A theorem of Joseph-Alfred Serret and its relation to perfect quantum state transfer

In this paper we recast the Serret theorem about a characterization of palindromic continued fractions in the context of polynomial continued fractions. Then, using the relation between symmetric tridiagonal matrices and polynomial continued fractions we give a quick exposition of the mathematical aspect of the perfect quantum state transfer problem.     

基于谷胱甘肽配体的ZnSe量子点对pH响应的时间分辨荧光光谱特性

当前,有关量子点pH响应方面的研究主要集中在含Cd（镉）类量子点,且都是研究其稳态荧光光谱对pH值的响应。然而,Cd类量子点对生物体系具有一定的毒性,且稳态荧光光谱法由于受浓度等因素的影响具有一定的不稳定性,因此应用于生物体系中作为pH探针具有明显的缺点。基于以上分析,通过水相合成法,我们制备出了基于谷胱甘肽配体的水溶性ZnSe量子点,该量子点具有毒性小,生物兼容性好等特点,适合被应用于生物体系中。利用所制备的ZnSe量子点,采用时间相关单光子计数技术,结合紫外可见吸收光谱和稳态荧光光谱,对pH值在5~11不同环境下的ZnSe量子点荧光动力学进行了系统性的研究。ZnSe量子点荧光衰减具有两个寿命组分,拟合得到分别为4和24 ns。通过采集不同探测波长下ZnSe量子点荧光衰减曲线,发现其长寿命组分随探测波长的增加而增加,而短寿命组分基本不随探测波长的改变而改变,结合有关报道分析判断,短寿命和长寿命组分分别来源于核内非局域载流子复合和表面态局域载流子复合。实验发现,处于不同pH值的环境下的ZnSe量子点具有不同的荧光寿命,其荧光寿命与pH值的变化呈负相关。通过比较ZnSe量子点两种荧光寿命组分随pH值的变化关系,发现ZnSe量子点的荧光寿命对pH值的响应主要来源于长寿命组分即表面态寿命,且在不同pH值范围内响应的灵敏度不同,在6~8的pH值范围内响应最为显著,表现为长寿命组分随pH值的增加出现一个较大幅度的衰减。实验进一步发现,ZnSe量子点两个寿命组分的比值在不同pH值范围内具有较好的线性相关性,但在不同pH值范围内斜率不同,通过比较,最大值在pH值为6~8的范围内。另外,与金属钠离子相互作用实验及相关报道表明,金属离子对ZnSe量子点荧光寿命的影响较小。以上研究表明,ZnSe量子点在生物体系pH值检测中具有良好的应用前景。     

The characterization of a class of quantum Markov semigroups and the associated operator-valued Dirichlet forms based on Hilbert <Emphasis Type="Italic">C</Emphasis>*-module <Emphasis Type="Italic">l</Emphasis><Subscript>2</Subscript>(<Emphasis Type="Italic">A</Emphasis>)

We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we introduce the concept of operator-valued quadratic forms,and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l2(A)and the set of non-negative densely defined A-valued quadratic forms.In the end,we obtain that a real and strongly continuous symmetric semigroup{Tt}t∈R+L(l2(A))being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form.     

Inhomogeneous Quantum Codes （III）： The Asymmetric Case

The stabilizer （additive） method and non-additive method for constructing asymmetric quantum codes have been established. In this paper, these methods are gen- eralized to inhomogeneous quantum codes.     

Embeddable quantum homogeneous spaces

We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we recall an interesting duality for such objects studied earlier by M. Izumi, R. Longo, S. Popa for compact Kac algebras and by M. Enock in the general case of locally compact quantum groups. A definition of a quantum homogeneous space is proposed along the lines of the pioneering work of Vaes on induction and imprimitivity for locally compact quantum groups. The concept of an embeddable quantum homogeneous space is selected and discussed in detail as it seems to be the natural candidate for the quantum analog of classical homogeneous spaces. Among various examples we single out the quantum analog of the quotient of the Cartesian product of a quantum group with itself by the diagonal subgroup, analogs of quotients by compact subgroups as well as quantum analogs of trivial principal bundles. The former turns out to be an interesting application of the duality mentioned above.     

Complex classical fields: An example

We study complex, classical, scalar fields within a new framework introduced in a previous work. We replace the usual functional integral by a complex functional arising from a boosted Hamiltonian. We generalize the Feynman–Kac relation to this setting, and use it to establish the spectral condition on a cylinder. We consider also positive-temperature states.     

温度为T时量子谐振子系统处在第n态的概率

研讨了温度为T时量子谐振子系统处在第n态的概率,并讨论了结果的物理意义．