Related papers: Particle on a Torus Knot: Anholonomy and Hannay An…
The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked the Chern number, a topological invariant characterizing the quantum Hall effect in…
Topological magnetic textures confined to two-dimensional (2D) non-orientable manifolds exhibit behaviors absent in planar systems. We investigate bimerons on M\"obius surfaces and show that the lack of global orientation alters…
The transport on top of a periodic two-dimensional hexagonal magnetic pattern of (i) a single macroscopic steel sphere, (ii) a doublet of wax/magnetite composite spheres, and (iii) an immiscible mixture of ferrofluid droplets with a…
The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally…
The N=2 spinning particle action describes the propagation of antisymmetric tensor fields, including vector fields as a special case. In this paper we study the path integral quantization on a one-dimensional torus of the N=2 spinning…
Given a normed plane $\mathcal{P}$, we call $\mathcal{P}$-cycloids the planar curves which are homothetic to their double $\mathcal{P}$-evolutes. It turns out that the radius of curvature and the support function of a $\mathcal{P}$-cycloid…
The quantum conductance of one-dimensional (1D) circuits built on flat (Euclidean) two-dimensional electron gases (2DEGs) is known to display a symmetric response to the inversion of Rashba spin-orbit coupling fields in Aharonov-Casher (AC)…
This paper concerns connections between dynamical systems, knots and helicity of vector fields. For a divergence-free vector field on a closed $3$-manifold that generates an Anosov flow, we show that the helicity of the vector field may be…
In the Stokesian limit, the streamline topology around a single neutrally buoyant sphere is identical to the topology of pair-sphere pathlines, both in an ambient simple shear flow. In both cases there are fore-aft symmetric open and closed…
In [Orbit equivalences of pseudo-Anosov flows, arXiv:2211.10505], it was proved that transitive pseudo-Anosov flows on any closed 3-manifold are determined up to orbit equivalence by the set of free homotopy classes represented by periodic…
We numerically investigate the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius. Two limiting cases are considered in detail, namely,…
For certain pseudo-Anosov flows $\phi$ on closed $3$-manifolds, unpublished work of Agol--Gu\'eritaud produces a veering triangulation $\tau$ on the manifold $M$ obtained by deleting $\phi$'s singular orbits. We show that $\tau$ can be…
The Heisenberg uncertainty principle suggests that it is impossible to determine the trajectory of a quantum particle in the same way as a classical particle. However, we may still yield insight into novel behavior of photons based on the…
We consider S^1-families of Legendrian knots in the standard contact R^3. We define the monodromy of such a loop, which is an automorphism of the Chekanov-Eliashberg contact homology of the starting (and ending) point. We prove this…
Electron transport through multi-terminal rectangular arrays of quantum rings is studied in the presence of Rashba-type spin-orbit interaction (SOI) and of a perpendicular magnetic field. Using the analytic expressions for the transmission…
While winding a particle-like excitation around a loop-like excitation yields the celebrated Aharonov-Bohm phase, we find a distinctive braiding phase in the absence of such mutual winding. In this work, we propose an exotic…
In most topological insulators, the valence and conduction band appear in reverse or inverted order compared to an equivalent insulator with isolated atoms. Here, we explore a different route towards topologically nontrivial states that may…
We study the probability that a loop is null-homotopic -- that is, bounded by the continuous image of a disk -- in plaquette percolation on $\mathbb{Z}^3.$ Locally, the event that there is a ``horizontal disk crossing'' of a rectangular…
The study of the propagation of electrons with a varying spinor orientability is performed using the coordinate transformation method. Topological Insulators are characterized by an odd number of changes of the orientability in the…
Coronal loops in active regions are often characterized by quasi-circular and helically twisted (sigmoidal) geometries, which are consistent with dipolar potential field models in the former case, and with nonlinear force-free field models…