On Computability of Decaying and Nondecaying States in Quantum Systems with Cantor Spectra

We study Hamiltonians with singular spectra of Cantor type with a constant ratio of dissection. The decay properties of the states in such systems depend on the nature of the dissection rate that can be characterized in terms of the algebraic number theory. We show that in spite of simplicity of the considered model the computational modeling of nondecaying states is in general impossible.     

Correct Evaluation of the Effect of Transverse Effective Charges on Phonons in AlAs Quantum Dots

An improved valence force field model (VFFM) is suggested to calculate the phonon modes in both bulk specimens and quantum dots (QDs) of AlAs taking account of the effect of transverse effective charges (TCs) correctly.The resultant dispersions of AlAs bulk phonons are in accord better with the results carefully fitted to the experimental data by using 11-parameters rigid-ion model, than those got by ordinary VFFM, especially in the region of near F point. For AlAs QDs, TCs are evaluated bond by bond for each phonon mode of QD and its effect on the change of the force on atoms is taken into account to modify further the phonon spectrum. The frequency spectra and densities of phonon states of different irreducible representations calculated by using improved VFFM are compared with the results of ordinary VFFM. The correct evaluation of the TCs is not only important in calculating the phonon spectrum of both bulk and QD specimens accurately, but is also in the further discussion of the electron-phonon (e-ph) interaction, which can be directly related to TCs of ions in QD.     

广义非简谐振子的多尺度微扰理论

应用多尺度微扰理论到广义非简谐振子, 得到了一阶经典和量子微扰解. 特别是 我们的量子解在极限条件下能方便地转变为经典解, 并且坐标和动量算符的对易 关系的简化十分自然. 与Taylor级数解相比较, 无论是在经典还是在量子解 中频率移动都出现在各阶振动表达式中, 所以多尺度微扰解是弱耦合非简谐振动的较好解法.     

一种新型频域均衡器在水声通信中的应用

在传统频域均衡器的基础上,结合多载波频移键控调制方式的频谱结构,利用接收信号和参考信号的相关性及均衡器的滤波系数,提出了一种兼具均衡与解调功能的新型频域均衡器结构.该均衡器简单、有效地克服了水声信道中多径传播产生的码间干扰和频率选择性衰落等问题,简化了水声通信系统接收机的复杂度. 新型频域均衡器的解调原理以非相关解调算法为基础,但由于利用了均衡器的计算结果,其差错性能优于传统的非相关解调算法,计算机仿真试验表明,改进后的方法使差错性能提高了2 dB;实际水声通信实验表明,该均衡器能够有效地提高水声通信系统的可靠性,具有很好的应用前景.     

Formation of long range ordered arrangement of quantum dots with the help of lateral centripetal flow

A simple “chimney” method was used to eliminate the voids in an arrangement of quantum dots sized 2 nm on a solid substrate, which resulted in a large well ordered superlattice of area in the order more than 1 μm². Based on the principle of speeding up the interparticle interaction of nanoparticles to overcome the particle-substrate one, a lateral centripetal force originated from a glass tube acting as a chimney in a simple evaporation device is imposed. This method allows the packing process to be controlled in a mechanical force field, that is, with the same nanogold dispersion different patterns on a substrate—from separate dots to an ordered compact monolayer or even a multilayer structure—could be easily obtained.     

Symmetric form of the Hudson-Parthasarathy stochastic equation

We prove that the Hudson-Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 726–750, November, 1996.     

Noncommutative differential geometry on the quantum SU(2), I: An algebraic viewpoint

We compute the cyclic homology of the coordinate ring A(SL_q(2)) of the quantum algebraic group SL _q (2). We observe a degeneration of the noncommutative de Rham complex. The results are also verified from the point of view of Connes' noncommutative differential geometry.     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.