Related papers: Topological antiqued mechanical toy
A formalism is presented to construct a non-perturbative Grand Unified Theory when gravitational Planck-scale phenomena are included. The fundamental object on the Planck scale is the three-torus T^3 from which the known properties of…
The classical dynamics of collisionless cold dark matter, commonly described by fluid variables or a phase-space distribution, can be captured in a single semiclassical wavefunction. We illustrate how classical multi-streaming creates wave…
The realization of the Hofstadter model in a strongly anisotropic ladder geometry has now become possible in one-dimensional optical lattices with a synthetic dimension. In this work, we show how the Hofstadter Hamiltonian in such ladder…
A family of solitary waves is constructed in Frenkel-Kontorova model and its continuum and quasi-continuum approximations. Each solitary waves is characterised by the number of local maxima in its profile and a relation between external…
The Marolf-Maxfield topological toy model for 2D gravity gives the full spectrum of boundary theories, but can not describe any evolution. In order to obtain the expected evolution from Hartle-Hawking state to one of the superselection…
Topological materials exhibit protected edge modes that have been proposed for applications in for example spintronics and quantum computation. While a number of such systems exist, it would be desirable to be able to test theoretical…
We study the dynamical response of a diatomic periodic chain of rotors coupled by springs, whose unit cell breaks spatial inversion symmetry. In the continuum description, we derive a nonlinear field theory which admits topological kinks…
The identification, description, and classification of topological features is an engine of discovery and innovation in several fields of physics. This research encompasses a broad variety of systems, from the integer and fractional Chern…
The toy model of a particle on a vertical rotating circle in the presence of uniform gravitational/ magnetic fields is explored in detail. After an analysis of the classical mechanics of the problem we then discuss the quantum mechanics…
While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…
We show that the simplest of existing molecules -- closed-shell diatomics not interacting with one another -- host topological charges when driven by periodic far-off-resonant laser pulses. A periodically kicked molecular rotor can be…
In theories where spacetime is a direct product of Minkowski space ($M^4$) and a d dimensional compact space ($K^d$), there can exist topological solitons that simultaneously wind around $R^3$ (or $R^2$ or $R^1$) in $M^4$ and the compact…
An array of spheres descending slowly through a viscous fluid always clumps [J.M. Crowley, J. Fluid Mech. {\bf 45}, 151 (1971)]. We show that anisotropic particle shape qualitatively transforms this iconic instability of collective…
Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is an…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
The purpose of this article is to study the relation between combinatorial equivalence and topological conjugacy, specifically how a certain type of combinatorial equivalence implies topological conjugacy. We introduce the concept of…
A thought experiment is formulated to unify quantum mechanics and general relativity in a topological manner. An analysis of the interactions in Nature is then presented. The universal ground state of the constructed theory derives from the…
Electronic flat bands have localized Wannier-like orbitals as zero modes. In the Lieb or the kagome models, the localized orbitals satisfy a topological condition that entails two non-contractible loop eigenstates along $x/y$-axis in real…
In this article, we investigate the kinetic/fluid coupling on a toy model. We obtain it rigorously from a hydrodynamical limit. The idea is that at the level of the full kinetic model, the coupling is obvious. We then investigate the…
Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects.…