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For models of noninteracting fermions moving within sites arranged on a surface in three-dimensional space, there can be obstructions to finding localized Wannier functions. We show that such obstructions are K K -theoretic obstructions to approximating almost commuting, complex-valued matrices...
The relation between thermostats of “isoenergetic” and “frictionless” kind is studied and their equivalence in the thermodynamic limit is proven in space dimension d = 1,2 d = 1 , 2 and for special geometries, d = 3 d = 3 .
We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of...
In this article, we consider a class of ground states with spectral gap for quantum spin chains on an integer lattice and we prove that the factorization lemma of Hastings “Topology and phases in fermionic systems,” J. Stat. Mech.: Theory Exp. 2008 , L01001 implies split property (weak...
This paper is an overview of the concept of complementarity, the relation to state estimation, to Connes–Størmer conditional (or relative) entropy, and to uncertainty relation. Complementary Abelian and noncommutative subalgebras are analyzed. All the known results about complementary...
We formulate and prove a general central limit theorem for sums of independent identically distributed noncommutative random variables.
We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.
Recently, a rigorous foundation of several aspects of the theory of universality for statistical mechanics models with continuously varying exponents (among which are interacting planar Ising models, quantum spin chains, and one-dimensional Fermi systems) has been reached; it has its root in the...
We review recent rigorous results concerning the ionization of model quantum systems by time-periodic external fields. The systems we consider consist of a single particle (electron) with a reference Hamiltonian H 0 = −Δ+ V 0 ( x ) H 0 = − Δ + V 0 ( x ) ( x ∊ d ) ( x ∊ R d ) having both...
We consider Clifford quantum cellular automata (CQCAs) and their time-evolution. CQCAs are an especially simple type of quantum cellular automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum computation. In this work we study the time evolution of...
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