EXACT AND APPROXIMATE RELATIONS FOR THE SPIN-DEPENDENCE OF THE EXCHANGE ENERGY IN HIGH MAGNETIC FIELDS

The exchange energy of an arbitrary collinear-spin many-body system in an external magnetic field is a functional of the spin-resolved charge and current densities, E(x)[n(up arrow), n(down arrow), j(up arrow), j(down arrow)]. Within the framework of density-functional theory (DFT), we show that the dependence of this functional on the four densities can be fully reconstructed from either of two extreme limits: a fully polarized system or a completely unpolarized system. Reconstruction from the limit of an unpolarized system yields a generalization of the Oliver-Perdew spin scaling relations from spin-DFT to current-DFT. Reconstruction from the limit of a fully polarized system is used to derive the high-field form of the local-spin-density approximation to current-DFT and to magnetic-field DFT.

Direct versus kinetic exchange in multiband models for organic ferromagnetism

Multiband Hubbard and Pariser-Parr-Pople calculations have been carried out on mixed donor-acceptor (DA) stacks with doubly degenerate acceptor orbitals and nondegenerate donor orbitals at two-thirds filling. Model exact results for 2, 3, and 4 DA units show that McConnell's prediction of high-spin ground states in these systems is, in general, incorrect. The larger phase space available for the low-spin states leads to their kinetic stabilization in preference to high-spin states. However, for large electron-correlation strengths, the direct exchange dominates over the kinetic exchange resulting in a high-spin ground state

Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse sinh square of the distance. This interaction contains a variable range as a parameter and can thus interpolate between the known solutions for the nearest-neighbor chain and the inverse-square chain. The energy, susceptibility, charge stiffness, and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.

Model exact low-lying states and spin dynamics in ferric wheels: Fe-6 to Fe-12

Using an efficient numerical scheme that exploits spatial symmetries and spin parity, we have obtained the exact low-lying eigenstates of exchange Hamiltonians for ferric wheels up to Fe-12. The largest calculation involves the Fe-12 ring which spans a Hilbert space dimension of about 145x10(6) for the M-S=0 subspace. Our calculated gaps from the singlet ground state to the excited triplet state agree well with the experimentally measured values. Study of the static structure factor shows that the ground state is spontaneously dimerized for ferric wheels. The spin states of ferric wheels can be viewed as quantized states of a rigid rotor with the gap between the ground and first excited states defining the inverse of the moment of inertia. We have studied the quantum dynamics of Fe-10 as a representative of ferric wheels. We use the low-lying states of Fe-10 to solve exactly the time-dependent Schrodinger equation and find the magnetization of the molecule in the presence of an alternating magnetic field at zero temperature. We observe a nontrivial oscillation of the magnetization which is dependent on the amplitude of the ac field. We have also studied the torque response of Fe-12 as a function of a magnetic field, which clearly shows spin-state crossover.

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin Hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground-state configuration of all the members of the family on a periodic chain. The ground state is twofold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh Hamiltonian with a twofold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.

Theory of s-d exchange scattering in dilute magnetic alloys

The problem of s-d exchange scattering of conduction electrons off localized magnetic moments in dilute magnetic alloys is considered employing formal methods of quantum field theoretical scattering. It is shown that such a treatment not only allows for the first time, the inclusion of multiparticle intermediate states in single particle scattering equations but also results in extremely simple and straight forward mathematical analysis. These equations are proved to be exact in the thermodynamic limit. A self-consistent integral equation for electron self energy is derived and approximately solved. The ground state and physical parameters of dilute magnetic alloys are discussed in terms of the theoretical results. Within the approximation of single particle intermediate states our results reduce to earlier versions. The following additional features are found as a consequence of the inclusion of multiparticle intermediate states;

(i) A non analytic binding energy is pre sent for both, antiferromagnetic (J < o) and ferromagnetic (J > o) couplings of the electron plus impurity system.

(ii) The correct behavior of the energy difference of the conduction electron plus impurity system and the free electron system is found which is free of unphysical singularities present in earlier versions of the theories.

(iii) The ground state of the conduction electron plus impurity system is shown to be a many-body condensate state for J < o and J > o, both. However, a distinction is made between the usual terminology of "Singlet" and "Triplet" ground states and nature of our ground state.

(iv) It is shown that a long range ordering, leading to an ordering of the magnetic moments can result from a contact interaction such as the s-d exchange interaction.

(v) The explicit dependence of the excess specific heat of the Kondo systems is obtained and found to be linear in temperatures as T→ o and T ℓnT for 0.3 T_K ≤ T ≤ 0.6 T_K. A rise in (ΔC/T) for temperatures in the region 0 < T ≤ 0.1 T_K is predicted. These results are found to be in excellent agreement with experiments.

(vi) The existence of a critical temperature for Ferromagnetic coupling (J > o) is shown. On the basis of this the apparent contradiction of the simultaneous existence of giant moments and Kondo effect is resolved.

