Entropy, Lyapunov exponents, and mean free path for billiards

We review known results and derive some new ones about the mean free path, Kolmogorov-Sinai entropy, and Lyapunov exponents for billiard-type dynamical systems. We focus on exact and asymptotic formulas for these quantities. The dynamical systems covered in this paper include the priodic Lorentz gas, the stadium and its modifications, and the gas of hard balls. Some open questions and numerical observations are discussed.     

Correlation between zeroes and poles ofS matrix for complex potentials

Using several illustrative examples, the nature of resonance poles and the corresponding zeroes of the s-waveS matrix is examined for several potentials having an absorptive pocket followed by a barrier. It is shown that even though the presence of absorption practically suppresses the manifestation of resonance in the elastic scattering cross section, the effect of the resonances generated by the absorptive pocket is more clearly manifested in the absorption cross section provided the barrier width is not too large. We further find that the signature of barrier top resonances are also more clearly manifested in the absorption cross section rather than in the elastic scattering cross section. These results have been interpreted in terms of complex resonance poles and corresponding zeroes of theS matrix. This implies that in complex potential scattering like heavy ion collisions, the reaction channel cross section peak is a more reliable signature of resonance phenomenon than the variation of the elastic channel cross section with energy.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.     

A difference-equation formalism for the nodal domains of separable billiards

Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in Samajdar and Jain (2014). The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.     

A new computation scheme for triangular quantum billiards

A new scheme for computing the eigenvalues and eigenstates of the Laplacian with Dirichlet boundary conditions on arbitrary triangular domains is presented. Its reliability is tested by comparing numerical results with analytical ones whenever possible. The computation of eigenvalues shows a good agreement with analytical results. The procedure is shown to give accurate results also in the case of eigenfunctions computation. Finally, the sensitivity of our scheme to the geometry of the domain is discussed and the algorithm is shown to detect small changes in the shape of the domain.     

The temporal Mueller matrix solution for polarimetric scattering from a layer of random non-spherical scatterers

The Mueller matrix solution of the vector radiative transfer equation with time dependence is derived in this paper. It is applied to simulation of polarimetric bistatic scattering from a layer of non-uniformly oriented, random non-spherical scatterers when a Gaussian plane pulse is incident upon. Co-polarized and cross-polarized bistatic scattering are numerically calculated. The pulse echoes are compared with the incidence, and demonstrate its functional dependence on the physical parameters of random medium, such as spatial orientation and fractional volume of scatterers, incidence angle and polarization, the layer depth and others.     

Optical properties of InAs quantum dots in a Si matrix

We report on the optical properties of nanoscale InAs quantum dots in a Si matrix. At a growth temperature of 400°C, the deposition of 7 ML InAs leads to the formation of coherent islands with dimensions in the 2–4 nm range with a high sheet density. Samples with such InAs quantum dots show a luminescence band in the 1.3 μm region for temperatures up to 170 K. The PL shows a pronounced blue shift with increasing excitation density and decays with a time constant of 440 ns. The optical properties suggest an indirect type II transition for the InAs/Si quantum dots. The electronic structure of InAs/Si QDs is discussed in view of available band offset information.     

Numerical study of the characterization of forward scattering Mueller matrix patterns of turbid media with triple forward scattering assumption

We propose a triple forward scattering model to numerically investigate the forward scattering Mueller matrix of a turbid medium. The calculated results show that the Mueller matrix based on the triple scattering model can completely describe the basic symmetries and azimuthal structures of the forward scattering Mueller matrix of a turbid medium. The results show that the forward scattering Mueller matrix is characterized with special symmetric structure compared with backscattering Mueller matrix patterns. The method will extend the investigation to light scattering mechanism from cells and to diagnosis of diabetes and other blood related diseases.     

Symmetry relations for the phase matrix of horizontally oriented particles

Seven symmetry relations, with a wide range of validity, are presented for the phase matrix of horizontally oriented particles. Three of these relations constitute a fundamental basis from which four others can be derived by making combinations. All seven relations can be used for many types of particles, including hexagonal plates and columns as well as spheroids, cylinders and cubes. Some applications are also pointed out.     

