Related papers: Differential Calculus on Manifolds with a Boundary…
The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular…
We present boundary-integral equations for Maxwell-type problems in a differential-form setting. Maxwell-type problems are governed by the differential equation $(\delta\mathrm{d}-k^2)\omega = 0$, where $k\in\mathbb{C}$ holds, subject to…
We investigate the differential calculus defined by Ashtekar and Lewandowski on projective limits of manifolds by means of cylindrical smooth functions and compare it with the C^infty calculus proposed by Froehlicher and Kriegl in more…
In this survey article, we discuss some recent progress on geometric analysis on manifold with ends. In the final section, we construct manifolds with ends with oscillating volume functions which may turn out to have a different heat kernel…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold $M$. We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the…
We study the entanglement of a multipartite quantum state. An inequality between the bipartite concurrence and the multipartite concurrence is obtained. More effective lower and upper bounds of the multipartite concurrence are obtained. By…
We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115, 020403 (2015)]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent…
Quantum computing is a new emerging computer technology. Current quantum computing devices are at a development stage where they are gradually becoming suitable for small real-world applications. This lecture is devoted to the practical…
These are extended notes of the course given by the author at RIMS, Kyoto, in October 2016. The aim is to give a self-contained overview on the recently developed approach to differential calculus on metric measure spaces. The effort is…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
An algebraic quantization procedure for discretized spacetime models is suggested based on the duality between finitary substitutes and their incidence algebras. The provided limiting procedure that yields conventional manifold…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
We introduce boundary special generic maps, a class of submersions from manifolds with boundary to Euclidean spaces whose restriction to the boundary has only boundary definite fold points as its singular points. We derive the…
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer…
This paper deals with bounded solutions of quasilinear elliptic equations on Riemannian manifolds satisfying special condition.
Given a smooth manifold $M$ (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differential operators) and the G\r{a}rding inequality…
We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.