Spin-resolved second-order correlation energy of the two-dimensional uniform electron gas

For the two-dimensional electron gas, the exact high-density limit of the correlation energy is evaluated here numerically for all values of the spin polarization. The result is spin-resolved into $\uparrow\uparrow$, $\uparrow\downarrow$, and $\downarrow\downarrow$ contributions and parametrized analytically. Interaction-strength interpolation yields a simple model (LSD) for the correlation energy at finite densities.Comment: 5 pages, 2 figure

The Consultant-Client Relationship: A Systems-Theoretical Perspective

The aim of this paper is to explain consulting failure from a systems-theoretical perspective and to provide a new framework for analysing consultant–client relationships. By drawing on Luhmann’s systems theory, clients and consultants are conceptualised as two autopoietic communication systems that operate according to idiosyncratic logics. They are structurally coupled through a third system, the so-called “contact system”, which constitutes a separate discourse. Due to their different logics no transfer of meaning between the three discourses is possible. This contradicts the traditional notion of consulting as a means of providing solutions to the client’s problems: neither is the consultant able to understand the client’s problems nor is it possible to transfer any solutions into the client system. Instead, consulting interventions only cause perturbations in the client system. Consequently, the traditional functions of consulting are called into question. The paper discusses the implications of this analysis with relation to the traditional approach to consulting, and presents a tentative framework for a systemic concept of consulting

The Consultant-Client Relationship: A Systems-Theoretical Perspective

The aim of this paper is to explain consulting failure from a systems-theoretical perspective and to provide a new framework for analysing consultant–client relationships. By drawing on Luhmann’s systems theory, clients and consultants are conceptualised as two autopoietic communication systems that operate according to idiosyncratic logics. They are structurally coupled through a third system, the so-called “contact system”, which constitutes a separate discourse. Due to their different logics no transfer of meaning between the three discourses is possible. This contradicts the traditional notion of consulting as a means of providing solutions to the client’s problems: neither is the consultant able to understand the client’s problems nor is it possible to transfer any solutions into the client system. Instead, consulting interventions only cause perturbations in the client system. Consequently, the traditional functions of consulting are called into question. The paper discusses the implications of this analysis with relation to the traditional approach to consulting, and presents a tentative framework for a systemic concept of consulting.Consulting; Consultant-Client Relation; Consulting Failure; Systems Theory

Electronic zero-point oscillations in the strong-interaction limit of density functional theory

The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron hamiltonian, this same operator is multiplied by a real parameter $\lambda$ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of density functional theory, defined as the limit $\lambda\to\infty$, turns out to be, like the opposite non-interacting Kohn-Sham limit ($\lambda\to 0$) mathematically simpler than the physical ($\lambda=1$) case, and can be used to build an approximate interpolation formula between $\lambda\to 0$ and $\lambda\to\infty$ for the exchange-correlation energy. Here we extend the exact treatment of the $\lambda\to\infty$ limit [Phys. Rev. A {\bf 75}, 042511 (2007)] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.Comment: 11 pages, submitted to J. Chem. Theory Compu

Challenging the Lieb-Oxford Bound in a systematic way

The Lieb-Oxford bound, a nontrivial inequality for the indirect part of the many-body Coulomb repulsion in an electronic system, plays an important role in the construction of approximations in density functional theory. Using the wavefunction for strictly-correlated electrons of a given density, we turn the search over wavefunctions appearing in the original bound into a more manageable search over electron densities. This allows us to challenge the bound in a systematic way. We find that a maximizing density for the bound, if it exists, must have compact support. We also find that, at least for particle numbers $N\le 60$, a uniform density profile is not the most challenging for the bound. With our construction we improve the bound for $N=2$ electrons that was originally found by Lieb and Oxford, we give a new lower bound to the constant appearing in the Lieb-Oxford inequality valid for any $N$, and we provide an improved upper bound for the low-density uniform electron gas indirect energy.Comment: accepted in Mol. Phys. in the special issue in honour of Andreas Savin; revised version with new calculation

Density functional theory for strongly interacting electrons

We present an alternative to the Kohn-Sham formulation of density functional theory for the ground-state properties of strongly interacting electronic systems. The idea is to start from the limit of zero kinetic energy and systematically expand the universal energy functional of the density in powers of a "coupling constant" that controls the magnitude of the kinetic energy. The problem of minimizing the energy is reduced to the solution of a strictly correlated electron problem in the presence of an effective potential, which plays in our theory the same role that the Kohn-Sham potential plays in the traditional formulation. We discuss several schemes for approximating the energy functional, and report preliminary results for low-density quantum dots.Comment: Revised version, to appear in Phys. Rev. Let

Theorizing the client-consultant relationship from the perspective of social-systems theory

Over the last few years research on management consulting has established itself as an important area in management studies. While, traditionally, consulting research has been predominantly a-theoretical, lately researchers have been calling for an exploration of different theoretical approaches. This article has been written in response to these calls. It explores a new perspective for theorizing the client–consultant relationship based on the theory of social systems by Niklas Luhmann. According to this approach, clients and consultants can be conceptualized as two autopoietic communication systems that operate according to idiosyncratic logics. They are structurally coupled through a third system, the so-called ‘contact system’. Due to the different logics of these systems, the transfer of meaning between them is not possible. This theoretical position has interesting implications for the way we conceptualize consulting, challenging many traditional assumptions. Instead of supporting the client in finding solutions to their problems, this perspective emphasizes that consulting firms can only cause ‘perturbations’ in the client’s communication processes, inducing the client system to construct its own meaning from it

Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory

We derive an explicit expression for the functional derivative of the subleading term in the strong interaction limit expansion of the generalized Levy--Lieb functional for the special case of two electrons in one dimension. The expression is derived from the zero point energy (ZPE) functional, which is valid if the quantum state reduces to strongly correlated electrons in the strong coupling limit. The explicit expression is confirmed numerically and respects the relevant sum-rule. We also show that the ZPE potential is able to generate a bond mid-point peak for homo-nuclear dissociation and is properly of purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems, whereas the exact peaks should be finite.Comment: 12 pages, 7 figure

Modelling understorey dynamics in temperate forests under global change : challenges and perspectives

The understorey harbours a substantial part of vascular plant diversity in temperate forests and plays an important functional role, affecting ecosystem processes such as nutrient cycling and overstorey regeneration. Global change, however, is putting these understorey communities on trajectories of change, potentially altering and reducing their functioning in the future. Developing mitigation strategies to safeguard the diversity and functioning of temperate forests in the future is challenging and requires improved predictive capacity. Process-based models that predict understorey community composition over time, based on first principles of ecology, have the potential to guide mitigation endeavours but such approaches are rare. Here, we review fourteen understorey modelling approaches that have been proposed during the last three decades. We evaluate their inclusion of mechanisms that are required to predict the impact of global change on understorey communities. We conclude that none of the currently existing models fully accounts for all processes that we deem important based on empirical and experimental evidence. Based on this review, we contend new models are needed to project the complex impacts of global change on forest understoreys. Plant functional traits should be central to such future model developments, as they drive community assembly processes and provide valuable information on the functioning of the understorey. Given the important role of the overstorey, a coupling of understorey models to overstorey models will be essential to predict the impact of global change on understorey composition and structure, and how it will affect the functioning of temperate forests in the future