RSA-Based Password-Authenticated Key Exchange, Revisited

The RSA-based Password-Authenticated Key Exchange (PAKE) protocols have been proposed to realize both mutual authentication and generation of secure session keys where a client is sharing his/her password only with a server and the latter should generate its RSA public/private key pair (e, n), (d, n) every time due to the lack of PKI (Public-Key Infrastructures). One of the ways to avoid a special kind of off-line (so called e-residue) attacks in the RSA-based PAKE protocols is to deploy a challenge/response method by which a client verifies the relative primality of e and φ(n) interactively with a server. However, this kind of RSA-based PAKE protocols did not give any proof of the underlying challenge/response method and therefore could not specify the exact complexity of their protocols since there exists another security parameter, needed in the challenge/response method. In this paper, we first present an RSA-based PAKE (RSA-PAKE) protocol that can deploy two different challenge/response methods (denoted by Challenge/Response Method1 and Challenge/Response Method2). The main contributions of this work include: (1) Based on the number theory, we prove that the Challenge/Response Method1 and the Challenge/Response Method2 are secure against e-residue attacks for any odd prime e; (2) With the security parameter for the on-line attacks, we show that the RSA-PAKE protocol is provably secure in the random oracle model where all of the off-line attacks are not more efficient than on-line dictionary attacks; and (3) By considering the Hamming weight of e and its complexity in the RSA-PAKE protocol, we search for primes to be recommended for a practical use. We also compare the RSA-PAKE protocol with the previous ones mainly in terms of computation and communication complexities.

Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995.

Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

In this paper, we propose exact inference procedures for asset pricing models that can be formulated in the framework of a multivariate linear regression (CAPM), allowing for stable error distributions. The normality assumption on the distribution of stock returns is usually rejected in empirical studies, due to excess kurtosis and asymmetry. To model such data, we propose a comprehensive statistical approach which allows for alternative - possibly asymmetric - heavy tailed distributions without the use of large-sample approximations. The methods suggested are based on Monte Carlo test techniques. Goodness-of-fit tests are formally incorporated to ensure that the error distributions considered are empirically sustainable, from which exact confidence sets for the unknown tail area and asymmetry parameters of the stable error distribution are derived. Tests for the efficiency of the market portfolio (zero intercepts) which explicitly allow for the presence of (unknown) nuisance parameter in the stable error distribution are derived. The methods proposed are applied to monthly returns on 12 portfolios of the New York Stock Exchange over the period 1926-1995 (5 year subperiods). We find that stable possibly skewed distributions provide statistically significant improvement in goodness-of-fit and lead to fewer rejections of the efficiency hypothesis.

E-commerce system simulation for construction and demolition waste exchange

This article introduces a quantitative approach to e-commerce system evaluation based on the theory of process simulation. The general concept of e-commerce system simulation is presented based on the considerations of some limitations in e-commerce system development such as the huge amount of initial investments of time and money, and the long period from business planning to system development, then to system test and operation, and finally to exact return; in other words, currently used system analysis and development method cannot tell investors about some keen attentions such as how good their e-commerce system could be, how many investment repayments they could have, and which area they should improve regarding the initial business plan. In order to exam the value and its potential effects of an e-commerce business plan, it is necessary to use a quantitative evaluation approach and the authors of this article believe that process simulation is an appropriate option. The overall objective of this article is to apply the theory of process simulation to e-commerce system evaluation, and the authors will achieve this though an experimental study on a business plan for online construction and demolition waste exchange. The methodologies adopted in this article include literature review, system analysis and development, simulation modelling and analysis, and case study. The results from this article include the concept of e-commerce system simulation, a comprehensive review of simulation methods adopted in e-commerce system evaluation, and a real case study of applying simulation to e-commerce system evaluation. Furthermore, the authors hope that the adoption and implementation of the process simulation approach can effectively support business decision-making, and improve the efficiency of e-commerce systems.

Spin-density functional for exchange anisotropic Heisenberg model

Ground-state energies for anti ferromagnetic Heisenberg models with exchange anisotropy are estimated by means of a local-spin approximation made in the context of the density functional theory. Correlation energy is obtained using the non-linear spin-wave theory for homogeneous systems from which the spin functional is built. Although applicable to chains of any size, the results are shown for small number of sites, to exhibit finite-size effects and allow comparison with exact-numerical data from direct diagonalization of small chains. (C) 2009 Elsevier B.V. All rights reserved.

Contract enforcement and incentive compatibility in large economies with differential information: the role of exact feasibility

We consider exchange economies with a continuum of agents and differential information about finitely many states of nature. It was proved in Einy, Moreno and Shitovitz (2001) that if we allow for free disposal in the market clearing (feasibility) constraints then an irreducible economy has a competitive (or Walrasian expectations) equilibrium, and moreover, the set of competitive equilibrium allocations coincides with the private core. However when feasibility is defined with free disposal, competitive equilibrium allocations may not be incentive compatible and contracts may not be enforceable (see e.g. Glycopantis, Muir and Yannelis (2002)). This is the main motivation for considering equilibrium solutions with exact feasibility. We first prove that the results in Einy et al. (2001) are still valid without free-disposal. Then we define an incentive compatibility property motivated by the issue of contracts’ execution and we prove that every Pareto optimal exact feasible allocation is incentive compatible, implying that contracts of a competitive or core allocations are enforceable.

