Characterization of entanglement transformation via group representation theory

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group SL(2, C) circle times SL(2, C), composed of local operators acting on the binary composite system, is realized in the four-dimensional complex space in terms of a set of novel bases that are pseudo-orthonormalized. The two-to-one homomorphism is then established for the group SL(2, C) circle times SL(2, C) onto the SO(4, C). It is shown that the resulting representation theory leads to the complete characterization for the entanglement transformation of the binary composite system.

听觉想象的大脑表征

As a species of internal representation, how is mental imagery organized in the brain? There are two issues related to this question: the time course and the nature of mental imagery. On the nature of mental imagery, today's imagery debate is influenced by two opposing theories: (1) Pylyshyn’s propositional theory and (2) Kosslyn’s depictive representation theory. Behavioural studies indicated that imagery encodes properties of the physical world, such as the spacial and size information of the visual world. Neuroimaging and neuropsychological data indicated that sensory cortex; especially the primary sensory cortex, is involved in imagery. In visual modality, neuroimaging data further indicated that during visual imagery, spatial information is mapped in the primary visual, providing strong evidences for depictive theory. In the auditory modality, behavioural studies also indicated that auditory imagery represents loudness and pitch of sound; this kind of neuroimaging evidence, however, is absent. The aim of the present study was to investigate the time course of auditory imagery processing, and to provide the neuroimaging evidence that imaginal auditory representations encode loudness and pitch information, using the ERP method and a cue-imagery (S1)-S2 paradigm. The results revealed that imagery effects started with an enhancement of the P2, probably indexing the top-down allocation of attention to the imagery task; and continued into a more positive-going late positive potentials (LPC), probably reflecting the formation of auditory imagery. The amplitude of this LPC was inversely related to the pitch of the imagined sound, but directly related to the loudness of the imagined sound, which were consistent with auditory perception related N1 component, providing evidences that auditory imagery encodes pitch and loudness information. When the S2 showed difference in pitch of loudness from the previously imagined S1, the behavioral performance were significantly worse and accordingly a conflict related N2 was elicited; and the high conflict elicited greater N2 amplitude than low conflict condition, providing further evidences that imagery is analog of perception and can encode pitch and loudness information. The present study suggests that imagery starts with an mechanism of top-down allocation of attention to the imagery task; and continuing into the step of imagery formation during which the physical features of the imagined stimulus can be encoded, providing supports to Kosslyn’s depictive representation theory.

Series representation of the Gaussian beam far-field diffracted by annular aperture

Accurate, analytical series expressions for the far-field diffraction of it Gaussian beam normally incident on a circular and central obscured aperture are derived with the help of the integration of parts method. With this expression, the far-field intensity distribution pattern can be obtained and the divergence angle is deduced too. Using the first five items of the series, the accuracy can satisfy most laser application fields. Compared with the conventional numerical integral method, the series representation is very convenient for understanding the physical meanings. (C) 2007 Elsevier GmbH. All rights reserved.

Unified theory for Goos-Hanchen and imbert-fedorov effects

A unified theory is advanced to describe both the lateral Goos-Hanchen (GH) effect and the transverse Imbert-Fedorov (IF) effect, through representing the vector angular spectrum of a three-dimensional light beam in terms of a two-form angular spectrum consisting of its two orthogonal polarized components. From this theory, the quantization characteristics of the GH and IF displacements are obtained, and the Artmann formula for the GH displacement is derived. It is found that the eigenstates of the GH displacement are the two orthogonal linear polarizations in this two-form representation, and the eigenstates of the IF displacement are the two orthogonal circular polarizations. The theoretical predictions are found to be in agreement with recent experimental results.

Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between different source functions, and its second order part represents the contribution of microscale wave propagation.