Search for Tracker Potentials in Quintessence Theory

We report a significant finding in Quintessence theory that the the scalar fields with tracker potentials have a model-independent scaling behaviour in the expanding universe. So far widely discussed exponential,power law or hyperbolic potentials can simply mimic the tracking behaviour over a limited range of redshift. In the small redshift range where the variation of the tracking parameter $\epsilon$ may be taken to be negligible, the differential equation of generic potentials leads to hyperbolic sine and hyperbolic cosine potentials which may approximate tracker field in the present day universe. We have plotted the variation of tracker potential and the equation of state of the tracker field as function of the redshift $z$ for the model-independent relation derived from tracker field theory; we have also plotted the variation of $V(\Phi)$ in terms of the scalar field $\Phi$ for the chosen hyperbolic cosine function and have compared with the curves obtained by reconstruction of $V(\phi)$ from the real observational data from the supernovae.Comment: 11 pages, 3 figures, late

Online Appendix to "Delivering endogenous inertia in prices and output"

This appendix provides simulation results for consumption, invest- ment and hours series for the "full model" discussed in the paper. The graphs also plot the relevant data for the US.

Learning-by-doing and Endogenous Price-level Inertia

This paper presents a DGE model in which aggregate price level inertia is generated endogenously by the optimizing behaviour of price setting firms. All the usual sources of inertia are absent here ie., all firms are simultaneously free to change their price once every period and face no adjustment costs in doing so. Despite this, the model generates persistent movements in aggregate output and in\u2021ation in response to a nominal shock. This occurs because firms temper their desire to raise prices after a positive money growth shock in order to learn and lower future costs.Endogenous price stickiness, Business Cycles, Inf1ation, Nominal rigidities, Learning-by-doing, Propagation mechanisms.

Delivering Endogenous Inertia in Prices and Output

This paper presents a DGE model in which aggregate price level inertia is generated endogenously by the optimizing behaviour of price setting ?rms. All the usual sources of inertia are absent here ie., all fi?rms are simultaneously free to change their price once every period and face no adjustment costs in doing so. Despite this, the model generates persistent movements in aggregate output and in?ation in response to a nominal shock. Two modi?cations of a standard one-quarter pre-set price model deliver these results: learning-by-doing and habit formation in leisure.Endogenous price stickiness, Business Cycles, Inflation, Nominal rigidities, Learning-by-doing, Habit formation, Propagation mechanisms, Persistence.

"Rare" Fluctuation Effects in the Anderson Model of Localization

We discuss the role of rare fluctuation effects in quantum condensed matter systems. In particular, we present recent numerical results of the effect of resonant states in Anderson's original model of electron localization. We find that such resonances give rise to anomalous behavior of eigenstates not just far in the Lifshitz tail, but rather for a substantial fraction of eigenstates, especially for intermediate disorder. The anomalous behavior includes non-analyticity in various properties as a characteristic. The effect of dimensionality on the singularity, which is present in all dimensions, is described, and the behavior for bounded and unbounded disorder is contrasted

Middlemen and the Allocation of Heterogeneous Goods

This paper presents a general equilibrium model in which middlemen emerge to facilitate trade in an environment of idiosyncratic tastes and heterogeneous goods. The gains to the traders can be measured along three dimensions: the rate of production, the time preference losses generated by the matching process, and the quality of the match between consumers’ preferences and the goods they ultimately consume.

Singular Behavior of Eigenstates in Anderson's Model of Localization

We observe a singularity in the electronic properties of the Anderson Model of Localization with bounded diagonal disorder, which is clearly distinct from the well-established mobility edge (localization-delocalization transition) that occurs in dimensions $d>2$. We present results of numerical calculations for Anderson's original (box) distribution of onsite disorder in dimensions $d$ = 1, 2 and 3. To establish this hitherto unreported behavior, and to understand its evolution with disorder, we contrast the behavior of two different measures of the localization length of the electronic wavefunctions - the averaged inverse participation ratio and the Lyapunov exponent. Our data suggest that Anderson's model exhibits richer behavior than has been established so far.Comment: Correction to v1: Fig.3 caption now displaye

Large Disorder Renormalization Group Study of the Anderson Model of Localization

We describe a large disorder renormalization group (LDRG) method for the Anderson model of localization in one dimension which decimates eigenstates based on the size of their wavefunctions rather than their energy. We show that our LDRG scheme flows to infinite disorder, and thus becomes asymptotically exact. We use it to obtain the disorder-averaged inverse participation ratio and density of states for the entire spectrum. A modified scheme is formulated for higher dimensions, which is found to be less efficient, but capable of improvement