An indirect approach for quantum-mechanical eigenproblems: duality transforms

We suggest an indirect approach for solving eigenproblems in quantum mechanics. Unlike the usual method, this method is not a technique for solving differential equations. There exists a duality among potentials in quantum mechanics. The first example is the Newton–Hooke duality revealed by Newton in Principia. Potentials that are dual to each other form a duality family consisting of infinite numbers of family members. If one potential in a duality family is solved, the solutions of all other potentials in the family can be obtained by duality transforms. Instead of directly solving the eigenequation of a given potential, we turn to solve one of its dual potentials which is easier to solve. The solution of the given potential can then be obtained from the solution of this dual potential by a duality transform. The approach is as follows: first to construct the duality family of the given potential, then to find a dual potential which is easier to solve in the family and solve it, and finally to obtain the solution of the given potential by the duality transform. In this paper, as examples, we solve exact solutions for general polynomial potentials.     

String Cosmological Solutions with O(d,d) Duality Symmetry and Matter Coupling

The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.     

广义量子干涉原理及对偶量子计算机

我们综述最近提出的广义量子干涉原理及其在量子计算中的应用。广义量子干涉原理是对狄拉克单光子干涉原理的具体化和多光子推广,不但对像原子这样的紧致的量子力学体系适用,而且适用于几个独立的光子这样的松散量子体系。利用广义量子干涉原理,许多引起争议的问题都可以得到合理的解释,例如两个以上的单光子的干涉等问题。从广义量子干涉原理来看双光子或者多光子的干涉就是双光子和双光子自身的干涉,多光子和多光子自身的干涉。广义量子干涉原理可以利用多组分量子力学体系的广义Feynman积分表示,可以定量地计算。基于这个原理我们提出了一种新的计算机,波粒二象计算机,又称为对偶计算机。在原理上对偶计算机超越了经典的计算机和现有的量子计算机。在对偶计算机中,计算机的波函数被分成若干个子波并使其通过不同的路径,在这些路径上进行不同的量子计算门操作,而后这些子波重新合并产生干涉从而给出计算结果。除了量子计算机具有的量子平行性外,对偶计算机还具有对偶平行性。形象地说,对偶计算机是一台通过多狭缝的运动着的量子计算机,在不同的狭缝进行不同的量子操作,实现对偶平行性。目前已经建立起严格的对偶量子计算机的数学理论,为今后的进一步发展打下了基础。本文着重从物理的角度去综述广义量子干涉原理和对偶计算机。现在的研究已经证明,一台d狭缝的n比特的对偶计算机等同与一个n比特+一个d比特(qudit)的普通量子计算机,证明了对偶计算机具有比量子计算机更强大的能力。这样,我们可以使用一台具有n+log2d个比特的普通量子计算机去模拟一个d狭缝的n比特对偶计算机,省去了研制运动量子计算机的巨大的技术上的障碍。我们把这种量子计算机的运行模式称为对偶计算模式,或简称为对偶模式。利用这一联系反过来可以帮助我们理解广义量子干涉原理,因为在量子计算机中一切计算都是普通的量子力学所允许的量子操作,因此广义量子干涉原理就是普通的量子力学体系所允许的原理,而这个原理只是是在多体量子力学体系中才会表现出来。对偶计算机是一种新式的计算机,里面有许多问题期待研究和发展,同时也充满了机会。在对偶计算机中,除了幺正操作外,还可以允许非幺正操作,几乎包括我们可以想到的任何操作,我们称之为对偶门操作或者广义量子门操作。目前这已经引起了数学家的注意,并给出了广义量子门操作的一些数学性质。此外,利用量子计算机和对偶计算机的联系,可以将许多经典计算机的算法移植到量子计算机中,经过改造成为量子算法。由于对偶计算机中的演化是非幺正的,对偶量子计算机将可能在开放量子力学的体系的研究中起到重要的作用。     

Allowable Generalized Quantum Gates

In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form ∑i=0^d-1piUi,and the pi ＇s are complex numbers with module less or equal to 1 and constrained by｜∑iPi｜≤1.     

新型4d/5d基超导体的结构和物性

在强关联电子体系中,轨道、自旋和晶格等自由度之间的相互作用一直是研究的热点.这些自由度之间的竞争和共存产生了复杂新奇的物理现象,如超导现象、量子相变、自旋有序、拓扑相变、金属绝缘转变等,这些丰富的物理现象来源于不同的有序态或量子涨落之间的竞争和耦合.自旋轨道耦合作用是指粒子的自旋角动量和轨道角动量之间的相互作用,在4d/5d基化合物中,由于电子的运动速度较快,自旋轨道耦合的效应不可忽视,可能表现出与3d基化合物不同的物性.例如,在含4d/5d过渡族金属元素的超导体中,其电子配对的机制可能不同于常规的s波Bardeen-Cooper-Schrieffer超导体.本文以几种典型的4d/5d基超导体为例,对其晶体结构和超导物性及其内在联系进行了详细论述,重点探讨了阴离子共价键强弱对晶体结构、相变和超导物性的影响,希望引起相关研究者对该类超导体的重视.     

