Related papers: A Computational Non-Commutative Geometry Program f…
Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…
We develop a statistically robust framework for reconstructing metal--semiconductor contact regions using topological gradients. The inverse problem is formulated as the identification of an unknown contact region from boundary measurements…
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…
We consider the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal (T) invariant insulators. In 2D we use a gauge corresponding to hybrid Wannier functions that are maximally localized in one…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
We present an approach for the calculation of the $\mathbb{Z}_2$ topological invariant in non-crystalline two-dimensional quantum spin Hall insulators. While topological invariants were originally mathematically introduced for crystalline…
This is a compilation of some well known propositions of Alain Connes concerning the use of noncommutative geometry in mathematical physics.
A hybrid spectral/finite-element code is developed to numerically solve the resistive finite-pressure magnetohydrodynamic equilibria without the necessity of postulating nested magnetic flux surfaces in the non-axisymmetric toroidal…
Topological semimetals are under intensive theoretical and experimental studies. The first step of these studies is always the theoretical (numerical) predication of one of several candidate materials, starting from first principles. In…
Our aim in this review article is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played…
In this paper, we use the language of noncommutative differential geometry to formalise discrete differential calculus. We begin with a brief review of inverse limit of posets as an approximation of topological spaces. We then show how to…
In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…
In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. A special inequality which…
Atomic diffusion affects the properties of various engineering materials, which predominantly occur in the polycrystalline state. A rigorous description of polycrystalline diffusion must therefore account for crystallographic defects,…
Recent studies of disorder or non-Hermiticity induced topological insulators inject new ingredients for engineering topological matter. Here we consider the effect of purely non-Hermitian disorders, a combination of these two ingredients,…