Particle Distribution in Quantum Field Theory

The change of the particle distribution in space-time is analysed in the framework of quantum field theory. The formalism is turned out to be thermo field dynamics. The formulation suggests a unification of quantum field theory and statistical physics.     

Particle Correlation in Quantum Field Theory

The paper deals with studies of the angular correlation of two mono-energetic particles produced in several fundamental processes in quantum field theory. The angular correlation is defined as the average (expectation value) of the cosine of the angle between the momenta of the two outgoing particles. A positive correlation indicates, in a statistical sense, that the particles tend to travel in the same directions (as in beam formation) while a negative one indicates that they tend to travel in opposing directions. The angular correlations for photons and electrons produced by sources, and in quantum eletrodynamics, to lowest order, γγ produced in e⁺e⁻ collision (annihilation), e⁺e⁻ pair production in γγ collision, and finally e⁺e⁻ pair production by a Nambu string are studied in detail.     

Physics of a Kind of Normally Ordered Gaussian Operators in Quantum Optics

Based on the technique of integration within an ordered product of operators we investigate a completeness relation of pure states （such as the coordinate eigenstate, the momentum eigenstate and the coherent state） into normally ordered Gaussian forms. The Weyl ordering invariance under similarity transformations is employed to reveal physical meaning of a kind of normally ordered Gaussian operators, which have the similar forms to the bivariate normal distributions in statistics, i.e., the thermo mixed state density matrix.     

Particle Trajectories for Quantum Field Theory

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic quantum field theories to generate dynamics for the underlying fields. However, it does not produce trajectories for the particles associated with these fields. Bell has shown that an extension of Bohm’s approach can be used to provide dynamics for the fermionic occupation numbers in a relativistic quantum field theory. In the present paper, Bell’s formulation is adopted and elaborated on, with a full account of all technical detail required to apply his approach to a bosonic quantum field theory on a lattice. This allows an explicit computation of (stochastic) trajectories for massive and massless particles in this theory. Also particle creation and annihilation, and their impact on particle propagation, is illustrated using this model.     

Quantum Random Walks with General Particle States

A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This unifies and extends previous work on repeated-interactions models, including that of Attal and Pautrat (Ann Henri Poincaré 7:59–104 2006) and Belton (J Lond Math Soc 81:412–434, 2010; Commun Math Phys 300:317–329, 2010). When the random-walk generator acts by ampliation and either multiplication or conjugation by a unitary operator, it is shown that the quantum stochastic cocycle which arises in the limit is driven by a unitary process.     

EPR States and Bell Correlated States in Algebraic Quantum Field Theory

A mathematical rigorous definition of EPR states has been introduced by Arens and Varadarajan for finite dimensional systems, and extended by Werner to general systems. In the present paper we follow a definition of EPR states due to Werner. Then we show that an EPR state for incommensurable pairs is Bell correlated, and that the set of EPR states for incommensurable pairs is norm dense between two strictly space-like separated regions in algebraic quantum field theory.     

Particle Correlation in Quantum Field Theory. II

This is the second and last instalment of the investigation of particle correlation in quantum field theory for fundamental processes with two-mono-energetic particle productions. The angular correlation is defined as the average (epectation value) of the cosine of the angle between the momenta of the two outgoing particles. A positive correlation indicates, in a statistical sense, that the particles tend to travel in the same directions (as in beam formation) while a negative one that they tend to travel in opposing directions. The angular correlation of γγ produced in pair annihilation of charged particles in scalar quantum electrodynamics, scalar-pair production by charged and neutral Nambu strings, as well as e⁺e^— pair-production by a Neutral Nambu string are studied in detail.     

A Quantum Particle in a One-Dimensional Fractal Field

Algorithms have been obtained for calculating reflection coefficients for a particle incident on a fractal potential barrier or on a fractal potential well. It has been investigated how these coefficients vary with the energy of the particle and with the fractal dimension and other parameters of the barrier or well. The energies of the bound states of fractal potential wells have been calculated.     

Tomography of Nonclassical States

A review of the symplectic tomography method is presented. Superpositions of different types of photon states are considered within the framework of the tomography approach. Such nonclassical photon states as even and odd coherent states, crystallized Schrödinger cat states, and other superposition states are studied using the construction of symplectic tomograms (tomographic symbols) and the star-product formalism for tomograms.     

量子信息光学

介绍了一门新的学科分支－量子信息光学。它是量子光学与信息科学相结合的产物。光场的量子效应在实现大容量的信息传输，超高精度的信息检测以及不可破译、不可窃听的量子密码术方面有着极其重要的应用前景，在光子学的发展中将发挥独特的作用。该文阐述了量子信息光学中若干物理问题和研究方向，包括超低噪声光源、量子信息复制、量子态工程、量子非破坏性测量和量子密码术。     

粒子数态波函数推导的新方法

Fock表象是量子光学理论中的基本表象,我们给出粒子数态｜n＞在坐标表象＜x ｜中的波函数的新方法,我们用有序算符内积分技术(IWOP)推导它,这一形式具有简洁优美的特点,并且可推广到其它情形.例如可以探讨在引入双模纠缠态表象后,双模粒子数态的波函数.     

Beam Optics and Particle Transport

Methods and results of beam optics with respect to the transport of charged particle beams in experiments on high energy accelerators are reviewed.