A new approach to the ϱ-meson in QCD

We examine whether strict local duality between the asymptotic and the resonance region, which is of course believed to be valid in QCD, already appears at the present stage of QCD calculations. For this purpose we propose a new method of stable analytic extrapolation which follows the spirit of a previously used method but has essential advantages compared to the original formulation. A careful analysis of the present QCD ?-amplitude leads indeed to a prominent bump structure in the resonance region. This is a first evidence for the validity of strictly local duality within QCD.     

Algebraic resolution of the duality ansatz for poincaré gauge fields

It has been known for sime time that exact torsion solutions of the Poincaré gauge theory with duality properties “live” on Einstein spaces. Via a (3+1)-decomposition we are now able to resolve the modified double duality ansatz for the Riemann-Cartan curvature in the static case. Thereby the independent linear connection can be expressed explicitly in terms of a given einsteinian coframe.     

Flux compactifications of string theory on twisted tori

Global aspects of Scherk‐Schwarz dimensional reduction are discussed and it is shown that it can usually be viewed as arising from a compactification on the compact space obtained by identifying a (possibly non‐compact) group manifold 𝒢 under a discrete subgroup Γ, followed by a truncation. This allows a generalisation of Scherk‐Schwarz reductions to string theory or M‐theory as compactifications on 𝒢/Γ, but only in those cases in which there is a suitable discrete subgroup of 𝒢. We analyse such compactifications with flux and investigate the gauge symmetry and its spontaneous breaking. We discuss the covariance under O(d,d), where d is the dimension of the group 𝒢, and the relation to reductions with duality twists. The compactified theories promote a subgroup of the O(d,d) that would arise from a toroidal reduction to a gauge symmetry, and we discuss the interplay between the gauge symmetry and the O(d,d,ℤ T‐duality group, suggesting the role that T‐duality should play in such compactifications.     

Reflectionless Analytic Difference Operators II. Relations to Soliton Systems

Abstract

This is the second part of a series of papers dealing with an extensive class of analytic difference operators admitting reflectionless eigenfunctions. In the first part, the pertinent difference operators and their reflectionless eigenfunctions are constructed from given “spectral data”, in analogy with the IST for reflectionless Schrödinger and Jacobi operators. In the present paper, we introduce a suitable time dependence in the data, arriving at explicit solutions to a nonlocal evolution equation of Toda type, which may be viewed as an analog of the KdV and Toda lattice equations for the latter operators. As a corollary, we reobtain various known results concerning reflectionless Schrödinger and Jacobi operators. Exploiting a reparametrization in terms of relativistic Calogero–Moser systems, we also present a detailed study of N-soliton solutions to our nonlocal evolution equation.     

Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations

This article considers a posteriori error estimation and anisotropic mesh refinement for three-dimensional laminar aerodynamic flow simulations. The optimal order symmetric interior penalty discontinuous Galerkin discretization which has previously been developed for the compressible Navier–Stokes equations in two dimensions is extended to three dimensions. Symmetry boundary conditions are given which allow to discretize and compute symmetric flows on the half model resulting in exactly the same flow solutions as if computed on the full model. Using duality arguments, an error estimation is derived for estimating the discretization error with respect to the aerodynamic force coefficients. Furthermore, residual-based indicators as well as adjoint-based indicators for goal-oriented refinement are derived. These refinement indicators are combined with anisotropy indicators which are particularly suited to the discontinuous Galerkin (DG) discretization. Two different approaches based on either a heuristic criterion or an anisotropic extension of the adjoint-based error estimation are presented. The performance of the proposed discretization, error estimation and adaptive mesh refinement algorithms is demonstrated for 3d aerodynamic flows.     

Physics of strongly coupled quark-gluon plasma

This review covers our current understanding of strongly coupled Quark-Gluon Plasma (sQGP), especially theoretical progress in: (i) explaining the RHIC data by hydrodynamics; (ii) describing lattice data using electric-magnetic duality; (iii) understanding of gauge-string duality known as AdS/CFT and its application for “conformal” plasma. In view of the interdisciplinary nature of the subject, we include a brief introduction into several topics “for pedestrians”. Some fundamental questions addressed are: Why is sQGP such a good liquid? What is the nature of (de)confinement and what do we know about “magnetic” objects creating it? Do they play any important role in sQGP physics? Can we understand the AdS/CFT predictions, from the gauge theory side? Can they be tested experimentally? Can AdS/CFT duality help us understand rapid equilibration/entropy production? Can we work out a complete dynamical “gravity dual” to heavy ion collisions?     

Topology and H-flux of T-dual manifolds

We present a general formula for the topology and H-flux of the T-dual of a type II compactification. Our results apply to T-dualities with respect to any free circle action. In particular, we find that the manifolds on each side of the duality are circle bundles whose curvatures are given by the integral of the dual H-flux over the dual circle. As a corollary we conjecture an obstruction to multiple T-dualities, generalizing the obstruction known to exist on the twisted torus. Examples include SU(2) Wess-Zumino-Witten models, lens spaces, and the supersymmetric string theory on the nonspin AdS5 x CP2 x S1 compactification.     

