Constructing generalized Drinfel'd quantum double

Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to be a bialgebra are proved. Then, B#^τδH is a coquasitriangular Hopf algebra under certain conditions. This coquasitriangular Hopf algerbra generalizes some known cross products. Finally, as an application, an explicit example is given.

C^＊-Structure of Quantum Double for Finite Hopf C^＊-Algebra

Let H be a finite Hopf C^＊ -algebra and H′be its dual Hopf algebra. Drinfeld＇s quantum double D（H） of H is a Hopf^＊-algebra. There is a faithful positive linear functional θ on D（H）. Through the associated Gelfand-Naimark-Segal （GNS） representation, D（H） has a faithful^＊ -representation so that it becomes a Hopf C^＊ -algebra. The canonical embedding map of H into D（H） is isometric.

On the structure and representations of non-balanced quantum doubles

For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space （kX°P）＊ kG （see Theorem 2.1）, called a non-balanced quantum double and denoted by Dx（G）. In this paper, some Hopf algebra properties of Dx （G） are given, the representation types of Dx （G） viewed as a k-algebra are discussed, the algebra structure and module category over Dx（G） are studied. Since the Hopf algebra structure of non-balanced quantum double DX （G） generMizes the usual quantum double D（G） for a finite group G, all results about Dx（G） in this paper can also be used to describe D（G） as a special case and the universal R-matrix of Dx （G） provides more solutions of Yang-Baxter equation.

Double quantum images encryption scheme based on chaotic system

This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated,offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps.Based on the DNEQR model and the hyperchaotic system,a double quantum images encryption algorithm is proposed.Firstly,two classical plaintext images are transformed into quantum states using the DNEQR model.Then,the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences.These chaotic sequences are utilized to perform pixel value and position operations on the quantum image,resulting in changes to both pixel values and positions.Finally,the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences.The corresponding quantum circuits are also given.Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission,improves the encryption efficiency,and enhances anti-interference and anti-attack capabilities.

Delayed response to the photovoltaic performance in a double quantum dots photocell with spatially correlated fluctuation

A viable strategy for enhancing photovoltaic performance is to comprehend the underlying quantum physical regime of charge transfer in a double quantum dots(DQD) photocell. This work explored the photovoltaic performance dependent spatially correlated fluctuation in a DQD photocell. The effects of spatially correlated fluctuation on charge transfer and output photovoltaic efficiency were explored in a proposed DQD photocell model. The results revealed that the charge transport process and the time to peak photovoltaic efficiency were both significantly delayed by the spatially correlated fluctuation, while the anti-spatially correlated fluctuation reduced the output peak photovoltaic efficiency. Further results revealed that the delayed response could be suppressed by gap difference and tunneling coefficient within two dots. Subsequent investigation demonstrated that the delayed response was caused by the spatial correlation fluctuation slowing the generative process of noise-induced coherence, which had previously been proven to improve the quantum photovoltaic performance in quantum photocells. And the reduced photovoltaic properties were verified by the damaged noise-induced coherence owing to the anti-spatial correlation fluctuation and a hotter thermal ambient environment. The discovery of delayed response generated by the spatially correlated fluctuations will deepen the understanding of quantum features of electron transfer, as well as promises to take our understanding even further concerning quantum techniques for high efficiency DQD solar cells.

Pairing and Quantum Double of Finite Hopf C~*-Algebras

This paper defines a pairing of two finite Hopf C^＊-algebras A and B, and investigates the interactions between them. If the pairing is non-degenerate, then the quantum double construction is given. This construction yields a new finite Hopf C^＊-algebra D（A, B）. The canonical embedding maps of A and B into the double are both isometric.

