that for anyons of infinite mass the gyromagnetic ratio ($g$-factor) is…
This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to a classical model of a spinless relativistic particle as well as…
We develop a systematic theory of symmetry fractionalization for fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group $G_f$. In general $G_f$ is a central extension of the bosonic symmetry group $G_b$ by…
We formulate lattice perturbation theory for gauge theories in noncommutative geometry. We apply it to three-dimensional noncommutative QED and calculate the effective action induced by Dirac fermions. In particular "parity invariance" of a…
We study the problem of particle indistinguishability for the three cases known in nature: identical classical particles, identical bosons and identical fermions. By exploiting the fact that different types of particles are associated with…
Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor $\nu=1/m$ (where m…
We introduce topological magnetic field in two-dimensional flat space, which admits a solution of scalar monopole that describes the nontrivial topology. In the Chern-Simons gauge field theory of anyons, we interpret the anyons as the…
We consider weighted $L^p$-Hardy inequalities involving the distance to the boundary of a domain in the $n$-dimensional Euclidean space with nonempty boundary. Using criticality theory, we give an alternative proof of the following result…
We show that the low-energy dynamics of anyons in (1+1)-dimensions with the smallest number of derivatives and C, P and T symmetric interactions, are dual to the sine-Gordon model for bosonic fields. We discuss in particular the…
Fractional statistics give rise to quantum behaviors that differ fundamentally from those of bosons and fermions. While two-dimensional anyons play a major role in strongly correlated systems and topological quantum computing, the nature of…
We consider the Lieb-Thirring inequalities on the d-dimensional torus with arbitrary periods. In the space of functions with zero average with respect to the shortest coordinate we prove the Lieb-Thirring inequalities for the…
The existence of anyons, \textit{i.e.} quantum states with an arbitrary spin, is a generic feature of standard quantum mechanics in $(2+1)-$dimensional Minkowski spacetime. Here it is shown that relativistic anyons may exist also in quantum…