Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Interference in hyperbolic space

The interference in a phase space algorithm of Schleich and Wheeler [Nature 326, 574 (1987)] is extended to the hyperbolic space underlying the group SU(1,1). The extension involves introducing the notion of weighted areas. Analytic expressions for the asymptotic forms for overlaps between the eigenstates of the generators of su(1,1) thus obtained are found to be in excellent agreement with the numerical results.[S1050-2947(98)08602-8].

Casimir invariants and characteristic identities for gl(infinity)

A full set of (higher-order) Casimir invariants for the Lie algebra gl(infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American Institute of Physics.

Super-Yangian double and its central extension

We introduce the super-Yangian double DY(h over bar), [gl(m/n)] and its central extension DY(h over bar)[gl(m/n)]. We give their defining relations in terms of current generators and obtain Drinfeld co-multiplication. (C) 1997 Elsevier Science B.V.

Comments on the Drinfeld realization of the quantum affine superalgebra U-q[gl(m backslash n)(1)] and its Hopf algebra structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain the Drinfeld current realization for the quantum affine superalgebra U-q[gl(m\n)((1))]. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.

Temporal relationship between the auditory brainstem response and focal responses of auditory nerve root and cochlear nucleus during development in the tammar wallaby (Macropus eugenii)

Thirty-two pouch-young tammar wallabies were used to discover the generators of the auditory brainstem response (ABR) during development by the use of simultaneous ABR and focal brainstem recordings. A click response from the auditory nerve root (ANR) in the wallaby was recorded from postnatal day (PND) 101, when no central auditory station was functional, and coincided with the ABR, a simple positive wave. The response of the cochlear nucleus (CN) was detected from PND 110, when the ABR had developed 1 positive and 1 negative peak. The dominant component of the focal ANR response, the N-1 wave, coincided with the first half of the ABR P wave, and that of the focal CN response, the N-1 wave, coincided with the later two thirds. In older animals, the ANR response coincided with the ABR's N-1, wave, while the CN response coincided with the ABR's P-2, N-2 and P-3 waves, with its contribution to the ABR P-2 dominant. The protracted development of the marsupial auditory system which facilitated these correlations makes the tammar wallaby a particularly suitable model. Copyright (C) 2001 S. Karger AG, Basel.

Breadth-first search and the Andrews-Curtis conjecture

Andrews and Curtis conjectured in 1965 that every balanced presentation of the trivial group can be transformed into a standard presentation by a finite sequence of elementary transformations. Recent computational work by Miasnikov and Myasnikov on this problem has been based on genetic algorithms. We show that a computational attack based on a breadth-first search of the tree of equivalent presentations is also viable, and seems to outperform that based on genetic algorithms. It allows us to extract shorter proofs (in some cases, provably shortest) and to consider the length thirteen case for two generators. We prove that, up to equivalence, there is a unique minimum potential counterexample.

Teleonomic entropy: measuring the phase-space of end-directed systems

We introduce a novel way of measuring the entropy of a set of values undergoing changes. Such a measure becomes useful when analyzing the temporal development of an algorithm designed to numerically update a collection of values such as artificial neural network weights undergoing adjustments during learning. We measure the entropy as a function of the phase-space of the values, i.e. their magnitude and velocity of change, using a method based on the abstract measure of entropy introduced by the philosopher Rudolf Carnap. By constructing a time-dynamic two-dimensional Voronoi diagram using Voronoi cell generators with coordinates of value- and value-velocity (change of magnitude), the entropy becomes a function of the cell areas. We term this measure teleonomic entropy since it can be used to describe changes in any end-directed (teleonomic) system. The usefulness of the method is illustrated when comparing the different approaches of two search algorithms, a learning artificial neural network and a population of discovering agents. (C) 2004 Elsevier Inc. All rights reserved.

