Time dependent Schrödinger equation for black hole evaporation: No information loss

In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state”. ¹ This was the starting point of the popular “black hole (BH) information paradox”.     

管理中的Nash平衡与Braess悖论现象

本给出了交通规划、经济贸易以及其它管理中的一些Nash平衡和Braess悖论实例，分析了Nash平衡和Braess悖论现象及其本质特征，指出它们在管理工作中具有普遗性和潜在应用性。     

Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

The Downs-Thomson Paradox: Existence, Uniqueness and Stability of User Equilibria

Consider a network where two routes are available for users wishing to travel from a source to a destination. On one route (which could be viewed as private transport) service slows as traffic increases. On the other (which could be viewed as public transport) the service frequency increases with demand. The Downs-Thomson paradox occurs when improvements in service produce an overall decline in performance as user equilibria adjust. Using the model proposed by Calvert [10], with a ⋅|M|1 queue corresponding to the private transport route, and a bulk-service infinite server queue modelling the public transport route, we give a complete analysis of this system in the setting of probabilistic routing. We obtain the user equilibria (which are not always unique), and determine their stability.AMS subject classification: 60K30, 90B15, 90B20, 91A10, 91A13This revised version was published online in June 2005 with corrected coverdate     

The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars. ¹ Both authors contributed equally to this paper.     

Lorentz-Compton佯谬与一个双赢判决性散射实验设计

通过对“可见光区域是否存在Compton效应”的讨论而进一步深化到经典条件下“光的量子理论能否包含光的经典电磁理论”的实验验证,发现了Lorentz-Compton佯谬,并基于逆Compton散射设计了一个敏感而又可行的双赢判决性散射实验来解决此佯谬。     

Twin Paradox and the Logical Foundation of Relativity Theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND.     

《务虚笔记》:两极悖论的沉思

中国当代文坛因为有了史铁生才显得不那么浅陋与浮华,在繁华人生的热闹处,他显得孤独而凄惶。但是,他对人的生与死、苦与乐、爱与欲、残与全等等人们本不该忽略的大命题进行了深入而有力的拷问。面对人类无法挣脱的多种根本性的生存困境,他以自己的生命来思考,并给我们指引了一条通向理想天国的朝圣之路。     

全球化语境中的"民族国家悖论"及其哲学维度

通过揭示全球化语境中民族国家在全球主义和民族主义两大对立思潮的挑战下的“悖反”处境，从哲学维度，以唯物史观的基本原理和相关理论为方法论基础，对民族国家这一现代最具普遍性的政治形式的历史建构、基本要素和在全球化时代面临的现实挑战以及未来发展趋势进行总体性研究和概括性把握。     

洛伦兹变换的地位、作用及其物理意义

洛伦兹变换是一物理事件相对两个不同惯性系之间的时空坐标变换方程。它以严谨的数学语言反映了狭义相对论新的时空观。由此统一了物理学中的宏观低速领域与微观高速领域。并为现代物理学的发展提供了广阔的空间。本用定性的物理分析和定量的数学推导相结合。着重阐述了洛伦兹变换在狭义相对论中的地位、作用及其物理意义。