Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles

As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum dependent terms, and we determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe Ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta- and (so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the other model we write down explicit formulas for all eigenfunctions.Comment: 23 pages v2: references adde

Kinetic model of II-VI(001) semiconductor surfaces: Growth rates in atomic layer epitaxy

We present a zinc-blende lattice gas model of II-VI(001) surfaces, which is investigated by means of Kinetic Monte Carlo (KMC) simulations. Anisotropic effective interactions between surface metal atoms allow for the description of, e.g., the sublimation of CdTe(001), including the reconstruction of Cd-terminated surfaces and its dependence on the substrate temperature T. Our model also includes Te-dimerization and the potential presence of excess Te in a reservoir of weakly bound atoms at the surface. We study the self-regulation of atomic layer epitaxy (ALE) and demonstrate how the interplay of the reservoir occupation with the surface kinetics results in two different regimes: at high T the growth rate is limited to 0.5 layers per ALE cycle, whereas at low enough T each cycle adds a complete layer of CdTe. The transition between the two regimes occurs at a characteristic temperature and its dependence on external parameters is studied. Comparing the temperature dependence of the ALE growth rate in our model with experimental results for CdTe we find qualitative agreement.Comment: 9 pages (REVTeX), 8 figures (EPS). Content revised, references added, typos correcte

Causal Consistency of Structural Equation Models

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.Comment: equal contribution between Rubenstein and Weichwald; accepted manuscrip

Chirality and Dirac Operator on Noncommutative Sphere

We give a derivation of the Dirac operator on the noncommutative $2$-sphere within the framework of the bosonic fuzzy sphere and define Connes' triple. It turns out that there are two different types of spectra of the Dirac operator and correspondingly there are two classes of quantized algebras. As a result we obtain a new restriction on the Planck constant in Berezin's quantization. The map to the local frame in noncommutative geometry is also discussed.Comment: 24 pages, latex, no figure

Boundary effect of a partition in a quantum well

The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one dimensional potential well that is divided into two halves by a thin separating wall. The two half wells are populated by the same type and number of particles and are kept at the same temperature. The only difference is in the boundary condition imposed at the two sides of the separating wall, which is the Dirichlet condition from the left and the Neumann condition from the right. The resulting different energy spectra cause a difference in the quantum statistically emerging pressure on the two sides. The net force acting on the separating wall proves to be nonzero at any temperature and, after a weak decrease in the low temperature domain, to increase and diverge with a square-root-of-temperature asymptotics for high temperatures. These observations hold for both bosonic and fermionic type particles, but with quantitative differences. We work out several analytic approximations to explain these differences and the various aspects of the found unexpectedly complex picture.Comment: LaTeX (with iopart.cls, iopart10.clo and iopart12.clo), 28 pages, 17 figure

On divergent 3-vertices in noncommutative SU(2)gauge theory

We analyze divergencies in 2-point and 3-point functions for noncommutative $\theta$-expanded SU(2)-gauge theory with massless fermions. We show that, after field redefinition and renormalization of couplings, one divergent term remains.Comment: 7 page

Non-commutative SU(N) gauge theories and asymptotic freedom

In this paper we analyze the one-loop renormalization of the $\theta$-expanded $\rm SU(N)$ Yang-Mills theory. We show that the {\it freedom parameter} $a$, key to renormalization, originates from higher order non-commutative gauge interaction, represented by a higher derivative term $b h \theta^{\mu\nu}\hat F_{\mu\nu}\star\hat F_{\rho\sigma}\star\hat F^{\rho\sigma}$. The renormalization condition fixes the allowed values of the parameter $a$ to one of the two solutions: $a=1$ or $a=3$, i.e. to $b=0$ or to $b=1/2$, respectively. When the higher order interaction is switched on, ($a=3$), pure non-commutative SU(N) gauge theory at first order in $\theta$-expansion becomes one-loop renormalizable for various representations of the gauge group. We also show that, in the case $a=3$ and the adjoint representation of the gauge fields, the non-commutative deformation parameter $h$ has to be renormalized and it is asymptotically free.Comment: 16 pages, no figure

The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4

We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized at the one-loop level by multiplicative dimensional renormalization of the coupling constant and fields of the theory. We compute the beta function of the theory and conclude that the theory is asymptotically free. We also show that the Weyl-Moyal matrix defining the deformed product over the space of functions on R^4 is not renormalized at the one-loop level.Comment: 8 pages. A missing complex "i" is included in the field strength and the divergent contributions corrected accordingly. As a result the model turns out to be asymptotically fre

UV/IR duality in noncommutative quantum field theory

We review the construction of renormalizable noncommutative euclidean phi(4)-theories based on the UV/IR duality covariant modification of the standard field theory, and how the formalism can be extended to scalar field theories defined on noncommutative Minkowski space.Comment: 12 pages; v2: minor corrections, note and references added; Contribution to proceedings of the 2nd School on "Quantum Gravity and Quantum Geometry" session of the 9th Hellenic School on Elementary Particle Physics and Gravity, Corfu, Greece, September 13-20 2009. To be published in General Relativity and Gravitatio

Your Governance or Mine?

In response to criticism directed at the resource sector's corporate governance, this paper examines the corporate governance and underlying firm characteristics of resource development stage entities (DSEs) relative to a size-matched sample of non-resource firms. We find that resource DSEs have different governance characteristics in the measures of board independence, chair/CEO duality and CEO cash bonuses. Furthermore, there are differences in the information environment measures of analyst following, debt levels, stock market return and stock turnover. Considering we document substantial differences in underlying firm characteristics, corporate governance differences are likely appropriate to the mining industry and should not be uniformly labelled as 'bad'. Our results suggest that media rankings based on corporate governance scores may not accurately portray the resource sector. Overall, our results are of interest to Australian investors and regulators and contribute to a broader understanding of contextually contingent corporate governance. © 2011 CPA Australia