Some Aspects of Quantum Entanglement for CAR Systems

We show some distinct features of quantum entanglement for bipartite CAR systems such as the failure of triangle inequality of von Neumann entropy and the possible change of our entanglement degree under local operations. Those are due to the nonindependence of CAR systems and never occur in any algebraic independent systems. We introduce a new notion half-sided entanglement.     

Quantum Transport through a Triple Quantum Dot System in the Presence of Majorana Bound States

We study the electron transport through a special quantum-dot(QD)structure composed of three QDs and two Majorana bound states(MBSs)using the nonequilibrium Green’s function technique.This QD-MBS ring structure includes two channels with the two coupled MBSs being Channel 1 and one QD being Channel 2,and three types of transport processes such as the electron transmission(ET),the Andreev reflection(AR),and the crossed Andreev reflection(CAR).By comparing the ET,AR,and CAR processes through Channels 1 and 2,we make a systematic study on the transport properties of the QD-MBS ring.It is shown that there appear two kinds of characteristic transport patterns for Channels 1 and 2,as well as the interplay between the two patterns.Of particular interest is that there exists an AR-assisted ET process in Channel 2,which is different from that in Channel 1.Thus a clear"X"pattern due to the ET and AR processes appears in the ET,AR,and CAR transmission coefficients.Moreover,we study how Channel 2 affects the three transport processes when Channel 1 is tuned in the ET and CAR regimes.It is shown that the transport properties of the ET,AR and CAR processes can be adjusted by tuning the energy level of the QD embedded in Channel 2.We believe this research should be a helpful reference for understanding the transport properties in the QD-MBS coupled systems.     

Crossed Andreev reflection in a quantum dot coupled to a topological superconducting single-stranded DNA

We investigate the crossed Andreev reflection (CAR) through a quantum dot (QD) coupled to topological superconducting single-stranded DNA (ssDNA). It is found that the topological nontrivial states appear in the QD due to leakage of the Majorana zero mode. Majorana zero mode can be identified by measuring the CAR. This device can be used as a Majorana zero mode detector that relies on the system parameters, such as the spin orbit coupling, the twist angle, molecular length. A high efficiency Cooper pair splitter can be realized by regulating the magnitude and direction of the gate voltage. In additions, the signature of CAR is robust against the Coulomb blockade and the disorder induced by distinct amino acids. This work provides an alternative method for detection of Majorana zero mode in ssDNA.     

Irreversible dynamics of infinite fermion systems

We investigate the irreversible dynamics of infinite systems as specified by completely positive, strongly continuous, one-parameter semigroups on a suitableC*-algebra. Having shown how to construct such a semigroup from a fairly general evolution equation we determine when the semigroup is spatial with respect to a given representation of the algebra. A special class of exactly soluble evolution equations on the CAR algebra is studied in detail in order to test conjectured extensions of the theory.     

Majorana fermion realization and relevant transport processes in a triple-quantum dot system

Nonequilibrium electronic transports through a system hosting three quantum dots hybridized with superconductors are investigated. By tuning the relative positions of the dot levels, we illustrate the existence of Majorana fermions and show that the Majorana feimions will either survive separately on single dots or distribute themselves among different dots with tunable probabilities. As a result, different physical mechanisms appear, including local Andreev reflection(LAR),cross Andreev reflection(CAR), and cross resonant tunneling(CRT). The resulting characteristics may be used to reveal the unique properties of Majorana fermions. In addition, we discuss the spin-polarized transports and find a pure spin current and a spin filter effect due to the joint effect of CRT and CAR, which is important for designing spintronic devices.     

Ground states of Fermions on lattices

We consider Fermion systems on integer lattices. We establish the existence of dynamics for a class of long range interactions. The infinite volume ground states are considered. The equivalence of the variational principle and ground state conditions is proved for long range interactions. We also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full CAR algebra for the Hamiltonian with a chemical potential (equivalence of ensemble for canonical and ground canonical states at the zero temperature).     

Quantum information capsule in multiple-qudit systems and continuous-variable systems

Quantum correlations in an entangled many-body system are capable of storing information. Even when the information is injected by a local unitary operation to the system, the entanglement delocalizes it. In a recent study on multiple-qubit systems, it is shown that a virtual qubit defined in the correlation space plays a role of perfect storage of delocalized information, which is called a quantum information capsule (QIC). To enhance the capacity of quantum information storage, it is crucial to formulate the cases for multiple-qudit systems and continuous-variable (CV) systems. We analytically prove that it is possible to construct a QIC for general write operations of the systems. It turns out that the extension to quantum field theory is achievable. For Gaussian states, we explicitly construct a QIC for shift write operations. We analyze the time-evolution of QIC in a CV system to demonstrate the diffusion of information in entangled pure states.     

