Deformations of compact quantum groups via Rieffel's quantization

It is shown that compact quantum groups containing torus subgroups can be deformed into new compact quantum groups under Rieffel's quantization. This is applied to showing that the two classes of compact quantum groupsK _q ^u andK _q studied by Levendorkii and Soibelman are strict deformation quantization of each other, and that the quantum groupsA _u (m) have many deformations.     

Regularization in quantum field theory from the causal point of view

The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973 [12]. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glaser solved this problem for a special class of distributions, the time-ordered products, that fulfill a causality condition, which itself is a basic requirement in axiomatic quantum field theory. In their original work, Epstein and Glaser studied only theories involving scalar particles. In this review, the extension of the method to theories with higher spin, including gravity, is presented. Furthermore, specific examples are presented in order to highlight the technical differences between the causal method and other regularization methods, like, e.g. dimensional regularization.     

量子点接触中有关电导0.7结构的研究

研究了由鞍形势描述的量子点接触中的电子输运性质,利用Hartree-Fock近似与低维纳米器件中Thomas-Fermi近似方法处理了电子-电子之间的相互作用,采用格点格林函数方法计算了零温下体系的电导、电子的自旋积累以及散粒噪声,重现了0.7结构这个反常的实验现象.计算结果加深了我们关于半导体纳米器件中的强关联互作用对自旋输运影响的理解.     

Revision of probability theory from the point of view of quantum statistics

Distributions for time series corresponding to problems related to Kolmogorov complexity are obtained. The notions of negative dimension and of quantization of spaces of positive and negative dimension are introduced. Applications of these notions to a broad spectrum of problems are considered, from linguistics to isotropic turbulence.     

Republication of: The beginning of the world from the point of view of quantum theory

This is a reprinting of a very short note by Georges Lemaitre, first published in Nature in 1931, in which he envisages the Universe evolving out of a single atom by quantum processes. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Jean-Pierre Luminet.     

Geometry from the spectral point of view

In this Letter, we develop geometry from a spectral point of view, the geometric data being encoded by a triple (A. H. D.) of an algebraA represented in a Hilbert spaceH with selfadjoint operatorD. This point of view is dictated by the general framework of noncommutative geometry and allows us to use geometric ideas in many situations beyond Riemannian geometry.

This paper is dedicated to the memory of J. Schwinger     

On a heuristic point of view related to quantum nonequilibrium statistical mechanics

In this paper I propose a new way for counting the microstates of a system out of equilibrium. As, according to quantum mechanics, things happen as if a given particle can be found in more than one state at once, I extend this concept to propose the coherent access by a particle to the available states of a system. By coherent access I mean the possibility for the particle to act as if it is populating more than one microstate at once. This hypothesis has experimental implications, since the thermodynamical probability and, as a consequence, the Bose-Einstein distribution as well as the argument of the Boltzmann factor is modified.     

The quantum state of the universe from deformation quantization and classical-quantum correlation

In this paper we study the quantum cosmology of homogeneous and isotropic cosmology, via the Weyl–Wigner–Groenewold–Moyal formalism of phase space quantization, with perfect fluid as a matter source. The corresponding quantum cosmology is described by the Moyal–Wheeler-DeWitt equation which has exact solutions in Moyal phase space, resulting in Wigner quasiprobability distribution functions peaking around the classical paths for large values of scale factor. We show that the Wigner functions of these models are peaked around the non-singular universes with quantum modified density parameter of radiation.     

Generalized Weyl quantization on the cylinder and the quantum phase

Generalized Weyl quantization formalism for the cylindrical phase space S¹×R¹$S^1\times {\mathbb{R}}^1$ is developed. It is shown that the quantum observables relevant to the phase of the linear harmonic oscillator or electromagnetic field can be represented within this formalism by the self-adjoint operators on the Hilbert space L²(S¹)$L^2\left(S^1\right)$.     

The logical quantization of algebraic groups

In a previous paper we introduced a highly abstract framework within which the theory of manuals initiated by Foulis and Randall is to be developed. The framework enabled us in a subsequent paper to quantize the notion of a set. Following these lines, this paper is devoted to quantizing algebraic groups viewed from Grothendieck's functorial standpoint.     

Remarks on quantum groups

We give a Poisson-bracket realization of SL _q (2) in the phase space ². We then discuss the physical meaning of such a realization in terms of a modified (regularized) toy model, the nonregularized version of which is due to Klauder.Some general remarks and suggestions are also presented in this Letter.     

Master-slave synchronization from the point of view of global dynamics

We present a mathematical framework for the theory of a synchronization phenomenon for dynamical systems discovered by Pecora and Carroll [Phys. Rev. Lett. 64, 821-824 (1990)]. From this perspective, we can synchronize, using a single coordinate, an open dense set of linear systems. We use our insights to synchronize nonlinear systems which were not previously recognized as being synchronizable. (c) 1995 American Institute of Physics.     

Holography: an interpretation from the phase-space point of view

The formation of holograms is interpreted as the consequence of the bilinearity of the ambiguity function. Reconstruction can then be regarded as the manipulation of the ambiguity function. Specifically, we show that in the case of in-line holography, the reconstruction can be regarded as phase tomography. In this way we provide a unified picture for the formulation of both noninterferometric and interferometric phase-retrieval techniques.     

Thin film substrates from the Raman spectroscopy point of view

We have investigated ten standard single crystal substrates of complex oxides on the account of their applicability in the Raman spectroscopy‐based thin film research. In this study, we suggest a spectra normalization procedure that utilizes a comparison of the substrate's Raman spectra to those of well‐established Raman reference materials. We demonstrate that MgO, LaGaO₃, (LaAlO₃)_0.3(Sr₂AlTaO₆)_0.7 (LSAT), DyScO₃, YAlO₃, and LaAlO₃ can be of potential use for Raman‐based thin film research. At the same time TiO₂ (rutile), NdGaO₃, SrLaAlO₄, and SrTiO₃ single crystals exhibit multiple phonon modes accompanied by strong Raman background that substantially hinder Raman‐based thin film experiments. Copyright © 2014 John Wiley & Sons, Ltd.