Related papers: Quantum semigroups: A survey
Development of conceptual multiple-choice tests related to a particular physics topic is important for designing research-based learning tools to reduce the difficulties. We explore the difficulties that the advanced undergraduate and…
Computer simulations allow us to explore non-perturbative phenomena in physics. This has the potential to help us understand quantum gravity. Finding a theory of quantum gravity is a hard problem, but in the last decades many promising and…
A version of quantum orbit method is presented for real forms of equal rank of quantum complex simple groups. A quantum moment map is constructed, based on the canonical isomorphism between a quantum Heisenberg algebra and an algebra of…
We examine the question of quasidiagonality for C*-algebras of discrete amenable groups from a variety of angles. We give a quantitative version of Rosenberg's theorem via paradoxical decompositions and a characterization of…
This article is the writing notes of a talk on Lie Antialgebras given by the second author at the conference "3Quantum: Algebra Geometry Information" that held in Tallinn in July 2012. The aim of this note is to give a brief survey of the…
We give a new sufficient condition on a spectral triple to ensure that the quantum group of orientation and volume preserving isometries defined in \cite{qorient} has a $C^*$-action on the underlying $C^*$ algebra.
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
Quantum computing is increasingly practiced through programming, yet most educational offerings emphasize algorithmic or framework-level use rather than software engineering concerns such as testing, abstraction, tooling, and lifecycle…
This is some lecture notes I wrote for the masterclass \emph{Rigidity of $C^*$-algebras associated to dynamics} held at the University of Copenhagen October 16-20, 2017. The notes is attempt to give an introduction to how \'etale groupoids…
We study the Cuntz semigroup for non-simple $\text{C}^*$-algebras in this paper. In particular, we use the extended Elliott invariant to characterize the Cuntz comparison for $\text{C}^*$-algebras with the projection property which have…
These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.
These pedagogical notes are dedicated to a derivation of the Unruh effect. There is special emphasis on the transparency of the arguments and the exhibition of detailed calculations. We assume the reader has a basic knowledge of quantum…
We introduce and study several amenability properties for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability or co-amenability of such groups. As a background for this…
These notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C^*-algebras, equivariant K-homology and…
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum…
We have written down a set of notes on compact quantum groups from which all the different aspects can be learned in an easy way and such that a lot of insight can be obtained without too much effort. Compact quantum groups have been…
A survey was developed to probe student understanding of quantum mechanics at the beginning of graduate instruction. The survey was administered to 202 physics graduate students enrolled in first-year quantum mechanics courses from seven…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
As per organizers' request, my talk at the 11th Marcel Grossmann Conference consisted of two parts. In the first, I illustrated recent advances in loop quantum gravity through examples. In the second, I presented an overall assessment of…