Bayesian L-optimal exact design of experiments for biological kinetic models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Formation and surface exchange of nitrous acid

Die salpetrige Säure (HONO) ist eine der reaktiven Stickstoffkomponenten der Atmosphäre und Pedosphäre. Die genauen Bildungswege von HONO, sowie der gegenseitige Austausch von HONO zwischen Atmosphäre und Pedosphäre sind noch nicht vollständig aufgedeckt. Bei der HONO-Photolyse entsteht das Hydroxylradikal (OH) und Stickstoffmonooxid (NO), was die Bedeutsamkeit von HONO für die atmosphärische Photochemie widerspiegelt.rnUm die genannte Bildung von HONO im Boden und dessen anschließenden Austausch mit der Atmosphäre zu untersuchen, wurden Messungen von Bodenproben mit dynamischen Kammern durchgeführt. Im Labor gemessene Emissionsflüsse von Wasser, NO und HONO zeigen, dass die Emission von HONO in vergleichbarem Umfang und im gleichen Bodenfeuchtebereich wie die für NO (von 6.5 bis 56.0 % WHC) stattfindet. Die Höhe der HONO-Emissionsflüsse bei neutralen bis basischen pH-Werten und die Aktivierungsenergie der HONO-Emissionsflüsse führen zu der Annahme, dass die mikrobielle Nitrifikation die Hauptquelle für die HONO-Emission darstellt. Inhibierungsexperimente mit einer Bodenprobe und die Messung einer Reinkultur von Nitrosomonas europaea bestärkten diese Theorie. Als Schlussfolgerung wurde das konzeptionelle Model der Bodenemission verschiedener Stickstoffkomponenten in Abhängigkeit von dem Wasserhaushalt des Bodens für HONO erweitert.rnIn einem weiteren Versuch wurde zum Spülen der dynamischen Kammer Luft mit erhöhtem Mischungsverhältnis von HONO verwendet. Die Messung einer hervorragend charakterisierten Bodenprobe zeigte bidirektionale Flüsse von HONO. Somit können Böden nicht nur als HONO-Quelle, sondern auch je nach Bedingungen als effektive Senke dienen. rnAußerdem konnte gezeigt werden, dass das Verhältnis von HONO- zu NO-Emissionen mit dem pH-Wert des Bodens korreliert. Grund könnte die erhöhte Reaktivität von HONO bei niedrigem pH-Wert und die längere Aufenthaltsdauer von HONO verursacht durch reduzierte Gasdiffusion im Bodenporenraum sein, da ein niedriger pH-Wert mit erhöhter Bodenfeuchte am Maximum der Emission einhergeht. Es konnte gezeigt werden, dass die effektive Diffusion von Gasen im Bodenporenraum und die effektive Diffusion von Ionen in der Bodenlösung die HONO-Produktion und den Austausch von HONO mit der Atmosphäre begrenzen. rnErgänzend zu den Messungen im Labor wurde HONO während der Messkampagne HUMPPA-COPEC 2010 im borealen Nadelwald simultan in der Höhe von 1 m über dem Boden und 2 bis 3 m über dem Blätterdach gemessen. Die Budgetberechnungen für HONO zeigen, dass für HONO sämtliche bekannte Quellen und Senken in Bezug auf die übermächtige HONO-Photolyserate tagsüber vernachlässigbar sind (< 20%). Weder Bodenemissionen von HONO, noch die Photolyse von an Oberflächen adsorbierter Salpetersäure können die fehlende Quelle erklären. Die lichtinduzierte Reduktion von Stickstoffdioxid (NO2) an Oberflächen konnte nicht ausgeschlossen werden. Es zeigte sich jedoch, dass die fehlende Quelle stärker mit der HONO-Photolyserate korreliert als mit der entsprechenden Photolysefrequenz, die proportional zur Photolysefrequenz von NO2 ist. Somit lässt sich schlussfolgern, dass entweder die Photolyserate von HONO überschätzt wird oder dass immer noch eine unbekannte, HONO-Quelle existiert, die mit der Photolyserate sehr stark korreliert. rn rn

Anisotropic exchange interaction induced by a single photon in semiconductor microcavities

We investigate coupling of localized spins in a semiconductor quantum dot embedded in a microcavity. The lowest cavity mode and the quantum dot exciton are coupled and close in energy, forming a polariton. The fermions forming the exciton interact with localized spins via exchange. Exact diagonalization of a Hamiltonian in which photons, spins, and excitons are treated quantum mechanically shows that a single polariton induces a sizable indirect anisotropic exchange interaction between spins. At sufficiently low temperatures strong ferromagnetic correlations show up without an appreciable increase in exciton population. In the case of a (Cd,Mn)Te quantum dot, Mn-Mn ferromagnetic coupling is still significant at 1 K: spin-spin correlation around 3 for exciton occupation smaller than 0.3. We find that the interaction mediated by photon-polaritons is 10 times stronger than the one induced by a classical field for equal Rabi splitting.