Related papers: Topological Properties of Phase Singularities in W…
Singularities, i.e. places of discontinuities of parameters are extremely general objects appearing in electromagnetic waves and thus are the key to understanding fundamental wave processes. These structures commonly occur in purely…
Phase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects can lead to wavefront dislocations, as observed in a humongous number of classical wave experiments. Phase singularities of…
In this paper, knotted objects (RS vortices) in the theory of topological phase singularity in electromagnetic field have been investigated in details. By using the $\phi$-mapping topological current theory proposed by Prof. Duan, we…
Phase singularities are locations where light is twisted like a corkscrew, with positive or negative topological charge depending on the twisting direction. Among the multitude of singularities arising in random wave fields, some can be…
Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by Hopf index and Brouwer degree in topology. The coherence flux quantization…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
Topology is a fundamental aspect of quantum physics, and it has led to key breakthroughs and results in various fields of quantum materials. In condensed matters, this has culminated in the recent discovery of symmetry-protected topological…
We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…
Polarization singularities and topological polarization structures are generic features of inhomogeneous vector wave fields of any nature. However, their experimental studies mostly remain restricted to optical waves. Here we report…
Vortices, phase singularities, and topological defects of any kind often reflect information that is crucial for understanding physical systems in which such entities arise. With near-field experiments supported by numerical calculations,…
Topological phases of matter are generally characterized by topological properties of energy bands of a system. Their transitions under preserved symmetries occur through closing a gap of energy bands, leading to topologically protected…
We derive some more results on the nature of the singularities arising in the collapse of inhomogeneous dust spheres. (i) It is shown that there are future-pointing radial and non-radial time-like geodesics emerging from the singularity if…
We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not…
Within the framework of a one-dimensional model of interacting electrons, the ground state of an electron liquid is studied. Using the exact solution of the model, the ground state phase diagram and zero-energy Majorana edge functions in a…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…
Topological properties of photonic structures described by Hamiltonian matrices have been extensively studied in recent years. Photonic systems are often open systems, and their coupling with the environment is characterized by scattering…
We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. \textbf{106}, 240503 (2011) is detailed and extended to qudits of different dimensions.…
We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of…