Deformed Bosons: Combinatorics of Normal Ordering

We solve the normal ordering problem for (A A) ⁿ where A and A are one mode deformed ([A,A ] = [N+1] – [N]) bosonic ladder operators. The solution generalizes results known for canonical bosons. It involves combinatorial polynomials in the number operator N for which the generating function and explicit expressions are found. Simple deformations provide examples of the method.     

Combinatorial Coherent States via Normal Ordering of Bosons

We construct and analyze a family of coherent states built on sequences of integers originating from the solution of the boson normal ordering problem. These sequences generalize the conventional combinatorial Bell numbers and are shown to be moments of positive functions. Consequently, the resulting coherent states automatically satisfy the resolution of unity condition. In addition they display such non-classical fluctuation properties as super-Poissonian statistics and squeezing.     

Generalized Dirichlet Normal Ordering in Open Bosonic Strings

Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief check of the consistency of the theory under the newly introduced normal ordering.     

Normal Ordering the Squeeze Operator by Generalized Wick Theorem

The recently proposed generalized Wick theorem offers a simple way to normal ordering the squeeze operator, shown by the present notes dedicated to the memory of J. Janszky.     

正规排列和反正规排列相互展开的计算

文章给出了产生算符和湮灭算例的正规排列与反正规排列相互展开的二个计算公式为（^a)^n(^a^ )^m=p/∑／k=0m!n!/(m-k)!(n-k)!k!(^a^ )^m-k(^a)^n-k和（^a^ )^n(^a)^m)=p/∑k=0(-1)^km!n!/(m-k)!(n-k)!k!(^a)^m-k(^a^ )^n-k,式中求和的上项p取m和n中较小的一个正整数。并用数学归纳法进行了证明,本文给出的这二次公式可广泛应用于各类激发态光场量子统计性质的研究。     

Normal and Abnormal Grain Growth as Transient Phenomena

For the case of uniform grain boundaries the basic equations of the statistical theory of grain growth (GG) of the present authors are shortly reviewed and compared to the classical Hillert model. On the basis of this present theory normal and abnormal 3-D GG is simulated and particularly the effect of the initial grain size distribution function (SDF) on the GG behaviour which may lead to normal or abnormal GG is demonstrated. Finally results of simulations of normal 2-D GG by the statistical method and by a direct model (curvature driven grain boundaries (GBs)) are presented which exhibit good agreement with one another. It is shown by this comparison that the possibility of finding by such direct methods a self similar SDF as long time asymptote can be excluded because, in contrast to the simulations based on the statistical theory, for the direct models the very large computational capacities required for the long simulation times are not available yet. The conclusion repeatedly claimed in literature that the true self similar SDF deviates from the Hillert distribution can thus be shown not to be justified.     

Operator Formulas Involving Generalized Stirling Number Derived by Virtue of Normal Ordering of Vacuum Projector

By virtue of the normal ordering of vacuum projector we directly derive some new complicated operator identities, regarding to the generalized Stirling number.     

Time Ordering and Counting Statistics

The basic quantum mechanical relation between fluctuations of transported charge and current correlators is discussed. It is found that, as a rule, the correlators are to be time-ordered in an unusual way. Instances where the difference with the conventional ordering matters are illustrated by means of a simple scattering model. We apply the results to resolve a discrepancy concerning the third cumulant of charge transport across a tunnel junction.     

Ordering in alloys

Abstract

The continuous ordering process can be viewed as a development and a gradual amplification of concentration modulations with wave lengths of the order of a few lattice spacings. How the development of different concentration modulaltions leads to different superlattice structures in cubic systems is explained with the help of some illustrative examples. The importance of concentration modulations with special point wave vectors in the stability of the various coherent superlattice structures is discussed. Experimental evidences for such continuous ordering is cited from recent results on ordering in Ni-Mo alloys.

The evolution of ordering in some systems can also be viewed as progressively tiling the disordered lattice by superlattice tiles. When more than one type of coherent superlattice tiles compete, juxtaposition of different types of tiles can occur during the course of ordering. The transitional states between the short range and the long range ordered Ni-Mo alloys indeed exhibit such structures where different types of superlattice tiles decorate the fcc lattice. The role of special point concentration waves in the development of such structures will be discussed in relation to the secondary ordering processes involving two perpendicular ?1 ½ 0? waves and a combination of an ?1 ½ 0? and an appropriate ?100? wave.     

Generalized Weyl Ordering and Nonlinear Coherent States

In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl orderingoperator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operatorfunctions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship betweennormal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistenttheory for NLCS.     

Ordering and phase transitions in liquid crystals

Structures and properties of different types of liquid crystals are discussed from a uniform point of view. Apart from the traditional mesophases (nematics, cholesterics, smectics), some new examples, including polymeric, metalloorganic and ferromagnetic liquid crystals, are also investigated. Systems with several macroscopic scales on which the type of ordering may differ, are described and analysed. Phase transitions and certain types of critical behaviour in different liquid crystals are studied.     

Ordering and conformational transitions in cholesteryl benzoate

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 49, No. 5, pp. 833–839, November, 1988.     

Ordering energy and stability of perfect superlattices

The rigorous solution to the problem of stability of stochiometric ordered phases is considered. Conditions of stability are found relative to phases with maximal degree of order for given stochiometry. The treatment is given for all known superlattices that arise from an fcc solid solution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 22–26, September, 1980.     

Ordering of vacancies in LiAl

The intermetallic compound β-LiAl contains relatively high concentrations of constitutional vacancies on the Li sublattice for Li deficient compositions. Neutron diffraction measurements on a Li_0.486Al_0.514 single crystal show that these vacancies order on every tenth (840) plane at 97K. This vacancy ordering is responsible for the “100K” anomaly observed in several physical properties.     

Short-Range Ordering in Amorphous Structures

A numerical investigation is made of some details of the short-range order in model amorphous structures with free boundaries and a number of different interaction potentials. Five- and seven-member rings — typical features of amorphous structures — are found out in all two-dimensional cross-sections of the generated clusters. Histograms of distribution of the nearest-neighbor numbers are constructed and an analysis of the positions of atoms with different coordination numbers within a model cluster volume is performed. An evaluation is made of the effects of the boundary on the coordination number distribution. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 42–45, September, 2005.     

Ordering chaos by random shortcuts

In this Letter, the effects of random shortcuts in an array of coupled nonlinear chaotic pendulums and their ability to control the dynamical behavior of the system are investigated. We show that random shortcuts can induce periodic synchronized spatiotemporal motions, even though all oscillators are chaotic when uncoupled. This process exhibits a nonmonotonic dependence on the density of shortcuts. Specifically, there is an optimal amount of random shortcuts, which can induce the most ordered motion characterized by the largest order parameter that is introduced to measure the spatiotemporal order. Our results imply that topological randomness can tame spatiotemporal chaos.     

Ordering in binary FCC alloys

A new method of approximation for studying the order-disorder transition in binary alloys is presented. The formulation is in terms of face-centered cubic alloys, although the method can also be applied to other structures. The technique is essentially a generalization of the constant-coupling approximation. We have applied the principles of that method to derive the free energy of the alloy using a tetrahedral cluster of nearest neighbouring sites as the basic unit of the calculation. We only consider the case of nearest neighbour pair interactions, but show how the method can be generalized to include many body and second neighbour interactions. Numerical results are presented and comparison of these results is made with results of cluster variation calculations on the same system and with experimental results on the copper-gold alloy system.