基于运输问题悖论的最大运量问题以及运价合理性的研究

该文提出了判断运输问题悖论是否存在的对偶规划条件以及目标函数差值模型,并针对运输悖论中存在的两个颇有实际意义的问题:增加运量而总运费不增的最大调整量问题以及产销地的单位运价不合理问题,给出了用以获得最大运量调整方案的最大供需量模型以及通过改变不合理运价来消除悖论的合理定价法,并辅以实例加以验证。     

EPR entangled states and complex fractional Fourier transformation

Starting from the Einstein-Podolsky-Rosen entangled state representations of continuous variables we derive a new formulation of complex fractional Fourier transformation (CFFT). We find that two-variable Hermite polynomials are just the eigenmodes of the CFFT. In this way the CFFT is linked to the appropriate operator transformation between two kinds of entangled states in the context of quantum mechanics. In so doing, the CFFT of quantum mechanical wave functions can be derived more directly and concisely. Received 21 February 2002 / Received in final form 1st June 2002 Published online 24 September 2002 RID="*" ID="*"Work supported by National Natural Science Foundation of China under grant 10175057 and the President Foundation of Chinese Academy of Science. RID="a" ID="a"e-mail: fhym@ustc.edu.cn     

Noninertial Observers in Special Relativity and Clock Synchronization Debates

Selleri's arguments that a consideration of noninertial reference frames in the framework of special relativity identify “absolute simultaneity” as being “Nature's choice of synchronization” are considered. In the case of rectilinearly accelerating rockets, it is argued by considering two rockets which maintain a fixed proper separation rather than a fixed separation relative to the inertial frame in which they start from rest, that what seems the most “natural” choice for a simultaneity convention is problem-dependent and that Einstein's definition is the most “natural” (though still conventional) choice in this case. In addition, the supposed problems special relativity has with treating a rotating disk, namely how a pulse of light traveling around the circumference of the disk can have a local speed of light equal to c everywhere but a global speed not equal to c, and how coordinate transformations to the disk can give the Lorentz transformations in the limit of large disk radius but small angular velocity, are addressed. It is shown that the theory of Fermi frames solves both of these problems. It is also argued that the question of defining simultaneity relative to a uniformly rotating disk does not need to be resolved in order to resolve Ehrenfest's paradox.     

The Free Will Theorem

On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic and causal. We also establish the consistency of our axioms and discuss the philosophical implications.     

Quantum telegraph: is it possible?

The use of Einstein-Podolsky-Rosen (EPR) correlated microparticles for telecommunication purposes is considered from a new point of view. In spite of the fact that the usual nonlocality of EPR pairs is not controllable, the use of irreversible quantum systems opens new possibilities. A concrete scheme for a controllable correlated quantum system is considered. It might be used for non-wave-type communication over not very large distances.     

The Einstein–Podolsky–Rosen Effect: Paradox or Gate?

The Einstein–Podolsky–Rosen (EPR) paradox represents one of the most controversial aspects of quantum mechanics (QM). In this paper, we suggest that it can be solved by taking into account the fact that physical quantum phenomena can be extended backward in time (i.e. we take into account two arrows of time instead of one). We derive such a strong statement as a consequence of symmetries and conservation laws implying field equations which are invariant under time reversal. Our approach, violating Einstein's locality postulate, confirms QM predictions and explains the failure of Bell's inequalities.     

关于两篇文章的一点注记

本文就LP问题多解判定及LP问题“悖论”产生提出一些简单的诠释或说明或简例。     

Pairwise entanglement in symmetric multi-qubit systems

For pairs of particles extracted from a symmetric state of N two-level systems, the two-particle density matrix is expressed in terms of expectation values of collective spin operators for the large system. Results are presented for experimentally relevant examples of pure states: Dicke states | S, M>, spin coherent, and spin squeezed states, where only the symmetric subspace, S = N/2 is populated, and for thermally entangled mixed states populating also lower S values. The entanglement of the extracted pair is then quantified by a calculation of the concurrence, which provides directly the entanglement of formation of the pair. Received 9 May 2001 and Received in final form 16 November 2001     

Decomposition of pure states of quantum register

The generalization of Schmidt decomposition due to Cartelet-Higuchi-Sudbery applied to quantum register (a system of N qubits) is shown to acquire direct geometrical meaning: any pure state is canonically associated with a chain of a simplicial complex. A leading vector method is presented to calculate the values of the coefficients of appropriate chain.     

A new explanation of the extinction paradox

This work presents a new explanation for the extinction paradox and shows that the canonical explanations are incorrect. This paradox refers to the large size limit of a particle's extinction cross section. It is called a paradox because the geometrical optics approximation, which should be valid in this limit, predicts a cross section that is half of the true value. The new explanation is achieved by formulating the scattered wave in terms of an integral over the particle's surface where the seemingly unrelated Ewald-Oseen theorem appears in the formulation. By expressing the cross section in terms of this surface integral, the Ewald-Oseen theorem is analytically connected to the cross section. Several illustrations are used to reveal the significance of this connection: The paradox is seen to be a consequence of the requirement that the incident wave be canceled within the particle by secondary radiation from its own internal field. Following this, the canonical explanations are examined to reveal serious problems. In the process, the same asymptotic extinction behavior is shown to occur for small highly refractive dielectric particles, and thus is not just a large particle size or small wavelength effect as is often stated. The traditional explanations cannot account for this behavior while the new one actually predicts it. All in all, this work constitutes a fundamental reworking of 60 years of accepted understanding for the cause of the asymptotic behavior of the extinction cross section.