Low-energy limit of the three-band model for electrons in a CuO2_{2} plane

The three-band model with the O-O direct hopping near to unit filling is considered. We present the general procedure of reduction of this model to the low-energy limit. At unit filling the three-band model in the charge-transfer limit is reduced to the Heisenberg model and we calculate the superexchange constant. For the case of the small electron doping the three-band model is reduced to the $t-J$ model and we calculate electron hopping parameters at the nearest and next neighbors. We derive the structure of corrections to the $t-J$ model and calculate their magnitude. The values of the hopping parameters for electron- and hole-doping differ approximately at 40 %.Comment: 10 pp. (LATEX

Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

We construct affinization of the algebra $gl_{\lambda}$ of ``complex size'' matrices, that contains the algebras $\hat{gl_n}$ for integral values of the parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra $\hat{gl_{\lambda}}$ results in the quadratic Gelfand--Dickey structure on the Poisson--Lie group of all pseudodifferential operators of fractional order. This construction is extended to the simultaneous deformation of orthogonal and simplectic algebras that produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure

Statistical Mechanics of Structural Fluctuations

The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture by constructing a renormalized Hamiltonian. The relative volumes occupied by each of the coexisting structures define the corresponding geometric probabilities. In the case of a frozen heterophase system these probabilities should be given a priori. And in the case of a thermal heterophase mixture the structural probabilities are to be defined self-consistently by minimizing a thermodynamical potential. This permits to find the temperature behavior of the probabilities which is especially important near the points of structural phase transitions. The presense of these structural fluctuations yields a softening of a crystal and a decrease of the effective Debye temperature. These effects can be directly seen by nuclear gamma resonance since the occurrence of structural fluctuations is accompanied by a noticeable sagging of the M\"ossbauer factor at the point of structural phase transition. The structural fluctuations also lead to the attenuation of sound and increase of isothermic compressibility.Comment: 1 file, 18 pages, RevTex, no figure

Nucleus-mediated spin-flip transitions in GaAs quantum dots

Spin-flip rates in GaAs quantum dots can be quite slow, thus opening up the possibilities to manipulate spin states in the dots. We present here estimations of inelastic spin-flip rates mediated by hyperfine interaction with nuclei. Under general assumptions the nucleus mediated rate is proportional to the phonon relaxation rate for the corresponding non-spin-flip transitions. The rate can be accelerated in the vicinity of a singlet-triplet excited states crossing. The small proportionality coefficient depends inversely on the number of nuclei in the quantum dot. We compare our results with known mechanisms of spin-flip in $GaAs$ quantum dot.Comment: RevTex 4 pages, 1 figure, submitted to Phys. Rev.

Instanton Corrections to Quark Form Factor at Large Momentum Transfer

Within the Wilson integral formalism, we discuss the structure of nonperturbative corrections to the quark form factor at large momentum transfer analyzing the infrared renormalon and instanton effects. We show that the nonperturbative effects determine the initial value for the perturbative evolution of the quark form factor and attribute their general structure to the renormalon ambiguities of the perturbative series. It is demonstrated that the instanton contributions result in the finite renormalization of the next-to-leading perturbative result and numerically are characterized by a small factor reflecting the diluteness of the QCD vacuum within the instanton liquid model.Comment: Version coincident with the journal publication, 9 pages; REVTe

Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics

In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924-1925. Although it failed to attract the attention of Einstein's contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein's quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein's confusion with his initial success in extending Bose's results and in realizing the consequences of what later became to be called Bose-Einstein statistics. We discuss Einstein's motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein's belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as well as of dimensional analysis. These techniques were well-known to Einstein from earlier work on Wien's displacement law, Planck's radiation theory, and the specific heat of solids. We also investigate the possible role of Ehrenfest in the gestation of the theory.Comment: 57 pp

New Faces and New Masks of Today's Consumer

In 1995, we proposed that consumption and contemporary consumerism could not be studied or understood separately from the world of work and production. We proposed that contemporary consumerism was built on the back of what we referred to as `the Fordist Deal'. This deal, pioneered by Henry Ford for his employees, was the promise of ever increasing standards of living in exchange for a quiescent labour force accepting alienating work. Since that deal was struck, consumerism came to signify a general pre-occupation with consumption standards and choice as well as a willingness to read meanings in material commodities and to equate happiness and success with material possessions. In this sense, Ford may be seen as the father both of mass production and mass consumption. Since the Fordist high noon of consumerism in the West, mass consumption is widely seen as having fragmented into a proliferation of highly individualized niche products. For its part, a considerable part of mass production has migrated to countries with lower wages and looser environmental and social controls, fueling their own variants of consumerism. In this article, we examine the gradual erosion of the Fordist Deal in the light of developments in the last 10 years or so, seeking to assess the future of consumerism at a global level. We also seek to identify and discuss some emerging conceptualizations of the consumer, some of the new faces and masks assumed by the archetypal character of our types. We analyse some of the tensions and contradictions lurking behind these conceptualizations and try to envisage some of the real choices facing consumers today and some of the processes of social change that hinge on the outcomes of these choices. The article identifies a fundamental paradox between the ubiquity of the consumer in contemporary discourses and the virtual impossibility of generalizing about consumers. We suggest, then, that the consumer may be viewed as one of those `essentially contested concepts' proposed by Gallie that defy domestication. The consumer, we argue, is unmanageable, both as a concept, since no-one can pin it down to one specific conceptualization at the expense of all others, and as an entity, since attempts to control and manage the consumer lead to the consumer mutating from one impersonation to another. It is precisely this paradox that we seek to capture in our article's title. The article concludes with a consideration of three basic challenges that are liable to lead to fundamental reorientation of consumption and production, as well as of our conceptualizations and theorizing about them. These challenges are the outcomes of environmental, demographic and social factors that, we argue, make the current situation unsustainable and will bring about its dissolution