Theory of Current and Shot Noise Spectroscopy in Single-Molecular Quantum Dots with Phonon Mode

Using the Keldysh nonequilibrium Green function technique, we study the current and shot noise spectroscopy of a single molecular quantum dot coupled to a local phonon mode. It is found that in the presence of electron-phonon coupling, in addition to the resonant peak associated with the single level of the dot, satellite peaks with the separation set by the frequency of phonon mode appear in the differential conductance. In the ``single level'' resonant tunneling region, the differential shot noise power exhibit two split peaks. However, only single peaks show up in the ``phonon assisted'' resonant-tunneling region. An experimental setup to test these predictions is also proposed.Comment: 5 pages, 3 eps figures embedde

Analytical Results for Individual and Group Selection of Any Intensity

The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (= fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in the limit of weak selection, where the game has a small effect on overall fitness. But this linear function makes the analysis of strong selection difficult. Here, we show that analytical results can be obtained for any intensity of selection, if fitness is defined as an exponential function of payoff. This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory