Electron teleportation with quantum dot arrays

An electron teleportation protocol, inspired by the scenario by Bennett et al., is proposed in a mesoscopic set-up. A superconducting circuit allows to both inject and measure entangled singlet electron pairs in an array of three normal quantum dots. The selection of the teleportation process is achieved in the steady state with the help of two superconducting dots and appropriate gating. Teleportation of the electron spin is detected by measuring the spin-polarized current through the normal dot array. This current is perfectly correlated to the pair current flowing inside the superconducting circuit. The classical channel required by Bennett's protocol, which signals the completion of a teleportation cycle, is identified with the detection of an electron pair charge in the superconducting circuit. Received 10 December 2002 / Received in final form 14 March 2003 Published online 7 May 2003     

Do performed optical tests disprove local realism?

In all the earlier performed optical experiments on the Einstein, Podolsky, and Rosen paradox additional assumptions have been introduced and inequalities stronger than Bell's original one have been deduced. It is stressed that these experimental results violate these stronger inequalities but are compatible with Bell's original inequality. Therefore the experiments in question cannot provide a conclusive proof of the violation of local realism in nature but probably only show that the additional assumptions are not true.     

Generalized Vogel law for glass-forming liquids

A model for non-Arrhenius structural and dielectric relaxation in glass-forming materials is based on defect clustering in supercooled liquids. Relaxation in the cold liquid is highly hindered, and assumed to require the presence of a mobile defect to loosen the structure near it. A mild distribution of free-energy barriers impeding defect hopping can generate a wide distribution of waiting times between relaxation events. When the mean waiting time is longer than the time of an experiment, no characteristic time scale exists. This case directly yields the Kohlrausch-Williams-Watts (KWW) relaxation law. A free-energy mismatch between defect and nondefect regions produces a defect-defect attraction, which can lead to aggregation. This may occur in defect-rich fragile liquids which also exhibit Vogel kinetics. Defect aggregation and correlation in the high-temperature region above the critical consolute temperatureT _c is described using the Ornstein-Zernike theory of critical fluctuations. For a defect correlation length divergence (T-T _c)^-/2, a generalized Vogel law for the structural relaxation time results: =₀exp[B./(T-T _c)^1.5] In the mean-field limit (=1) this provides as good an account of dielectric and structural relaxation in glycerol,n-propanol, andi-butyl bromide as does the original Vogel law, and for the mixed salt KNO₃–Ca(NO₃)₂ and B₂O₂ it also describes kinetics over their entire temperature ranges. A breakdown of the Vogel law in the immediate vicinity ofT _g is avoided, and the need to invoke extra low-temperature mechanisms to explain an apparent return to Arrhenius behavior is removed.This paper is dedicated to Prof. N. G. van Kampen on the occasion of his 67th birthday.     

狭义相对论中的与门佯谬

提出了一个所谓“与门佯谬”问题,并利用狭义相对论进行了详细的分析和计算,消除和此佯谬。     

用“帕普斯——古尔丁定理”解释“喇叭悖论”

对帕普斯——古尔丁定理给出了证明,并将之用于解释喇叭悖论.     

New distribution formulas for classical gas, clusters, and phase transitions

We obtain a Bose-Einstein-type distribution for the classical vapor. We show that the analogue of the Bose condensate is the formation of clusters. We write a new PV diagram for interaction with the form of the Lennard-Jones potential using scattering theory and a strict constraint. We compare our results with experimental data. Dedicated to the memory of a dear friend, Tolya Karatsuba __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 2, pp. 250–272, November, 2008.     

Space-Time Trigonometry and Formalization of the “Twin Paradox” for Uniform and Accelerated Motions

The formal structure of the early Einstein’s Special Relativity follows the axiomatic deductive method of Euclidean geometry. In this paper we show the deep-rooted relation between Euclidean and space-time geometries that are both linked to a two-dimensional number system: the complex and hyperbolic numbers, respectively. By studying the properties of these numbers together, pseudo-Euclidean trigonometry has been formalized with an axiomatic deductive method and this allows us to give a complete quantitative formalization of the twin paradox in a familiar “Euclidean” way for uniform motions as well as for accelerated ones.     

D'Alembert's paradox, 1900–1914: Levi-Civita and his Italian and French followers

Before the First World War, Tullio Levi-Civita (1873–1941) was already a well-known mathematician in Italy and abroad, in particular in France. Professor at the University of Padua since 1898, he had published important contributions to tensor calculus, theory of relativity, differential geometry, hydrodynamics, and the three-body problem. In 1918, when he moved to the University of Rome, he created an international school of mathematics. In this paper, we focus on d'Alembert's paradox to which Levi-Civita and some of his Italian and French followers contributed remarkable solutions. This case-study is used to illustrate Levi-Civita's approach to hydrodynamics and its influence in Italy and France, especially in the period 1910–1914.