Permutation complexity via duality between values and orderings

We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of all permutations of the same length. Second, on this basis, we give an elementary alternative proof of the equality between the permutation entropy rate and the entropy rate for a finite-state stationary stochastic processes first proved in [J.M. Amigó, M.B. Kennel, L. Kocarev, The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems, Physica D 210 (2005) 77-95]. Third, we show that further information on the relationship between the structure of values and the structure of orderings for finite-state stationary stochastic processes beyond the entropy rate can be obtained from the established duality. In particular, we prove that the permutation excess entropy is equal to the excess entropy, which is a measure of global correlation present in a stationary stochastic process, for finite-state stationary ergodic Markov processes.     

Minimum-error state discrimination and quantitative wave particle duality

We establish the link between minimum-error discrimination of two pure states and wave particle duality in two-path interferometers. In particular, the upper bound of the probability of success discrimination is derived directly from the corresponding duality relation. It is already known that quantum state discrimination can produce wave particle duality relations, here we show the converse is also true: Wave particle duality can be used to obtain information about state discrimination.     

Algebraic formulation of duality transformations for abelian lattice models

We derive duality relations for the generating functional of correlation-functions for disordered (“frustrated”) lattice Higgs and gauge models with arbitrary locally compact abelian symmetry groups. We examine the effects on duality of nontrivial lattice topology and of configurational boundary conditions. Technically, we employ some elementary concepts borrowed from algebraic topology. Combined with Fourier expansions on groups, they provide tools to handle functions on lattices in a very efficient way. For convenience, these concepts are described in some detail in the first part of the paper.     

Quantum equivalence of dual field theories

Motivated by the study of ultraviolet properties of different versions of supergravities duality transformations at the quantum level are discussed. Using the background field method it is proven on shell quantum equivalence for several pairs of dual field theories known to be classically equivalent. The examples considered include duality in chiral model, duality of scalars and second rank antisymmetric gauge tensors, vector duality and duality of the Einstein theory with cosmological term and the Eddington-Schrödinger theory.     

Evaluation and improvement of digital image correlation uncertainty in dynamic conditions

Dealing with a moving target causes a motion effect (i.e. blurring) on the acquired images. This factor is an important source of measurement uncertainty while exploiting the Digital Image Correlation (DIC) technique. Therefore, the present study aims to evaluate and improve DIC uncertainty in dynamic conditions in the case of translating target. The study focuses on 2D DIC. In the case of 3D DIC similar problems arise, and therefore a complete understanding of two dimensional conditions will be of great help for further studies which deal with 3D conditions. The whole work can be divided into two main parts. In the first part, two different methods to simulate the motion effect on a reference image are proposed, discussed and validated. These methods allow simulating the acquired images in a real dynamic test and estimating the measurement uncertainty caused by the motion effect. The validation is performed by conducting several harmonic vibration tests with an electromagnetic shaker. In the second part of the study a numerical technique is proposed to estimate the motion effect present in an acquired image. This technique gives two main advantages. First of all, since the motion effect itself has a known influence on the uncertainty of measurement (first part of the study), we can predict the DIC׳s uncertainty by just having an acquired image. Furthermore, this numerical technique is used in the last part of this work to improve the performances of DIC in dynamic applications. In this way the bias error and the uncertainty of measurements were considerably decreased.     

布阵声全息成象中复全息函数的实部与虚部的联系

本文提出一个从离散声全息成象的复全息函数实部导出其虚部的方法,以此虚部与原实部组成的复全息函数可以无共轭象地重建物象。方法的充分条件是物体线度小于或等于λz/2d,λ—波长,d—取样点间距,z—接收面与物间距离。作了计算机模拟计算,显示这方法的有效性。     

Survey of the present state of the art of piezoelectric linear motors

Piezoelectric ultrasonic motors have been investigated for several years and have already found their first practical applications. Their key feature is that they are able to produce a high thrust force related to their volume. Beside rotary drives like the travelling wave motor, linear drives have also been developed, but only a few are presently commercially available. In the present paper, we first describe the state of the art of linear piezoelectric motors. The motors are characterized with respect to their no-load velocity, maximum thrust force, efficiency and other technical properties. In the second part, we present a new motor, which is judged to be capable of surpassing the characteristics of other piezoelectric motors because of its unique design which allows the piezoelectric drive elements to be pre-stressed in the direction of their polarization. The piezoelectric elements convert energy using the longitudinal d33 effect which allows an improved reliability, large vibration amplitudes and excellent piezoelectric coupling. Energy loss by vibration damping is minimized, and the efficiency can be improved significantly. Experimental results show that the motor characteristics can be optimized for a particular task by choosing the appropriate operating parameters such as exciting voltage, exciting frequency and normal force.