Related papers: Generalized TKNN-equations
We propose a generalization of the double affine Hecke algebra of type-C C1 at specific parameters by introducing a ``Heegaard dual'' of the Hecke operators. Shown is a relationship with the skein algebra on double torus. We give…
Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the equations as well as the invariant and…
We investigate the Hall conductance of a two-dimensional Chern insulator coupled to an environment causing gain and loss. Introducing a biorthogonal linear response theory, we show that sufficiently strong gain and loss lead to a…
Simplicial toric stack bundles are smooth Deligne-Mumford stacks over smooth varieties with fibre a toric Deligne-Mumford stack. We compute the Grothendieck $K$-theory of simplicial toric stack bundles and study the Chern character…
Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…
We consider the Hall conductivity of two-dimensional non-interacting Bloch electrons when the magnetic flux per unit cell is a rational number $p/q$ where $p$ and $q$ are mutually coprime. We present a counter-example for the naive…
We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D Conformal Field Theory (CFT). A consistency equation, which gives a classification of twists, is…
One describes, using a detailed analysis of Atiyah--Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This…
We derive a multi-band formulation of the orbital magnetization in a normal periodic insulator (i.e., one in which the Chern invariant, or in 2d the Chern number, vanishes). Following the approach used recently to develop the single-band…
In this paper, we generalize the Kirchhoff-Sobolev parametrix of Klainerman and Rodnianski to systems of tensor wave equations with additional first-order terms. We also present a different derivation, which better highlights that such…
We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF…
General expressions are given for the coefficients of Chern forms up to the 13th order in curvature in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for…
We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear…
We present Hamilton's equations for the teleparallel equivalent of general relativity (TEGR), which is a reformulation of general relativity based on a curvatureless, metric compatible, and torsionful connection. For this, we consider the…
We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a…
The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a…
Weak gravitational, electromagnetic, neutrino and scalar fields, considered as perturbations on Kerr background satisfy Teukolsky Master Equation. The two non-trivial equations obtained after separating the variables are the polar angle…
The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition…
A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The obtained general quantum-mechanical solution of the relativistic paraxial equation contains the commonly accepted result as a…
We present the general framework of \'Ecalle's moulds in the case of linearization of a formal vector field without and within resonances. We enlighten the power of moulds by their universality, and calculability. We modify then \'Ecalle's…