A numerical simulation of pre-big bang cosmology

We analyse numerically the onset of pre-big bang inflation in an inhomogeneous, spherically symmetric Universe. Adding a small dilatonic perturbation to a trivial (Milne) background, we find that suitable regions of space undergo dilaton-driven inflation and quickly become spatially flat ($\Omega \to 1$). Numerical calculations are pushed close enough to the big bang singularity to allow cross checks against previously proposed analytic asymptotic solutions.Comment: 19 pages, revtex, matlab code available at http://www.fis.unipr.it/~onofr

Supersymmetry and Combinatorics

We show how a recently proposed supersymmetric quantum mechanics model leads to non-trivial results/conjectures on the combinatorics of binary necklaces and linear-feedback shift-registers. Pauli's exclusion principle plays a crucial role: by projecting out certain states/necklaces, it allows to represent the supersymmetry algebra in the resulting subspace. Some of our results can be rephrased in terms of generalizations of the well-known Witten index.Comment: 14 pages, 3 figures, text expanded, references adde

Public Inputs and Endogenous Growth in the Agricultural Sector: a Dynamic Dual Approach

This paper examines growth in the U.S. agricultural sector under the conditions hypothesized by endogenous growth theory. Public capital and R&D are explicitly considered to capture the effects of public inputs in a model based on dynamic duality theory. Results support some necessary conditions for this hypothesis to be true.International Development,

PUBLIC CAPITAL, R&D, AGRICULTURAL PRODUCTION AND ENDOGENOUS GROWTH

The paper examines growth in the U.S. agricultural sector under the conditions hypothesized by endogenous growth theory. Public capital and R&D in agriculture are explicitly considered to capture the effect of public inputs. Results support some of the necessary conditions for this hypothesis to be true.Agricultural and Food Policy, Public Economics,

Public Inputs and Productivty in the Agricultural Sector: A Dynamic Dual Approach

This paper introduces a dynamic model of productivity measurement based on recent endogenous growth theories. The model presented in this study is based on dynamic duality theory and incorporate public goods (public capital and R&D) as external factors to the firms. It also rationalizes the provision of public inputs by a benevolent social planner that internalizes the effects of them. Moreover, the Le Chatelier principle is extended for this dynamic duality modelin which the public factors are quasi-fixed for the firm and all firm-specific inputs can be adjusted in the long run. Therefore, increasing returns to scale over all inputs can still be tested at the long-run equilibrium perceived by the firm. Additionally, this model permits deriving testable hypotheses related to the two conditions of endogenous growth theory mentioned above. The model is tested with data for the U.S. agricultural sector.endogenous growth, dynamic productivity, public goods, duality, U.S. agriculture

The planar spectrum in U(N)-invariant quantum mechanics by Fock space methods: I. The bosonic case

Prompted by recent results on Susy-U(N)-invariant quantum mechanics in the large N limit by Veneziano and Wosiek, we have examined the planar spectrum in the full Hilbert space of U(N)-invariant states built on the Fock vacuum by applying any U(N)-invariant combinations of creation-operators. We present results about 1) the supersymmetric model in the bosonic sector, 2) the standard quartic Hamiltonian. This latter is useful to check our techniques against the exact result of Brezin et al. The SuSy case is where Fock space methods prove to be the most efficient: it turns out that the problem is separable and the exact planar spectrum can be expressed in terms of the single-trace spectrum. In the case of the anharmonic oscillator, on the other hand, the Fock space analysis is quite cumbersome due to the presence of large off-diagonal O(N) terms coupling subspaces with different number of traces; these terms should be absorbed before taking the planar limit and recovering the known planar spectrum. We give analytical and numerical evidence that good qualitative information on the spectrum can be obtained this way.Comment: 17 pages, 4 figures, uses youngtab.sty. Final versio

Dilatation operator and Cayley graphs

We use the algebraic definition of the Dilatation operator provided by Minahan, Zarembo, Beisert, Kristijansen, Staudacher, proper for single trace products of scalar fields, at leading order in the large-N 't Hooft limit to develop a new approach to the evaluation of the spectrum of the Dilatation operator. We discover a vast number of exact sequences of eigenstates.Comment: 30 pages and 3 eps figures, v2: few typos correcte

Four Loop Result in SU(3)SU(3) Lattice Gauge Theory by a Stochastic Method: Lattice Correction to the Condensate

We describe a stochastic technique which allows one to compute numerically the coefficients of the weak coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the link variables $U_\mu(x) \to \exp\{A_\mu(x)/\sqrt\beta\}$ into the Langevin algorithm and the observables and to perform the expansion in \beta^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of maps which can be exactly truncated at any order. We give the result for the simple plaquette of SU(3) up to fourth loop order (\beta^{-4}) which extends by one loop the previously known series.Comment: 9 pages. + 5 figures (postscript) appended at the end, (University of Parma, Dept.of Physics, report uprf-397-1994

A supersymmetric matrix model: II. Exploring higher-fermion-number sectors

Continuing our previous analysis of a supersymmetric quantum-mechanical matrix model, we study in detail the properties of its sectors with fermion number F=2 and 3. We confirm all previous expectations, modulo the appearance, at strong coupling, of {\it two} new bosonic ground states causing a further jump in Witten's index across a previously identified critical 't Hooft coupling $\lambda_c$. We are able to elucidate the origin of these new SUSY vacua by considering the $\lambda \to \infty$ limit and a strong coupling expansion around it.Comment: 14 pages, 4 figure