Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach

A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovian bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the fermion or boson bath interaction are found to be of the same path integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism is different due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed. (c) 2007 American Institute of Physics.

Quantum master equation scheme of time-dependent density functional theory to time-dependent transport in nanoelectronic devices

In this work a practical scheme is developed for the first-principles study of time-dependent quantum transport. The basic idea is to combine the transport master equation with the well-known time-dependent density functional theory. The key ingredients of this paper include (i) the partitioning-free initial condition and the consideration of the time-dependent bias voltages which base our treatment on the Runge-Gross existence theorem; (ii) the non-Markovian master equation for the reduced (many-body) central system (i.e., the device); and (iii) the construction of Kohn-Sham master equations for the reduced single-particle density matrix, where a number of auxiliary functions are introduced and their equations of motion (EOMs) are established based on the technique of spectral decomposition. As a result, starting with a well-defined initial state, the time-dependent transport current can be calculated simultaneously along with the propagation of the Kohn-Sham master equation and the EOMs of the auxiliary functions.

Formal specification and refinement of a safe train control function

Motivated by the design and development challenges of the BART case study, an approach for developing and analyzing a formal model for reactive systems is presented. The approach makes use of a domain specific language for specifying control algorithms able to satisfy competing properties such as safety and optimality. The domain language, called SPC, offers several key abstractions such as the state, the profile, and the constraint to facilitate problem specification. Using a high-level program transformation system such as HATS being developed at the University of Nebraska at Omaha, specifications in this modelling language can be transformed to ML code. The resulting executable specification can be further refined by applying generic transformations to the abstractions provided by the domain language. Problem dependent transformations utilizing the domain specific knowledge and properties may also be applied. The result is a significantly more efficient implementation which can be used for simulation and gaining deeper insight into design decisions and various control policies. The correctness of transformations can be established using a rewrite-rule based induction theorem prover Rewrite Rule Laboratory developed at the University of New Mexico.

An automata theoretic decision procedure for the propositional mu-calculus

The propositional mu-calculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the propositional dynamic logic of Fischer and Ladner, the infinite looping construct of Streett, and the game logic of Parikh. We give an elementary time decision procedure, using a reduction to the emptiness problem for automata on infinite trees. A small model theorem is obtained as a corollary.

A logic for default reasoning

The need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds. Inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations. It is this property which leads to the non-monotonicity of any logic of defaults. In this paper we propose a logic for default reasoning. We then specialize our treatment to a very large class of commonly occuring defaults. For this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover. Finally, we provide criteria under which the revision of derived beliefs must be effected.

automatic construction of finite algebras

This paper deals withmodel generation for equational theories, i.e., automatically generating (finite) models of a given set of (logical) equations. Our method of finite model generation and a tool for automatic construction of finite algebras is described. Some examples are given to show the applications of our program. We argue that, the combination of model generators and theorem provers enables us to get a better understanding of logical theories. A brief comparison between our tool and other similar tools is also presented.

Green's function of a two-dimensional interacting electron gas in a perpendicular magnetic field

It is rigorously proved that the Green's function of a uniform two-dimensional interacting electron gas in a perpendicular magnetic field is diagonal with respect to single-particle states in the Landau gauge. The implication of this theorem is briefly discussed.

Theoretical and experimental investigations of flexural wave propagation in periodic grid structures designed with the idea of phononic crystals

The propagation characteristics of fiexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11 × 11 unit cells. The fiexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.

基于Isabelle定理证明器算法程序的形式化验证

形式化验证对保证软件的正确性和可靠性具有十分重要的意义.定理机械证明是形式化验证的一个重要研究领域,Isabelle系统是一个被广泛运用的定理证明辅助工具.本文在分析Dijkstra最弱前置谓词理论的基础上,根据PAR方法开发的算法程序循环不变式,提出了一种使用Isabelle定理证明器对算法程序进行机械验证的方法.该方法既克服了传统手工验证过程的繁琐性和易错性等缺点,又达到"提高验证效率和保证算法程序高可信"的目标,具有很好的实用价值.

