Related papers: Hopf Term for a Two-Dimensional Electron Gas
In our Comment (G.E. Volovik and V.M. Yakovenko, Phys. Rev. Lett. 79 (1997) 3792) to the Letter by W. Apel and Yu.A. Bychkov (Phys. Rev. Lett. 78 (1997) 2188) we questioned the derivation of the Hopf term in the hydrodynamic action for the…
Hopf terms are topological theta terms that are associated with a host of interesting physics, including anyons, statistical transmutation, chiral edge states, and the spin quantum Hall effect. Here, we show that Hopf terms can appear in…
It is known that a two-dimensional spin system can acquire a topological Hopf term by coupling to massless Dirac fermions whose energy spectrum has a single cone. But it is challenging to realize the Hopf term in condensed matter physics…
In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…
The Hopf term in the $2 + 1$ dimensional O(3) nonlinear sigma model, which is known to be responsible for fractional spin and statistics, is re-examined from the viewpoint of quantization ambiguity. It is confirmed that the Hopf term can be…
We present a topological characterization of time-periodically driven two-band models in 2+1 dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional…
Properties of superfluid states of two-dimensional electron systems with critical antiferromagnetic fluctuations are investigated. These correlations are found to result in the emergence of rapidly varying in the momentum space terms in all…
We report an universal behaviour of hopping transport in strongly interacting mesoscopic two-dimensional electron systems (2DES). In a certain window of background disorder, the resistivity at low perpendicular magnetic fields follows the…
This paper pursues the study carried out by the authors in {\it Stability and Hopf bifurcation in the Watt governor system} \cite{smb}, focusing on the codimension one Hopf bifurcations in the centrifugal Watt governor differential system,…
Topological terms in the O(3) nonlinear sigma model in (1+1) and (2+1) dimensions are re-examined based on the description of the SU(2)-valued field $g$. We first show that the topological soliton term in (1+1) dimensions arises from the…
It is known that the topological Hopf term in two-dimensional (2D) spin systems can be derived by coupling to massless Dirac fermions. We establish a universal rule governing the generation of Hopf terms in 2D quantum spin systems coupled…
We introduce new three-dimensional topological phases of two-band models using the Pontryagin-Thom construction. In symmetry class A these are the infinitely many Hopf-Chern topological insulators, which are hybrids of layered Chern…
The equivariant Hopf bifurcation dynamics of a class of system of partial differential equations is carefully studied. The connections between the current dynamics and fundamental concepts in hyperbolic conservation laws are explained. The…
A ferrofluid droplet confined in a Hele-Shaw cell can be deformed into a stably spinning ``gear,'' using crossed magnetic fields. Previously, fully nonlinear simulation revealed that the spinning gear emerges as a stable traveling wave…
For systems of delay differential equations the Hopf bifurcation was investigated by several authors. The problem we consider here is that of the possibility of emergence of a codimension two bifurcation, namely the Bautin bifurcation, for…
We calculate the magnetoconductivity tensor of a 2D electron gas in a 1D periodic potential and quantising magnetic fields. We study the internal structure of the Shubnikov-de Haas peaks and analyse recent experimental results. The…
An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in…
We provide a very brief review of the description of colored invariants for the Hopf link in terms of characters, which need to be taken at a peculiar deformation of the topological locus, depending on one of the two representations…
There are two notions of exponent of finite-dimensional Hopf algebras introduced and studied in the literature. In this note, we discuss and compare their properties including invariance and finiteness in this note. Specifically, one notion…
Using geometric inversion with respect to the origin we extend the definition of box dimension to the case of unbounded subsets of Euclidean spaces. Alternative but equivalent definition is provided using stereographic projection on the…