Atomic Effect Algebras with the Riesz Decomposition Property

We discuss the relationships between effect algebras with the Riesz Decomposition Property and partially ordered groups with interpolation. We show that any σ-orthocomplete atomic effect algebra with the Riesz Decomposition Property is an MV-effect algebras, and we apply this result for pseudo-effect algebras and for states.     

Effect Algebras with the Riesz Decomposition Property and AF C*-Algebras

Relations between effect algebras with Riesz decomposition properties and AF C^*-algebras are studied. The well-known one-one correspondence between countable MV-algebras and unital AF C^*-algebras whose Murray-von Neumann order is a lattice is extended to any unital AF C^* algebras and some more general effect algebras having the Riesz decomposition property. One-one correspondence between tracial states on AF C^*-algebras and states on the corresponding effect algebras is proved. In particular, pure (faithful) tracial states correspond to extremal (faithful) states on corresponding effect algebras.     

Probability Weights and Measures on Finite Effect Algebras

We study probability weights and measures onfinite effect algebras, thus generalizing the existingtheory for orthomodular posets and orthoalgebras. Ourdevelopment proceeds somewhat more generally in that we study weights and measures associatedwith an antichain in the positive cone of a euclideanvector space with the standard partialordering.     

Super Quantum Measures on Finite Spaces

In this paper, the properties of the super quantum measures are studied. Firstly, the products of Dirac measures are discussed; Secondly, based on the properties of Dirac measures, the structures of super quantum measures are characterized; At last, we prove that any super quantum measure can determine a unique diagonally positive strongly symmetric signed measure. This result verifies the conjecture which was proposed by Gudder.     

Quantum Enveloping Algebras with von Neumann Regular Cartan-like Generators and the Pierce Decomposition

Quantum bialgebras derivable from U _q (sl ₂) which contain idempotents and von Neumann regular Cartan-like generators are introduced and investigated. Various types of antipodes (invertible and von Neumann regular) on these bialgebras are constructed, which leads to a Hopf algebra structure and a von Neumann-Hopf algebra structure, respectively. For them, explicit forms of some particular R-matrices (also, invertible and von Neumann regular) are presented, and the latter respects the Pierce decomposition. Dedicated to the memory of our colleague Leonid L. Vaksman (1951–2007) On leave of absence from: TheoryGroup, Nuclear Physics Laboratory,V.N.Karazin Kharkov National University, Svoboda Sq. 4, Kharkov 61077, Ukraine. E-mail: sduplij@gmail.com;     

Decomposition Properties of Quantum Discord

The quantum discord was introduced by Ollivier,Zurek,Henderson,and Vedral as an indicator of the degree of quantumness of mixed states.In this paper,we provide a decomposition condition for quantum discord.Moreover,we show that under the condition,the quantum correlations between the quantum systems can be captured completely by the entanglement measure.Finally,we present examples of our conclusions.     

Quantum Observables and Effect Algebras

We study observables on monotone σ-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. We characterize sharp observables of a monotone σ-complete homogeneous effect algebra using its orthoalgebraic skeleton. In addition, we study compatibility in orthoalgebras and we show that every orthoalgebra satisfying RIP is an orthomodular poset.     

Specification of Finite Effect Algebras

We study and relate five basic methods for specifying or describing a finite effectalgebra, indicate some computational algorithms for dealing with effect algebrasso specified, and mention in passing some open questions that await solution.     

Quantum Chains of Hopf Algebras with Quantum Double Cosymmetry

Given a finite dimensional C ^*-Hopf algebra H and its dual Ĥ we construct the infinite crossed product and study its superselection sectors in the framework of algebraic quantum field theory. is the observable algebra of a generalized quantum spin chain with H-order and Ĥ-disorder symmetries, where by a duality transformation the role of order and disorder may also appear interchanged. If is a group algebra then becomes an ordinary G-spin model. We classify all DHR-sectors of – relative to some Haag dual vacuum representation – and prove that their symmetry is described by the Drinfeld double . To achieve this we construct localized coactions and use a certain compressibility property to prove that they are universal amplimorphisms on . In this way the double can be recovered from the observable algebra as a universal cosymmetry. Received: 4 September 1995\,/\,Accepted: 3 December 1996     

Quantum and Classical Implication Algebras with Primitive Implications

Join in an orthomodular lattice is obtained inthe same form for all five quantum implications. Theform holds for the classical implication in adistributive lattice as well. Even more, the definition added to an ortholattice makes it orthomodularfor quantum implications and distributive for theclassical one. Based on this result a quantumimplication algebra with a single primitive — andin this sense unique — implication is formulated. Acorresponding classical implication algebra is alsoformulated. The algebras are shown to be special casesof a universal implication algebra.     

Monotonicity Properties of Certain Measures over the Two-Level Quantum Systems

We demonstrate – using the case of the two-dimensional quantum systems – that the 'natural measure in the space of density matrices describing N-dimensional quantum systems' proposed by yczkowski et al. [Phys. Rev. A 58 (1998), 883] does not belong to the class of normalized volume elements of monotone metrics on the quantum systems. Such metrics possess the statistically important property of being decreasing under stochastic mappings (coarse-grainings). We do note that the proposed natural measure (and certain evident variations upon it) exhibit quite specific monotonicity characteristics, but not of the form required for membership in that distinguished class.     

