Resolving the rules

James K. Freericks, Khadijeh Najafi, Alexander F. Kemper +1 more

We derive frequency moment sum rules for the retarded electronic Green's function and self-energy of the Holstein model for both equilibrium and nonequilibrium cases. We also derive sum rules for the phonon propagator in equilibrium and nonequilibrium. These sum rules allow one to benchmark nonequilibrium calculations and help with interpreting the behavior of electrons driven out of equilibrium by an applied electric field. We exactly evaluate the sum rules when the system is in the atomic limit. We also discuss the application of these sum rules to pump/probe experiments like time-resolved angle-resolved photoemission spectroscopy.

Iulia Georgescu

David Pogue

Freericks, J. K. [Georgetown Univ., Washington, DC (United States)]; Najafi, Khadijeh [Georgetown Univ., Washington, DC (United States)]; Kemper, A. F. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)]; Devereaux, T. P. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States). Geballe Lab. for Advanced Materials]

We derive frequency moment sum rules for the retarded electronic Green's function and self-energy of the Holstein model for both equilibrium and nonequilibrium cases. We also derive sum rules for the phonon propagator in equilibrium and nonequilibrium. These sum rules allow one to benchmark nonequilibrium calculations and help with interpreting the behavior of electrons driven out of equilibrium by an applied electric field. We exactly evaluate the sum rules when the system is in the atomic limit. We also discuss the application of these sum rules to pump/probe experiments like time-resolved angle-resolved photoemission spectroscopy.

Richard A. Mould

This paper elaborates on four previously proposed rules of engagement between conscious states and physiological states. A new rule is proposed that applies to a continuous model of conscious brain states that cannot precisely resolve eigenvalues. If two apparatus states are in superposition, and if their eigenvalues are so close together that they cannot be consciously resolved on this model, then it is shown that observation will not generally reduce the superposition to just one of its member eigenstates. In general, the observation of a quantum mechanical superposition results in another superposition. Key words: Brain states, consciousness, conscious observer, macroscopic superposition, measurement, state reduction, state collapse, von Neumann.

R. Shankar