Electronic structure of GaAs/A1GaAs quantum double rings in lateral electric field

A three-dimensional model of GaAs/A1GaAs quantum double rings in the lateral static electric field is investigated theoretically. The eigenvalue problem with the effective-mass approximation is solved by means of the finite-element method. The energy levels and wave functions of quantum-confined electrons and heavy holes are obtained and show an agreement with our previous theoretical and experimental studies. It is shown in the approximation of neglecting the Coulomb attraction between the electron and heavy hole that a relatively large Stark shift of exciton emission of 4 meV is attainable with an applied electric field of 0.7 kV/cm.

Quantum Double Constructions for Compact Quantum Group

For a non-degenerate pair of compact quantum groups, we first construct the quantum double as an algebraic compact quantum group in an algebraic framework. Then by adopting some completion procedure, we give the universal and reduced quantum double constructions in the correspondence C＊-algebraic settings, which generalize Drinfeld＇s quantum double construction and yield new C＊-algebraic compact quantum groups.

The Cell Modules of the Green Algebra of Drinfel'd Quantum Double D(H_(4))

This paper is devoted to studying the structures of the cell modules of the complexified Green algebra R(D(H_(4))),where D(H_(4))is the Drinfel'd quantum double of Sweedler's 4-dimensional Hopf algebra H_(4).We show that R(D(H_(4)))has one infinite dimensional cell module,one 4-dimensional cell module generated by all finite dimensional indecomposable projective modules of D(H_(4))and infinitely many 2-dimensional cell modules.More precisely,we obtain the decompositions of all finite dimensional cell modules into the direct sum of indecomposable submodules,and show that the infinite dimensional cell module can be written as the direct sum of two infinite dimensional indecomposable submodules.

The binding energy of a hydrogenic impurity in self-assembled double quantum dots

The binding energy of a hydrogenic impurity in self-assembled double quantum dots is calculated via the finitedifference method. The variation in binding energy with donor position, structure parameters and external magnetic field is studied in detail. The results found are： （i） the binding energy has a complex behaviour due to coupling between the two dots; （ii） the binding energy is much larger when the donor is placed in the centre of one dot than in other positions; and （iii） the external magnetic field has different effects on the binding energy for different quantum-dot sizes or lateral confinements.

InGaAsP/InP Double Quantum Well Intermixing Induced by Phosphorus Ion Implantation

A quantum well intermixing（QW1） investigation on double quantum well（DQW） structure with two different emitting wavelength caused by phosphorus ion implantation and following rapid thermal annealing （RTA） was carried out by means of photoluminescence（PL）. The ion implantation was performed at the energy of 120 keV with the dose ranging from 1 × 10^11cm^-2 to 1× 10^14cm^-2. The RTA was performed at the temperature of 700 ℃ for 30 s under pure nitrogen protection. The PL measurement implied that the band gap blue-shift from the upper well increases with the ion dose faster than that from lower well and the PL peaks from both QWs remained well separated under the lower dose implantation（-1 × 10^11cm^-2） indicating that the implant vacancy distribution affects the QWl. When the ion dose is over - 1 × 10^12cm^-2, the band gap blue-shift from both wells increases with the ion dose and finally the two peaks merge together as one peak indicating the ion implantation caused a total intermixing of both quantum wells.

Magnetotransport through an Aharonov-Bohm ring with parallel double quantum dots coupled to ferromagnetic leads

Using the Keldysh nonequilibrium Green function and equation-of-motion technique, this paper studies the mag- netotransport through an Aharonov-Bohm （AB） ring with parallel double quantum dots coupled to ferromagnetic leads. It calculates the transmission probability in both the equilibrium and the nonequilibrium case, analyses the conduc- tance and the tunnel magnetoresistance for various parameters, and obtains some new results. These results show that this system is provided with an excellent spin filtering property, and that a large tunnelling magnetoresistance and a negative tunnelling magnetoresistance can arise by adjusting relative parameters; these facts indicate that this system is a possible candidate for spin valve transistors, and has important applications in spintronics.

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 selfconsistent 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.

