Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

f(R) theories

http://cds.cern.ch/record/262851/files/9405029.pdf

Supersymmetry and quantum mechanics

http://nuclear.korea.ac.kr/~bhong/class/WhitePaper_PHENIX_RUN1-3.pdf

Formation of dense partonic matter in relativistic nucleus–nucleus collisions at RHIC: Experimental evaluation by the PHENIX Collaboration

Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes. A large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker–Planck equation (Metzler R and Klafter J 2000a, Phys. Rep. 339 1–77). It therefore appears timely to put these new works in a cohesive perspective. In this review we cover both the theoretical modelling of sub- and superdiffusive processes, placing emphasis on superdiffusion, and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function. We also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems.

/pdf/the-restaurant-at-the-end-of-the-random-walk-recent-1w7yr3snyb.pdf

The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics

Brownian motors: noisy transport far from equilibrium

We find that the single-particle distribution $\frac{\mathrm{EdN}}{{d}^{3}p}$ for an expanding relativistic gas described by a distribution function obeying the Boltzmann transport equation is not of the form of an integral over collective motions of a velocity weight function times a "Lorentz-transformed" rest-frame distribution function. This casts doubt on the algorithms of Milekhin and Hagedorn for determining the single-particle distribution function in their models of particle production. For the hydrodynamic model, the correct algorithm is presented.

Single-particle distribution in the hydrodynamic and statistical thermodynamic models of multiparticle production

Aspects of Supersymmetric Quantum Mechanics

We investigate whether a general class of solvable potentials, the Natanzon potentials (those potentials whose solutions are hypergeometric functions), and their supersymmetric partner potentials are related by a discrete reparametrization invariance called ``shape invariance'' discovered by Genden- shtein. We present evidence that this is not the case in general. Instead we find that the Natanzon class of potentials is not the most general class of solvable potentials but instead belongs to a wider class of potentials generated by supersymmetry and factorization whose eigenfunctions are sums of hypergeometric functions. The series of Hamiltonians, together with the corresponding supersymmetric charges form the graded Lie algebra sl(1/1)\ensuremath{\bigotimes}SU(2). We also present a strategy for solving, in a limited domain, the discrete reparametrization invariance equations connected with ``shape invariance.''

Relationship between supersymmetry and solvable potentials.

We investigate the mechanism of pair creation in scalar QED from spatially homogeneous strong electric fields in 1+1 dimensions. Solution of the semiclassical field equations shows particle creation followed by plasma oscillations. We compare our results with a model based on a relativistic Boltzmann-Vlasov equation with a pair-creation source term related to the Schwinger mechanism. The time evolution of the electric field and the current obtained from the Boltzmann-Vlasov model is surprisingly similar to that found in the semiclassical calculation.

Fred Cooper

Papers

Supersymmetry and quantum mechanics

Single-particle distribution in the hydrodynamic and statistical thermodynamic models of multiparticle production

Aspects of Supersymmetric Quantum Mechanics

Relationship between supersymmetry and solvable potentials.

Pair production in a strong electric field.