Spin-dependent Andreev reflection in a three-terminal Aharonov-Bohm interferometer with coherent indirect coupling

Within the framework of non-equilibrium Green’s functions, we investigate the spin-dependent Andreev reflection (AR) in a three-terminal Aharonov-Bohm interferometer with double quantum dot, taking account of the coherent indirect coupling via the superconducting reservoir. It is found that the time-reversal symmetry is broken by the crossed Andreev reflection (CAR) process, and moreover that the spin-value effect of the linear conductance, the spin-polarised AR current, and a pure spin current can be generated by means of the normal AR and the CAR. Expressions for the AR conductances (the transport coefficients) governing the AR properties of this system are derived analytically. The effect of the coherent indirect coupling on the conductance, the Andreev reflected tunneling magnetoresistance (ARTMR), and the spin-related current in the presence of the AR are amply analyzed. Our results indicate that the optimal properties of this system can be realised by tuning the external parameters.     

Anisotropic pairing symmetry effect on crossed Andreev reflection in a graphene-based transistor

Crossed Andreev reflection (CAR) under the influence of anisotropic pairing symmetry is considered. It is shown that CAR is sensitive to the Fermi energy and the orientation of the gap. In addition, the oscillatory period of CAR can be not only tunable by the potential energy in the superconductor region, it also can be modulated by the length of the superconductor region. The physical origination for those phenomena has also been analyzed.     

Spin qubits for quantum simulations

The investigation of quantum mechanical systems mostly concentrates on single elementary particles. If we combine such particles into a composite quantum system, the number of degrees of freedom of the combined system grows exponentially with the number of particles. This is a major difficulty when we try to describe the dynamics of such a system, since the computational resources required for this task also grow exponentially. In the context of quantum information processing, this difficulty becomes the main source of power: in some situations, information processors based in quantum mechanics can process information exponentially faster than classical systems. From the perspective of a physicist, one of the most interesting applications of this type of information processing is the simulation of quantum systems. We call a quantum information processor that simulates other quantum systems a quantum simulator.     

Modal identification based on Gaussian continuous time autoregressive moving average model

A new time-domain modal identification method of the linear time-invariant system driven by the non-stationary Gaussian random force is presented in this paper. The proposed technique is based on the multivariate continuous time autoregressive moving average (CARMA) model. This method can identify physical parameters of a system from the response-only data. To do this, we first transform the structural dynamic equation into the CARMA model, and subsequently rewrite it in the state-space form. Second, we present the exact maximum likelihood estimators of parameters of the continuous time autoregressive (CAR) model by virtue of the Girsanov theorem, under the assumption that the uniformly modulated function is approximately equal to a constant matrix over a very short period of time. Then, based on the relation between the CAR model and the CARMA model, we present the exact maximum likelihood estimators of parameters of the CARMA model. Finally, the modal parameters are identified by the eigenvalue analysis method. Numerical results show that the method we introduced here not only has high precision and robustness, but also has very high computing efficiency. Therefore, it is suitable for real-time modal identification.     

Information-theoretic limits of control

Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation required by open-loop control. In addition, an information-theoretic analysis of control systems shows feedback control to be a zero sum game: each bit of information gathered from a dynamical system by a control device can serve to decrease the entropy of that system by at most one bit additional to the reduction of entropy attainable without such information. Consequences for the control of discrete state systems and chaotic maps are discussed.     

Dynamical entropy of space translations of CAR and CCR algebras with respect to quasi-free states

We compute the dynamical entropy in the sense of Connes, Narnhofer and Thirring of space translations of the CAR and CCR algebras in -dimensional continuous spaces with respect to invariant quasi-free states. It turns out that the dynamical entropies are equal to the corresponding mean entropies of the systems under consideration. Computing the mean entropies explicitly we derive the entropy formulas for the systems.Research supported in part by the Basic Science Research Program, Ministry of Education, 1992Research supported in part by GARC in 1991–1992     

Automorphisms and quasi-free states of the CAR algebra

We study automorphisms of the CAR algebra which map the family of gauge-invariant, quasi-free states of the CAR algebra onto itself and show (Theorem 3.1) that they are one-particle automorphisms.     

