A Note on Kuhn's Theorem with Ambiguity Averse Players

Kuhn's Theorem shows that extensive games with perfect recall can equivalently be analyzed using mixed or behavioral strategies, as long as players are expected utility maximizers. This note constructs an example that illustrate the limits of Kuhn's Theorem in an environment with ambiguity averse players who use maxmin decision rule and full Bayesian updating.Comment: 7 figure

Why invest in rural America and how? : a critical public policy question for the 21st century

Significant portions of rural America are in trouble. For some parts of rural America, the slow slide to no longer being economically, socially, or politically viable is within sight. At the same time, without intending it, rural America appears headed for a land of the rich and the poor—a rural America of resorts and pockets of persistent poverty.> Yet current rural policies are designed for the past, not the future. In terms of public dollars committed, today’s rural policy focuses primarily on two areas—agriculture and manufacturing. Neither focus can meet the future needs of rural people and their communities.> In his paper presented at this year’s conference sponsored by the Center for the Study of Rural America, Exploring Policy Options for a New Rural America, Dr. Stauber discusses how a successful rural policy must be crafted with three key societal benefits in mind—the survival of the rural middle class, reducing concentrated rural poverty, and sustaining and improving the quality of the natural environment.Rural areas ; Rural development

Optical absorption in quantum dots: Coupling to longitudinal optical phonons treated exactly

Optical transitions in a semiconductor quantum dot are theoretically investigated, with emphasis on the coupling to longitudinal optical phonons, and including excitonic effects. When limiting to a finite number of $m$ electron and $n$ hole levels in the dot, the model can be solved exactly within numerical accuracy. Crucial for this to work is the absence of dispersion of the phonons. A suitable orthogonalization procedure leaves only $m(m+1)/2+n(n+1)/2-2$ phonon modes to be coupled to the electronic system. We calculate the linear optical polarization following a delta pulse excitation, and by a subsequent Fourier transformation the resulting optical absorption. This strict result is compared with a frequently used approximation modeling the absorption as a convolution between spectral functions of electron and hole, which tends to overestimate the effect of the phonon coupling. Numerical results are given for two electron and three hole states in a quantum dot made from the polar material CdSe. Parameter values are chosen such that a quantum dot with a resonant sublevel distance can be compared with a nonresonant one.Comment: 12 pages, 6 figure

Plasmons and near-field amplification in double-layer graphene

We study the optical properties of double-layer graphene for linearly polarized evanescent modes and discuss the in-phase and out-of-phase plasmon modes for both, longitudinal and transverse polarization. We find a energy for which reflection is zero, leading to exponentially amplified transmitted modes similar to what happens in left-handed materials. For layers with equal densities $n=10^{12}$cm$^{-2}$, we find a typical layer separation of $d\approx500\mu$m to detect this amplification for transverse polarization which may serve as an indirect observation of transverse plasmons. When the two graphene layers lie on different chemical potentials, the exponential amplification either follows the in-phase or out-of-phase plasmon mode depending on the order of the low- and high-density layer. This opens up the possibility of a tunable near-field amplifier or switch.Comment: 9 pages, 8 figure

Plasmonics in Dirac systems: from graphene to topological insulators

The recent developments in the emerging field of plasmonics in graphene and other Dirac systems are reviewed and a comprehensive introduction to the standard models and techniques is given. In particular, we discuss intrinsic plasmon excitations of single and bilayer graphene via hydrodynamic equations and the random phase approximation, but also comment on double and multilayer structures. Additionally, we address Dirac systems in the retardation limit and also with large spin-orbit coupling including topological insulators. Finally, we summarize basic properties of the charge, current and photon linear response functions in an appendix.Comment: 25 pages, 10 figures; submitted to J. Phys.: TOPICAL REVIEW (invited

Analytical expressions for the polarizability of the honeycomb lattice

We present analytical expressions for the polarizability $P_\mu(q_x,\omega)$ of graphene modeled by the hexagonal tight-binding model for small wave number $q_x$, but arbitrary chemical potential $\mu$. Generally, we find $P_\mu(q_x,\omega)=P_\mu^(\omega)$ with $\omega_q=v_Fq_x$ the Dirac energy, where the first term is due to intra-band and the second due to inter-band transitions. Explicitly, we derive the analytical expression for the imaginary part of the polarizability including intra-band contributions and recover the result obtained from the Dirac cone approximation for $\mu\rightarrow0$. For $\mu<\sqrt{3}t$, there is a square-root singularity at $\omega_q=v_Fq_x$ independent of $\mu$. For doping levels close to the van Hove singularity, $\mu=t\pm\delta\mu$, $ImP_\mu(q_x,\omega)$ is constant for $\delta\mu/t<\omega/\omega_q\ll1$.Comment: 5 pages, 3 figures, 1 tabl