Related papers: Topological quantum mechanics and the first Chern …
The study of topological property of band insulators is an interesting branch of condensed matter physics. Two types of topologically nontrivial insulators have been extensively studied. The first type is characterized by a nonzero TKNN…
A particular approach to topology change in quantum gravity is reviewed, showing that several aspects of Stephen's work are intertwined with it in an essential way. Speculations are made on possible implications for the causal set approach…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in…
We develop the properties of the $n$-th sequential topological complexity $TC_n$, a homotopy invariant introduced by the third author as an extension of Farber's topological model for studying the complexity of motion planning algorithms in…
In the light of $\phi $--mapping method and topological current theory, the topological structure and the topological quantization of arbitrary dimensional topological defects are investigated. It is pointed out that the topological quantum…
We study the behaviour of a nonrelativistic quantum particle interacting with different potentials in the spacetimes of topological defects. We find the energy spectra and show how they differ from their free-space values.
Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom. In topological theories such non-local correlations can be given a very intuitive…
A new method is proposed to predict the topological properties of one-dimensional periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is constructed, exhibiting poles and…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an…
The motion of a quantum particle constrained to a two-dimensional non-compact Riemannian manifold with non-trivial metric can be described by a flat-space Schroedinger-type equation at the cost of introducing local mass and metric and…
Quantum effects play an important role in quantum measurement theory. The set of all quantum effects can be organized into an algebraical structure called effect algebra. In this paper, we study various topologies on the Hilbert space…
Discoveries of topological states and topological materials reshape our understanding of physics and materials over the last 15 years. First-principles calculations have been playing a significant role in bridging the theory of topology and…
Topology sheds new light on the emergence of unidirectional edge waves in a variety of physical systems, from condensed matter to artificial lattices. Waves observed in geophysical flows are also robust to perturbations, which suggests a…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may…
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system with a complex projective Hilbert space as its phase space, thus equipped with a Riemannian metric in addition to a symplectic structure.…