论动态信息理论

本文综述了作者的研究成果.近十年,作者将现有静态统计信息理论拓展至动态过程,建立了以表述动态信息演化规律的动态信息演化方程为核心的动态统计信息理论.基于服从随机性规律的动力学系统(如随机动力学系统和非平衡态统计物理系统)与遵守确定性规律的动力学系统(如电动力学系统)的态变量概率密度演化方程都可看成是其信息符号演化方程,推导出了动态信息(熵)演化方程.它们表明:对于服从随机性规律的动力学系统,动态信息密度随时间的变化率是由其在系统内部的态变量空间和传递过程的坐标空间的漂移、扩散和耗损三者引起的,而动态信息熵密度随时间的变化率则是由其在系统内部的态变量空间和传递过程的坐标空间的漂移、扩散和产生三者引起的.对于遵守确定性规律的动力学系统,动态信息(熵)演化方程与前者的相比,除动态信息(熵)密度在系统内部的态变量空间仅有漂移外,其余皆相同.信息和熵已与系统的状态和变化规律结合在一起,信息扩散和信息耗损同时存在.当空间噪声可略去时,将会出现信息波.若仅研究系统内部的信息变化,动态信息演化方程就约化为与表述上述动力学系统变化规律的动力学方程相对应的信息方程,它既可看成是表述动力学系统动态信息的演化规律,亦可看成是动力学系统的变化规律都可由信息方程表述.进而给出了漂移和扩散信息流公式、信息耗散率公式和信息熵产生率公式及动力学系统退化和进化的统一信息表述公式.得到了反映信息在传递过程中耗散特性的动态互信息公式和动态信道容量公式,它们在信道长度和信号传递速度之比趋于零的极限情况下变为现有的静态互信息公式和静态信道容量公式.所有这些新的理论公式和结果都是从动态信息演化方程统一推导出的.     

Template-directed hydrothermal synthesis of hydroxyapatite as a drug delivery system for the poorly water-soluble drug carvedilol

In order to improve the dissolution rate and increase the bioavailability of a poorly water-soluble drug, intended to be administered orally, the biocompatible and bioactive mesoporous hydroxyapatite (HA) was successfully synthesized. In the present study, mesoporous HA nanoparticles were produced using Pluronic block co-polymer F127 and cetyltrimethylammonium bromide (CTAB) as templates by the hydrothermal method. The obtained mesoporous HA was employed as a drug delivery carrier to investigate the drug storage/release properties using carvedilol (CAR) as a model drug. Characterizations of the raw CAR powder, mesoporous HA and CAR-loaded HA were carried out by the scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray powder diffraction (XRPD), differential scanning calorimetry (DSC), Fourier transform infrared (FT-IR) spectroscopy, N₂ adsorption/desorption, thermogravimetric analysis (TGA), and UV-VIS spectrophotometry. The results demonstrated that CAR was successfully incorporated into the mesoporous HA host. In vitro drug release studies showed that mesoporous HA had a high drug load efficiency and provided immediate release of CAR compared with micronized raw drug in simulated gastric fluid (pH 1.2) and intestinal fluid (pH 6.8). Consequently, mesoporous HA is a good candidate as a drug carrier for the oral delivery of poorly water-soluble drugs.     

Thermodynamic model for feedback control of systems with uncertain macroscopic states

Thermodynamics of feedback control processes, including the minimum work consumption of measurement, work extraction, and erasure processes of thermodynamic small systems have been investigated by researchers. We take systems with uncertain macroscopic states as the study object and study the feedback control processes of nonequilibrium macroscopic systems considering both the information entropy of microscopic states and macroscopic states. First we consider a system set that consists of systems with several macroscopic states and discuss the relations among the average information entropy of the system set, the thermodynamic entropy of the systems and the information entropy of macroscopic states of the systems. Then, we derive the expression of the average maximum net work obtained through feedback control, which relates to the free energy of the systems and the minimum work consumption of the measurement and erasure processes.     

Preference-Tree-Based Real-Time Recommendation System

In the current era of online information overload, recommendation systems are very useful for helping users locate content that may be of interest to them. A personalized recommendation system presents content based on information such as a user’s browsing history and the videos watched. However, information filtering-based recommendation systems are vulnerable to data sparsity and cold-start problems. Additionally, existing recommendation systems suffer from the large overhead incurred in learning regression models used for preference prediction or in selecting groups of similar users. In this study, we propose a preference-tree-based real-time recommendation system that uses various tree models to predict user preferences with a fast runtime. The proposed system predicts preferences based on two balance constants and one similarity threshold to recommend content with a high accuracy while balancing generalized and personalized preferences. The results of comparative experiments and ablation studies confirm that the proposed system can accurately recommend content to users. Specifically, we confirmed that the accuracy and novelty of the recommended content were, respectively, improved by 12.1% and 27.2% compared to existing systems. Furthermore, we verified that the proposed system satisfies real-time requirements and mitigates both cold-start and overfitting problems.