Quantum Image Encryption Based on Quantum Image Decomposition

Aiming at the slow processing speed of classic image encryption algorithms and the security analysis of existing quantum image encryption algorithms, this paper combines the representation method of quantum images and proposes a quantum image encryption algorithm based on image correlation decomposition. Using the principle of quantum state superposition and measurement, the association between image pixels is established, the image is decomposed into a series of feature sub-images and stored in a complete binary tree set, and different sub-images are operated and encrypted by random phase operation and quantum rotation operation. Then superimpose all the sub-images to obtain the ciphertext image. The algorithm has a larger key space so that it can resist brute force attacks. At the same time, the quantum encryption algorithm has lower computational complexity than classic encryption algorithms. In addition, because the ciphertext image is transmitted in the communication channel in the form of a quantum state, the security of quantum image encryption also surpasses the security of classical image encryption.

     

Quantum Double Actions on Operator Algebras and Orbifold Quantum Field Theories

Starting from a local quantum field theory with an unbroken compact symmetry group G in 1+1-dimensional spacetime we construct disorder fields implementing gauge transformations on the fields (order variables) localized in a wedge region. Enlarging the local algebras by these disorder fields we obtain a nonlocal field theory, the fixpoint algebras of which under the appropriately extended action of the group G are shown to satisfy Haag duality in every simple sector. The specifically 1+1 dimensional phenomenon of violation of Haag duality of fixpoint nets is thereby clarified. In the case of a finite group G the extended theory is acted upon in a completely canonical way by the quantum double D(G) and satisfies R-matrix commutation relations as well as a Verlinde algebra. Furthermore, our methods are suitable for a concise and transparent approach to bosonization. The main technical ingredient is a strengthened version of the split property which is expected to hold in all reasonable massive theories. In the appendices (part of) the results are extended to arbitrary locally compact groups and our methods are adapted to chiral theories on the circle. Received: 4 September 1996 / Accepted: 6 May 1997     

量子限制斯达克效应对三角形量子阱吸光特性的影响

本文通过计算量子力学波动方程以及载流子传输特性,哈密顿量的H能谱图和边界条件等的理论方法来分析量子限制斯达克效应对三角形量子阱体系吸收特性的影响,说明了选择合适的量子阱垒层对于提高三角形量子阱吸光率具有重要的意义。     

Effect of Doping on the Luminescent Properties of LED Heterostructures with Quantum Wells

Russian Physics Journal - It is established that the model of interband radiative recombination in a semiconductor under bipolar injection of charge carriers, in which the recombination rate is...     

Ultraviolet Finite Quantum Field Theory on Quantum Spacetime

 We discuss a formulation of quantum field theory on quantum space time where the perturbation expansion of the S-matrix is term by term ultraviolet finite. The characteristic feature of our approach is a quantum version of the Wick product at coinciding points: the differences of coordinates q _j −q _k are not set equal to zero, which would violate the commutation relation between their components. We show that the optimal degree of approximate coincidence can be defined by the evaluation of a conditional expectation which replaces each function of q _j −q _k by its expectation value in optimally localized states, while leaving the mean coordinates invariant. The resulting procedure is to a large extent unique, and is invariant under translations and rotations, but violates Lorentz invariance. Indeed, optimal localization refers to a specific Lorentz frame, where the electric and magnetic parts of the commutator of the coordinates have to coincide [11]. Employing an adiabatic switching, we show that the S-matrix is term by term finite. The matrix elements of the transfer matrix are determined, at each order in the perturbative expansion, by kernels with Gaussian decay in the Planck scale. The adiabatic limit and the large scale limit of this theory will be studied elsewhere. Received: 15 January 2003 / Accepted: 20 March 2003 Published online: 5 May 2003 RID="*" ID="*" Research supported by MIUR and GNAMPA-INDAM RID="*" ID="*" Research supported by MIUR and GNAMPA-INDAM Communicated by H. Araki and D. Buchholz     

Clifford Algebras and the Dirac-Bohm Quantum Hamilton-Jacobi Equation

In this paper we show how the dynamics of the Schr?dinger, Pauli and Dirac particles can be described in a hierarchy of Clifford algebras, C_1,3, C_3,0{\mathcal{C}}_{1,3}, {\mathcal{C}}_{3,0}, and C_0,1{\mathcal{C}}_{0,1}. Information normally carried by the wave function is encoded in elements of a minimal left ideal, so that all the physical information appears within the algebra itself. The state of the quantum process can be completely characterised by algebraic invariants of the first and second kind. The latter enables us to show that the Bohm energy and momentum emerge from the energy-momentum tensor of standard quantum field theory. Our approach provides a new mathematical setting for quantum mechanics that enables us to obtain a complete relativistic version of the Bohm model for the Dirac particle, deriving expressions for the Bohm energy-momentum, the quantum potential and the relativistic time evolution of its spin for the first time.