Quantum Double for Quasi-Hopf Algebras

We introduce a quantum double quasi-triangular quasi-Hopf algebra D(H) associated to any quasi-Hopf algebra H. The algebra structure is a cocycle double cross-product. We use categorical reconstruction methods. As an example, we recover the quasi-Hopf algebra of Dijkgraaf, Pasquier and Roche as the quantum double D(G) associated to a finite group G and group 3-cocycle .     

Generalization of Drinfeld Quantum Affine Algebras

Drinfeld gave a current realization of the quantum affine algebras as a Hopf algebra with a simple comultiplication for the quantum current operators. In this Letter, we will present a generalization of such a realization of quantum Hopf algebras. As a special case, we will choose the structure functions for this algebra to be elliptic functions to derive certain elliptic quantum groups as a Hopf algebra, which degenerates into quantum affine algebras if we take certain degeneration of the structure functions.     

Commutativity of Quantum Family Algebras

Recently, A. A. Kirillov introduced an important notion of classical and quantum family algebras. Here the criterion of commutativity is given. The quantum eigenvalues of are computed.     

Duality for Coloured Quantum Groups

Duality between the coloured quantum group and the coloured quantum algebra corresponding to GL(2) is established. The coloured L ^± functionals are constructed and the dual algebra is derived explicitly. These functionals are then employed to give a coloured generalisation of the differential calculus on quantum GL(2) within the framework of the R-matrix approach.     

Effect of Induced Transition on the Quantum Entanglement and Coherence in Two-Coupled Double Quantum Dot System

Studying quantum properties in solid-state systems is a significant avenue for research. In this scenario, double quantum dots appear as a versatile platform for technological breakthroughs in quantum computation and nanotechnology. This work inspects the thermal entanglement and quantum coherence in two-coupled DODs, where the system is exposed to an external stimulus that induces an electronic transition within each subsystem. The results show that the introduction of external stimulus induces a quantum level crossing that relies upon the Coulomb potential changing the degree of quantum entanglement and coherence of the system. Thus, the quantum properties of the system can be tuned by changing the transition frequency, leading to the enhancement of its quantum properties.     

双量子阱中的子带光吸收

由于微制造技术的不断发展,如液相外延(LPE),气相外延(VPE),金属有机化学气相沉积(MOCVD)以及分子束外延技术(MBE)等先进的材料生长技术方法也日趋完善,从而使得各种低维半导体量子器件(如半导体、超晶格、量子阱、量子线和量子点等)制造日趋成熟。由于这些低维半导体量子器件具有很强的非线性光效应,而且随着材料、外形、尺寸等的不同,非线性光效应也有很大的差别,更由于其可能存在的广泛的应用前景,所以近年来,一直是人们研究的重点。近来,由于人们相信,利用GaAs／AlGaAs量子阱有可能制造出一些新型的光学仪器,如光开关、光限幅器、光调制器等,所以,对不同势形的GaAs／AlGaAs量子阱的非线性光学特性一直吸引着人们进行理论和实验的研究。而在最近几年,对双量子阱的研究也成为了人们的研究重点。通过密度矩阵和迭代的方法,得到双量子阱中的第一、第三阶子带光吸收表达式,我们将用一个典型的GaAs／AlGaAs双量子阱代入其中进行数值计算,并进行讨论。我们的计算结果显示,阱的光吸收峰不但与中间的势垒宽度有关,更与入射光强有关。     

Non-commutative Low-dimension Spaces and Superspaces Associated with Contracted Quantum Groups and Supergroups

Quantum planes, which correspond to all one-parameter solutions of Quantum Yang-Baxter Equation (QYBE) for the two-dimensional case of GL-groups, are summarized and their geometrical interpretations are given. It is shown that the quantum dual plane is associated with an exotic solution of QYBE and the well-known quantum h-plane may be regarded as the quantum analog of the flag (or fiber) plane. Contractions of the quantum supergroup G L _q (12) and corresponding quantum superspace C _q (12) are considered in Cartesian basis. The contracted quantum superspace C _h (12);) is interpreted as the non-commutative analog of the superspace with the fiber odd part.     

Quantum Groups and Fuss--Catalan Algebras

The categories of representations of compact quantum groups of automorphisms of certain inclusions of finite dimensional ℂ^*-algebras are shown to be isomorphic to the categories of Fuss–Catalan diagrams. Received: 9 March 2001 / Accepted: 12 November 2001     

Universal R-Matrix for Esoteric Quantum Groups

The universal R-matrix for a class of esoteric (nonstandard) quantum groups q(gl(2N+1)) is constructed as a twisting of the universal R-matrix S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's (N) q (gl(2N+1))), providing the factorization property of . As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo.     

Bicross-Product Structure of Affine Quantum Groups

We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.     

Quantum Group Structure of the q-Deformed Virasoro Algebra

In this Letter, the quantum group structure of the q-deformed Virasoro algebra Vir_q will be given.     