BINDING ENERGY OF THE SHALLOW DONOR IN （CdTe）_m／（ZnTe）_n STRAINED DOUBLE QUANTUM WELL

In this paper the binding energy of the shallow.donor in CdTe/ZnTe strained double quantum well was calculated.The effect of the finite well potential and strain,resulting from the lattice mismatch,on the binding energy of the impurity is included in a variational framework.The binding energy is obtained as a function of the well width,barrier width,and impurity position in the barrier by using a variational method.The result of the present calculation shows that the variational law of the binding energy is similar to that of unstrained materials.

Transmission spectra through a photonic double quantum well system

By means of the modal expansion method with an R-matrix propagation algorithm, effects of the coupling between resonance photonic states on the resonance tunneling through a double quantum well structure are investigated. We examine the effects on the transmission spectra due to variation of the second well width and middle barrier thickness. Drastic change of the tunneling spectra is found and analyzed when the wells are filled with left-hand media.

Electron transfer properties of double quantum dot system in a fluctuating environment

Using the innovative method of the additional Bloch vector,the electron transfer properties of a double quantum dot(DQD) system measured by a quantum point contact(QPC) in a fluctuating environment are investigated.The results show that the environmental noises in transverse and longitudinal directions play different roles in the dynamical evolution of the open quantum systems.Considering the DQD with symmetric energy level,the Fano factor exhibits a slight peak with the increase of transverse noise amplitude σ_(T),which provides a basis for distinguishing dynamical phenomena caused by different directional fluctuation noises in symmetric DQD structures by studying the detector output.In the case of asymmetric DQD,the dependence of a detector current involving the level displacement is distinct when increasing the transverse noise damping coefficient τ_(T) and the longitudinal noise damping coefficient τ_(ε) respectively.Meanwhile,the transverse noise damping coefficient τ_(T) could significantly reduce the Fano factor and enhance the stability of the quantum system compared with the longitudinal one.The Fano factors with stable values as the enhancement of noise amplitudes show different external influences from the detector measurement,and provide a numerical reference for adjusting the noise amplitudes in both transverse and longitudinal directions appropriately in a microscopic experimental process to offset the decoherence effect caused by the measurements.Finally,the research of average waiting time provides unique insights to the development of single electron transfer theory in the short-time limit.

Asymmetric Double Quantum Dots as a Subminiature Mesoscopic Cell

A subminiature mesoscopic cell, consisting of asymmetric double quantum dots capacitively coupled to a nearby mesoscopic circuit, is proposed, which can transform disordered noise energy to ordered electric energy. Two schemes, the noises originating from the nearby mesoscopic circuit and from the electromagnetic wave disturbance in external environment, are investigated. We found that the proposed cell can manifest as a good constant current source and the output current may not reach its largest value even if the circuit is shorted.

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.

Giant Kondo Resonance of Parallel-Coupled Double Quantum Dots Embedded in an A-B Ring

We theoretically study the properties of the ground state of the parallel-coupled double quantum dots embedded in a mesoscopic ring in the Kondo regime by means of the two-impurity Anderson Hamiltonian. The Hamiltonian is solved by means of the slave-boson mean-field theory. We find that in this system, the persistent current depends sensitively on both the parity of this system and the size of the ring. In the strong coupling regime, the giant sharp current peak appears, at the same time, the parity dependence of the persistent current disappears. These imply that in the strong coupling regime, there exists giant Kondo resonance and the two dots can be coupled coherently. Thus this system might be a candidate for future device applications.

Spin-flip process through double quantum dots coupled to two half-metallic ferromagnetic leads

We investigate the spin-flip process through double quantum dots coupled to two half-metallic ferromagnetic leads in series. By means of the slave-boson mean-field approximation, we calculate the density of states in the Kondo regime for two different configurations of the leads. It is found that the transport shows some remarkable properties depending on the spin-flip strength. These effects may be useful in exploiting the role of electronic correlation in spintronics.