Interpreting Observables in a Quantum World from the Categorial Standpoint

We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime.     

Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.     

The Study of MMW and MW Attenuation Considering Multiple Scattering Effect in Sand and Dust Storms at Slant Paths

The influence of sand and dust storms on modern MMW and satellite communication systems reliability have been paid more attention to. The attenuations induced by sand and dust storms are estimated by means of Mie-theory and Rayleigh approximation, in the case of the tenuous distribution of particles. With the particle density increasing, however, these method become inadequate, the multiple scattering effects then become dominant for attenuation estimation. The attenuations considering multiple scattering effects are estimated by Monte-Carlo and four fluxes method at horizontal paths. At slant paths, based on multi-layer media model, the attenuations considering multiple scattering effects are calculated by layered Monte-Carlo method at 100, 37, 24, and 14GHz. It is shown that the multiple scattering effects should be considered at the attenuation prediction in the sand and dust storm, which the visibility is about 0.5km and smaller than 0.5km and frequency is about 20GHz. Above 30GHz, the multiple scattering effects due to sand and dust particles should be considered, as visibility is about 1km and smaller than 1km at slant paths.     

Quantum Dynamics of Systems Connected by a Canonical Transformation

Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively.     

Lifetime analysis of quasibound states in coupled quantum wells

A simple time-dependent model is presented to investigate lifetimes of the quasibound states in coupled quantum wells (CQWs). The transfer matrix approach is employed to discretize the conduction-band profile of the heterostructure and form a dispersion equation whose zeros correspond to the complex eigenenergies. Both the bound and quasibound states are extracted numerically in the complex plane by Newton's method. The lower and higher well subbands are found to have negative and positive energy shift, respectively, as following the no level crossing theorem. Besides, the decay rate of the quasibound state is approximately proportional to the absolute energy shift. The quasibound states, which have larger energy shift, have shorter lifetime and decay more quickly. Furthermore, the differences in lifetime between the quasibound states in CQWs can be easily realized as all the wave functions are specially adjusted to form the relative probability density distributions.     

Remarks on Mohrhoff's Interpretation of Quantum Mechanics

In a recently proposed interpretation of quantum mechanics, U. Mohrhoff advocates original and thought-provoking views on space and time, the definition of macroscopic objects, and the meaning of probability statements. The interpretation also addresses a number of questions about factual events and the nature of reality. The purpose of this note is to examine several issues raised by Mohrhoff's interpretation, and to assess whether it helps providing solutions to the long-standing problems of quantum mechanics.     

Modeling of the Kinetics of Intramolecular Processes and Transient Spectra with Allowance for Nonradiative Transitions

It has been shown that the kinetics of intramolecular processes and time-resolved spectra with allowance for the quantum beats of the resonant states of isomers or isolated subsystems of levels of one isomeric form can be described with the use of a molecular model interpreting the effect of beats as a nonradiative transition. We have obtained an expression for the nonradiative transition probability, which is directly proportional to the beat frequency and depends oscillatorily on time, thus modeling the effect of beats. The parameter of the molecular system model is the beat frequency directly related to the parameter characterizing the intramolecular interisomeric interactions (the corresponding nondiagonal element of the energy matrix) rather than the value of the nonradiative transition probability. The character of the change in the level populations and, accordingly, in the band intensities in the spectra in the proposed model is in good agreement with the experiment, including the fine structure of the time dependences — oscillations of the line intensities. In analyzing the temporal experiment with a high resolution, it is necessary to take into account the instrument function leading to quantitative and qualitative changes in the time dependences. The traditional model of nonradiative transitions with a constant probability value has a very limited range of applicability — very high beat frequencies compared to the probability of optical transitions.     

利用拉曼型的Jaynes-Cummings模型传送两比特的未知原子态

实现量子态的隐形传送、尤其是多比特量子态的隐形传送在量子信息领域中有非常重要的作用，提出了一种隐形传送两比特未知原子态的方案，在此方案中，用两个两粒子纠缠态代替一个三粒子纠缠态作为量子信道，而且此方案可推广到隐形传送N比特的未知原子态。     

激发相干态下双模介观传输线的量子效应

将介观无损耗传输线中的驻波场看成作相对运动的两列同频率的行波的叠加，此电路量子化后成为两个频率相同、不同模的光子场。计算和分析了激发相干态下电压和电流梯度的量子涨落，指出了双模传输线与一般的LC电路、双模传输线与单模传输线量子涨落的异同之处。     

Tensor Products of Quantum Structures and Their Applications in Quantum Measurements

Tensor products of quantum logics and effect algebras with some known problems are reviewed. It is noticed that although tensor products of effect algebras having at least one state exist, in the category of complex Hilbert space effect algebras similar problems as with tensor products of projection lattices occur. Nevertheless, if one of the two coupled physical systems is classical, tensor product exists and can be considered as a Boolean power. Some applications of tensor products (in the form of Boolean powers) to quantum measurements are reviewed.