Interaction induced delocalization of two particles: large system size calculations and dependence on interaction strength

The localization length $L_2$ of two interacting particles in a one-dimensional disordered system is studied for very large system sizes by two efficient and accurate variants of the Green function method. The numerical results (at the band center) can be well described by the functional form $L_2=L_1[0.5+c(U) L_1]$ where $L_1$ is the one-particle localization length and the coefficient $c(U)\approx 0.074 |U|/(1+|U|)$ depends on the strength $U$ of the on-site Hubbard interaction. The Breit-Wigner width or equivalently the (inverse) life time of non-interacting pair states is analytically calculated for small disorder and taking into account the energy dependence of the one-particle localization length. This provides a consistent theoretical explanation of the numerically found $U$-dependence of $c(U)$.Comment: 8 pages, 5 figures, LaTeX, EPJ macro package, submitted to the European Physical Journal

Localization and absence of Breit-Wigner form for Cauchy random band matrices

We analytically calculate the local density of states for Cauchy random band matrices with strongly fluctuating diagonal elements. The Breit-Wigner form for ordinary band matrices is replaced by a Levy distribution of index $\mu=1/2$ and the characteristic energy scale $\alpha$ is strongly enhanced as compared to the Breit-Wigner width. The unperturbed eigenstates decay according to the non-exponential law $\propto e^{-\sqrt{\alpha t}}$. We analytically determine the localization length by a new method to derive the supersymmetric non-linear $\sigma$ model for this type of band matrices.Comment: 4 pages, 1 figur

Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model

The localization properties of eigenfunctions for two interacting particles in the one-dimensional Anderson model are studied for system sizes up to $N=5000$ sites corresponding to a Hilbert space of dimension $\approx 10^7$ using the Green function Arnoldi method. The eigenfunction structure is illustrated in position, momentum and energy representation, the latter corresponding to an expansion in non-interacting product eigenfunctions. Different types of localization lengths are computed for parameter ranges in system size, disorder and interaction strengths inaccessible until now. We confirm that one-parameter scaling theory can be successfully applied provided that the condition of $N$ being significantly larger than the one-particle localization length $L_1$ is verified. The enhancement effect of the two-particle localization length $L_2$ behaving as $L_2\sim L_1^2$ is clearly confirmed for a certain quite large interval of optimal interactions strengths. Further new results for the interaction dependence in a very large interval, an energy value outside the band center, and different interaction ranges are obtained.Comment: 26 pages, 19 png and pdf figures, high quality gif files for panels of figures 1-4 are available at http://www.quantware.ups-tlse.fr/QWLIB/tipdisorder1d, final published version with minor corrections/revisions, addition of Journal reference and DO

Standards, Innovation Incentives, and the Formation of Patent Pools

Technological standards give rise to a complements problem that affects pricing and innovation incentives of technology producers. In this paper I discuss how patent pools can be used to solve these problems and what incentives patent holders have to form a patent pool. I offer some suggestions how competition authorities can foster the formation of welfare increasing patent pools

Theories of Fairness and Reciprocity

Most economic models are based on the self-interest hypothesis that assumes that all people are exclusively motivated by their material self-interest. In recent years experimental economists have gathered overwhelming evidence that systematically refutes the self-interest hypothesis and suggests that many people are strongly motivated by concerns for fairness and reciprocity. Moreover, several theoretical papers have been written showing that the observed phenomena can be explained in a rigorous and tractable manner. These theories in turn induced a new wave of experimental research offering additional exciting insights into the nature of preferences and into the relative performance of competing theories of fairness. The purpose of this paper is to review these recent developments, to point out open questions, and to suggest avenues for future research

Social Preferences and Competition

There is a general presumption that social preferences can be ignored if markets are competitive. Market experiments (Smith 1962) and recent theoretical results (Dufwenberg et al. 2008) suggest that competition forces people to behave as if they were purely self-interested. We qualify this view. Social preferences are irrelevant if and only if two conditions are met: separability of preferences and completeness of contracts. These conditions are often plausible, but they fail to hold when uncertainty is important (financial markets) or when incomplete contracts are traded (labor markets). Social preferences can explain many of the anomalies frequently observed on these markets.Social preferences; competition; separability; incomplete contracts; asset markets; labor markets

Complementary Patents and Market Structure

Many high technology goods are based on standards that require access to several patents that are owned by different IP holders. We investigate the royalties chosen by IP holders under different market structures. Vertical integration of an IP holder and a downstream producer solves the double mark-up problem between these firms. Nevertheless, it may raise royalty rates and reduce output as compared to non-integration. Horizontal integration of IP holders (or a patent pool) solves the complements problem but not the double mark-up problem. Vertical integration discourages entry and reduces innovation incentives, while horizontal integration always encourages entry and innovation.