Modern environmental improvement pathways for the coal power generation industry in Australia

In this work we assess the pathways for environmental improvement by the coal utilization industry for power generation in Australia. In terms of resources, our findings show that coal is a long term resource of concern as coal reserves are likely to last for the next 500 years or more. However, our analysis indicates that evaporation losses of water in power generation will approach 1000 Gl (gigalitres) per year, equivalent to a consumption of half of the Australian residential population. As Australia is the second driest continent on earth, water consumption by power generators is a resource of immediate concern with regards to sustainability. We also show that coal will continue to play a major role in energy generation in Australia and, hence, there is a need to employ new technologies that can minimize environmental impacts. The major technologies to reduce impacts to air, water and soils are addressed. Of major interest, there is a major potential for developing sequestration processes in Australia, in particular by enhanced coal bed methane (ECBM) recovery at the Bowen Basin, South Sydney Basin and Gunnedah Basin. Having said that, CO2 capture technologies require further development to support any sequestration processes in order to comply with the Kyoto Protocol. Current power generation cycles are thermodynamic limited, with 35-40% efficiencies. To move to a high efficiency cycle, it is required to change technologies of which integrated gasification combined cycle plus fuel cell is the most promising, with efficiencies expected to reach 60-65%. However, risks of moving towards an unproven technology means that power generators are likely to continue to use pulverized fuel technologies, aiming at incremental efficiency improvements (business as usual). As a big picture pathway, power generators are likely to play an increasing role in regional development; in particular EcoParks and reclaiming saline water for treatment as pressures to access fresh water supplies will significantly increase.

Measuring market power in electricity generation: A long-term perspective using a programming model

This paper focuses on measuring the extent to which market power has been exercised in a recently deregulated electricity generation sector. Our study emphasises the need to consider the concept of market power in a long-run dynamic context. A market power index is constructed focusing on differences between actual market returns and long-run competitive returns, estimated using a programming model devised by the authors. The market power implications of hedge contracts are briefly considered. The state of Queensland Australia is used as a context for the analysis. The results suggest that generators have exercised significant market power since deregulation.

Degrees of freedom and motor planning in purposive movement

This paper presents empirical evidence suggesting that healthy humans can perform a two degree of freedom visuo-motor pursuit tracking task with the same response time delay as a one degree of freedom task. In contrast, the time delay of the response is influenced markedly by the nature of the motor synergy required to produce it. We suggest a conceptual account of this evidence based on adaptive model theory, which combines theories of intermittency from psychology and adaptive optimal control from engineering. The intermittent response planning stage has a fixed period. It possesses multiple optimal trajectory generators such that multiple degrees of freedom can be planned concurrently, without requiring an increase in the planning period. In tasks which require unfamiliar motor synergies, or are deemed to be incompatible, internal adaptive models representing movement dynamics are inaccurate. This means that the actual response which is produced will deviate from the one which is planned. For a given target-response discrepancy, corrective response trajectories of longer duration are planned, consistent with the principle of speed-accuracy trade-off. Compared to familiar or compatible tasks, this results in a longer response time delay and reduced accuracy. From the standpoint of the intermittency approach, the findings of this study help make possible a more integral and predictive account of purposive action. (c) 2005 Elsevier B.V. All rights reserved.

Power flow based monetary flow method for electricity transmission and wheeling pricing

This paper proposes a transmission and wheeling pricing method based on the monetary flow tracing along power flow paths: the monetary flow-monetary path method. Active and reactive power flows are converted into monetary flows by using nodal prices. The method introduces a uniform measurement for transmission service usages by active and reactive powers. Because monetary flows are related to the nodal prices, the impacts of generators and loads on operation constraints and the interactive impacts between active and reactive powers can be considered. Total transmission service cost is separated into more practical line-related costs and system-wide cost, and can be flexibly distributed between generators and loads. The method is able to reconcile transmission service cost fairly and to optimize transmission system operation and development. The case study on the IEEE 30 bus test system shows that the proposed pricing method is effective in creating economic signals towards the efficient use and operation of the transmission system. (c) 2005 Elsevier B.V. All rights reserved.

Stabilizer formalism for operator quantum error correction

Operator quantum error correction is a recently developed theory that provides a generalized and unified framework for active error correction and passive error avoiding schemes. In this Letter, we describe these codes using the stabilizer formalism. This is achieved by adding a gauge group to stabilizer codes that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 3 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.