Incomplete active polarimetry: Measurement of the block-diagonal scattering matrix

The problem of measurement of block-diagonal scattering matrix as being part of the so-called incomplete or partial Mueller polarimetry is addressed. It has been shown that non-zero elements of the scattering matrix with block-diagonal structure can be measured using only two elliptical polarizations of input light. Optimal pairs of these polarizations are derived. Utilization of the optimal input polarizations results in halving measurement time and decreasing measurement errors by 30%.     

Scattering matrix theory for Cs Rydberg atoms in magnetic field

Based on the closed orbit theory framework together with the quantum defect theory and time-independent scattering matrices theory, we calculate the recurrence spectra of diamagnetic Cs atoms at several different scaled energies near the second ionization threshold. It is revealed that the new extra peaks in spectra are attributed to the combination recurrences of semiclassical closed orbits arising from core-scattered events. This method considers the dynamic states of the Rydberg electron in the core region and long-range region and can be analytically resumed to include all orders of core-scattering automatically. With this approach a convergent recurrence spectrum can be reasonably achieved. It is found that the spectral complexity depends highly sensitively on the scaled energy. With the increase of the scaled energy, the spectral structure changes from simple to complicate and the dynamic feature from regular to chaotic. The comparison of the recurrence spectra with Dando’s result under the same conditions demonstrates that there exist some similarities and differences between them, and furthermore, the feasibility of the scattering matrix method is explained. Supported by the National Natural Science Foundation of China (Grant Nos. 10774093 and 10374061)     

The influence of spin-flip scattering on the preparation and detection of a single spin state in a quantum dot attached to a spin battery

Recently, the possibility of an all electrical scheme of preparation and readout for a single spin state in a single quantum dot attached to spin biased leads has been shown [F. Chi et al. Phys. Rev. B 81, 075310 (2010)]. However, spin scattering mechanisms have been omitted. To remedy this lack we consider the influence of the spin-flip scattering process on the proposed preparation and readout scheme.     

L-酪氨酸与四氯对苯醌的荷移反应

L-酪氨酸与四氯对苯醌发生荷移反应 ,生成稳定的 2∶ 1络合物 ,其 λmax=348nm,表观摩尔吸光系数ε=9.5× 10 3 L·mol-1·cm-1,在 1.2 5— 12 .5 μg· m L-1的范围内符合比耳定律 ,用于测定药物样品含量 ,与文献方法测定结果一致 ,回收率 99.7%— 10 0 .2 % ,相对标准偏差在 1.5 %以内     

Random error of determining light scattering matrix elements at various polarization states of probing radiation

Using the method of mathematical modeling, we consider the transformation of a random error of light intensity measurement into an error of determining elements of the light scattering matrix. We consider a device in which the polarization properties of probing radiation change depending on the setting of the phase plate and polarization analysis of scattered radiation is performed while the second phase plate located ahead of a stationary analyzer is rotated. A set of settings of the first phase plate has been revealed, which provides a minimum random error in determining the scattered light matrix elements. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 4, pp. 520–523, July–August, 2000.     

牛磺酸与对苯醌的荷移反应

用分光光度法研究牛磺酸与对苯醌的荷移反应.实验表明,牛磺酸与对苯醌在pH 8.5的三酸缓冲溶液中,90℃水浴加热20min,可生成稳定的荷移络合物.荷移络合物的组成比为2∶1,最大吸收波长λmax=339nm,表观摩尔吸光系数ε=5.9×104L/mol·cm,在4-180μg/mL的范围内符合比耳定律,回收率在96....     

Power output and efficiency of quantum dot attached to ferromagnetic electrodes with non-collinear magnetic moments

Non-linear charge and heat transport through a single-level quantum dot in the Coulomb blockade regime is investigated within the framework of non-equilibrium Green function formalism and power output and efficiency of the device are studied. It is found that maximum power as well as efficiency depends on the relative orientation of magnetic moments in electrodes and can vary with polarization factor p. In general, power output is suppressed in magnetic systems and decreases with polarization. The highest efficiency can be attained in antiparallel configuration, and moreover, it does not depend on p. Spin power as well as spin efficiency of the system is introduced and discussed. It is also shown that in the Coulomb blockade regime the (spin) efficiency of the device operating under maximum power conditions varies with temperature bias in a non-monotonic way and shows a flat maximum for low ΔT.