Traces of Intertwiners for Quantum Groups and Difference Equations

In this Letter we study twisted traces of products of intertwining operators for quantum affine algebras. They are interesting special functions, depending on two weights ,, three scalar parameters q,,k, and spectral parameters z ₁,...,z _N , which may be regarded as q-analogs of conformal blocks of the Wess–Zumino–Witten model on an elliptic curve. It is expected that in the rank 1 case they essentially coincide with the elliptic hypergeometric functions defined by Felder and Varchenko. Our main result is that after a suitable renormalization the traces satisfy four systems of difference equations – the Macdonald–Ruijsenaars equation, the q-Knizhnik–Zamolodchikov–Bernard equation, and their dual versions. We also show that in the case when the twisting automorphism is trivial, the trace functions are symmetric under the permutation , k . Thus, our results generalize those of Etingof and Schiffmann, dealing with the case q=1, and Etingof, Varchenko, and Schiffmann, dealing with the finite-dimensional case.     

Interpretations of Quantum Mechanics in Terms of Beable Algebras

In terms of beable algebras Halvorson and Clifton [International Journal of Theoretical Physics 38 (1999) 2441–2484] generalized the uniqueness theorem (Studies in History and Philosophy of Modern Physics 27 (1996) 181–219] which characterizes interpretations of quantum mechanics by preferred observables. We examine whether dispersion-free states on beable algebras in the generalized uniqueness theorem can be regarded as truth-value assignments in the case where a preferred observable is the set of all spectral projections of a density operator, and in the case where a preferred observable is the set of all spectral projections of the position operator as well.     

Universal Framework for Quantum Error-Correcting Codes

We present a universal framework for quantum error-correcting codes, i.e., a framework that applies to the most general quantum error-correcting codes. This framework is based on the group algebra, an algebraic notation associated with nice error bases of quantum systems. The nicest thing about this framework is that we can characterize the properties of quantum codes by the properties of the group algebra. We show how it characterizes the properties of quantum codes as well as generates some new results about quantum codes.     

离子注入诱导的具有两个不同发射波长的混合双量子阱结构

叙述了磷离子注入方法诱导具有不同发射波长的InGaAsP双量子阱结构的混合,并通过光致发光谱和断面透射电子显微术对量子阱混合的程度进行了研究。在特定条件下快速热退火处理后,光致发光谱显示,在离子注入剂量低于7×10¹¹/cm²情况下,两个阱的谱峰能保持较好的分离,注入剂量从10¹¹ /cm²增大到10¹²/cm²的过程中,两个阱的带隙蓝移值都似乎存在一个极大值,并且在同样的条件下,上阱(发射波长为1.52 μm)的带隙蓝移值较下阱(发射波长为1.59 μm)大些。当离子注入剂量达到10¹²/cm²时,上阱的谱峰近乎消失,双阱光致发光谱出现了一个谱峰。用断面透射电子显微术对原生长样品与带隙蓝移具有极大值的退火样品进行微结构比较,结果显示,对比原生长样品,退火样品的晶格原子基本得到修复,但阱与垒间的界面显得模糊,这说明离子注入导致两阱完全混合。     

Thermal Entanglement and Correlated Coherence in Two Coupled Double Quantum Dots Systems

In this work, the thermal quantum correlations in two coupled double semiconductor charge qubits are investigated. This is carried out by deriving analytical expressions for both the thermal concurrence and the correlated coherence. The effects of the tunneling parameters, the Coulomb interaction, and the temperature on the thermal entanglement and on the correlated coherence are studied in detail. It is found that the Coulomb potential plays an important role in the thermal entanglement and in the correlated coherence of the system. The results also indicate that the Coulomb potential can be used for significant enhancement of the thermal entanglement and quantum coherence. One interesting aspect is that the correlated coherence capture all the thermal entanglement at low temperatures, that is, the local coherences are totally transferred to the thermal entanglement. Finally, the role played by thermal entanglement and the correlated coherence responsible for quantum correlations are focused on. It is shown that in all cases, the correlated coherence is more robust than the thermal entanglement so that quantum algorithms based only on correlated coherence may be more robust than those based on entanglement.     

Multiboson Realizations of Lie and Quant urn Algebras

A unified method to construct the (multi-)boson realizations of the Lie and quantum algebras is proposed based on a universal deformation of boson (Heisenberg-Weyl) algebra and its multiboson realization. Some explicit examples, the Lie algebras sl(2) and su (Ill), q-boson algebra, quantum algebras sl(2)_q and su (l,l)_q, along with the q-ladder algebra are studied in detail. In particular, the square boson realizations of su (1,l) and su (l,l)_q are naturally obtained as special cases.     

Quantum Information Transfer from a Double Quantum Dot System to a Cavity Field＊

In this paper, we propose a scheme to realize quantum information transfer from a double quantum dot （DQD） system to a quantized cavity field. The DQD and the cavity field are treated as a two-state charge qubit and a continuous-variable system, respectively. It is shown that quantum information encoded in the two-state DQD system can be transferred to quantum states of the cavity field with a continuous-variable basis through appropriate projective measurements with respect to the DQD.     

Transient Intersubband Optical Absorption in Double Quantum Well Structure

The microscopic equations of motion including many-body effects are derived to study the intersubband polarization in the double quantum well structure induced by an ultrafast pumping infrared light. Based on the self-consistent field theory, the transient probe absorption coefficient is calculated. These calculations are beyond the previous steady-state assumption. Transient probe absorption spectra are calculated under different pumping intensity and various pump probe delay.