界面张力引起的流动及界面特征研究

通过对单层流体浮力－热毛细对流和两层流体 B$\acute{\rm e}$nard-Marangoni对流的实验研究，探讨界面张力梯度引起的自然对流的特征及机理问题。考虑到表面张力是温度的函数，对上面是空气(或其蒸汽)的薄液层，加载水平温度梯度将使得气液表面上表面张力分布不均匀，耦合于地面的重力作用，将会驱动薄层流体形成浮力－热毛细对流运动。液层厚度和温度梯度的改变(引起系统长高比、Bond数、Rayleigh数以及Marangoni数的变化)直接影响到薄层流体的对流模式的变化，还可能使得浮力－热毛细对流从稳定发展到不稳定。本研究中以硅油为实验介质，应用高分辨率PIV技术对薄层流体的对流速度场进行了测量，观察到了对流由单胞结构向多胞结构以及由稳定对流向振荡对流的转捩过程，分析给出了对流模式结构变化的规律以及状态转变的临界参数。在浮力－热毛细对流发展过程中，流体表面的变形(形貌)和表面振荡直接反映了热毛细作用与浮力作用的耦合规律以及热毛细对流表面波的基本特征。实验中应用激光干涉技术以及高精度位移传感器对薄液层体系(液层厚度1mm$\sim$5mm)作了系统的研究，获得了微米量级面形形貌变化规律及其亚微米尺度的表面振荡特性。用FFT以及小波分析方法研究了流体自由面振荡的分岔转捩过程及通往混沌的转捩途径。该研究对理解流体热毛细对流的机理具有重要的意义。在自然界里和工程技术中，多层流体体系对流现象更为普遍。近20年来，互不混溶的两层液体体系成为了很多理论和实验研究的重要对象，其主要原因有：(1)在两层流体体系中，由于上下层对流的耦合作用，在临界点上存在HOPF分叉，使得两层模型成为非线性理论研究的理想模型；(2)两层流体模型被应用于地壳运动的研究和空间晶体生长等领域。近年，很多学者通过理论分析和数值模拟对加载垂直温度梯度的上下两层流体B$\acute{\rm e}$nard-Marangoni对流问题进行了研究。上下液层对流的耦合与竞争可以导致上下液层出现多种对流耦合模式和振荡规律，外加温差、液层厚度以及液层厚度比的变化是形成不同对流模式的重要因素。本研究以FC70和KF90-10为实验介质，应用高分辨率PIV技术对两薄层流体B$\acute{\rm e}$nard-Marangoni对流进行了测量，从实验中清晰地观测到了3种临界对流模式：机械耦合、热耦合、临界振荡，分析给出了3种对流转换的临界参数，发现临界振荡可以在峰值液层厚度比附近一个较大的区域范围出现，并且峰值厚度比远离平衡厚度比，这些结果与目前的理论研究有明显的的差异。总之，两种不同外加温度梯度方式，会导致两种不同机制的对流--热毛细对流和Marangoni对流，他们是微重力流体物理研究的重要内容。

Improvement of FEM's dynamic property

The discretization size is limited by the sampling theorem, and the limit is one half of the wavelength of the highest frequency of the problem. However, one half of the wavelength is an ideal value. In general, the discretization size that can ensure the accuracy of the simulation is much smaller than this value in the traditional finite element method. The possible reason of this phenomenon is analyzed in this paper, and an efficient method is given to improve the simulation accuracy.

SU(2)Chern-Simons涡旋解的拓扑结构

运用规范势分解理论研究了Dunne-Jackiw-Pi-Trugenberger模型中的自对偶方程,得到一个静态的自对偶Chern-Simons多涡旋解,每个涡旋由5个参数描述。发现了自对偶解与拓扑数之间的关系,而拓扑数由Brouwer度与Hopf指标确定。同时,也研究了该涡旋解的磁通量的拓扑量子化。

Topological structure of the many vortices solution in Jackiw-Pi model

By using the gauge potential decomposition, we discuss the self-dual equation and its solution in Jackiw-Pi model. We obtain a new concrete self-dual equation and find relationship between Chern-Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees of Psi-mapping. To show the meaning of topological number we give several figures with different topological numbers. In order to investigate the topological properties of many vortices, we use five parameters (two positions, one scale, one phase per vortex and one charge of each vortex) to describe each vortex in many vortices solutions in Jackiw-Pi model. For many vortices, we give three figures with different topological numbers to show the effect of the charge on the many vortices solutions. We also study the quantization of flux of those vortices related to the topological numbers in this case.