相关论文: Three Short Distance Structures from Quantum Algeb…

We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…

Quantum algebras U_q(su_n) used as the algebras of flavour symmetry (usually described by SU(n)) to study static properties of hadrons lead to intriguing results. In this contribution we focus on the peculiar properties manifested by…

This paper addresses the three following questions. (i) How the structures of group and of chain of groups enter nuclear, atomic and molecular spectroscopy? (ii) How these structures can be exploited, in a quantum- mechanical framework, in…

The purpose of the present paper is the communication of some results and observations which shed new light on the algebraic structure of the algebra of string observables both in the classical and in the quantum theory.

We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew…

In this paper, we mainly use classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct two new classes of quantum MDS codes. Most of our quantum MDS codes have minimum distance larger than q/2+1. Compared with…

An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula…

It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…

We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.

In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…

We re-examine the appearance of semiheaps and (para-associative) ternary algebras in quantum mechanics. In particular, we review the construction of a semiheap on a Hilbert space and the set of bounded operators on a Hilbert space. The new…

I give a brief non-technical review of "Quantum Gravity Phenomenology" and in particular I describe some studies which should soon allow to establish valuable data-based constraints on the short-distance structure of spacetime.

We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.

Quasi-one-dimensional quantum structures with spectra scaling faster than the square of the eigenmode number (superscaling) can generate intrinsic, off-resonant optical nonlinearities near the fundamental physical limits, independent of the…

\textit{Minimum distance diagrams}, also known as \textit{\textsf{L}--shapes}, have been used to study some properties related to \textit{weighted Cayley digraphs} of \textit{degree} two and \textit{embedding dimension three numerical…

The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…

Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical…

I give an overview of recent developments in the structure and classification theory of separable, simple, nuclear C*-algebras. I will in particular focus on the role of quasidiagonality and amenability for classification, and on the…