Classification of extended chaotic inflation potentials

Brans-Dicke gravity is remarkable not only in that General Relativity and Mach's Principle find a common enlarged scenario where they are mutually consistent, but also in that it provides a very interesting quantum cosmological model within the inflationary paradigm. The interplay between the Brans-Dicke scalar Φ and the inflaton field σ plays an important rôle during the course of inflation, and although the dynamics as such is governed by the potential, the onset and the end of inflation are determined by the values of both fields jointly. The relative position of the beginning – and end-of-inflation curves (BoI and EoI respectively) is the most relevant factor in determining the resulting quantum cosmological scenario. The classification of potentials that is given in this paper is based on the criterion of whether the BoI and EoI boundaries enclose a finite or infinite area in the (σ,Φ) plane where inflation takes place. It is shown that this qualitative classification distinguishes two classes of potentials that yield very different cosmologies and it is argued that only those theories in which BoI and EoI enclose a finite area in the (σ,Φ) plane are compatible with our observable universe.     

Renormalization of one-dimensional avalanche models

We investigate a renormalization group (RG) scheme for avalanche automata introduced recently by Pietroneroet al. to explain universality in self-organized criticality models. Using a modified approach, we construct exact RG equations for a one-dimensional model whose detailed dynamics is exactly solvable. We then investigate in detail the effect of approximations inherent in a practical implementation of the RG transformation where exact dynamical information is unavailable.     

Noise in one-dimensional diffusion models

The low-frequency voltage noise for charged particlesm moving in one-dimensional system in which the motion is dominated by thermally activated hopping over defect-induced barriers is determined. This is a model for certain ionic conductors. The low-frequency noise is anomalous and diverges if there is a significant distribution of high barriers.     

Antiholons in one-dimensional t-J models

Using a newly developed hybrid Monte Carlo algorithm for the nearest-neighbor (nn) t-J model, we show that antiholons identified in the supersymmetric inverse squared (IS) t-J model are clearly visible in the electron-addition spectrum of the nn t-J model at J=2t and also for J=0.5t, a value of experimental relevance.     

Exactly solvable one-dimensional inhomogeneous models

We present a simple way of constructing one-dimensional inhomogeneous models (random or quasiperiodic) which can be solved exactly. We treat the example of an Ising chain in a varying magnetic field, but our procedure can easily be extended to other one-dimensional inhomogeneous models. For all the models we can construct, the free energy and its derivatives with respect to temperature can be computed exactly at one particular temperature.     

Solvable one-dimensional models of particle production

We discuss a variety of simple one-dimensional models for particle production. For each of these models we derive a closed form for the generating functional which allows one to calculate the totality of inclusive, semi-inclusive and exclusive distributions. The models discussed include an n-trajectory multiperipheral model and a general cluster model. In this latter model we derive a parameter independent relation between semi-inclusive cross sections.     

Robust stability of extended delayed-feedback control in one-dimensional chaotic systems

This paper investigates robust stability of the extended delayed-feedback control method [Phys. Rev. E 50 (1994) 3245] from the viewpoint of control theory. The feedback-gain range where control can be achieved for this method is wider than that of the original delayed-feedback control method. We provide a procedure to design the extended delayed-feedback controller with a minimum amount of a priori knowledge for chaotic systems including a parameter uncertainty. Some numerical experiments are given to check the results.     

Localized defects in classical one-dimensional models

Several aspects of localized defects in the Frenkel-Kontorova, classicalXY chain and analogous models with a finite range of interactions are discussed from a general point of view. Precise definitions are given for defect phase shifts (charges) and for creation, pinning, and interaction energies. Corresponding definitions are also provided for interfaces (localized regions separating two phases). For the nearest-neighbor Frenkel-Kontorova model, the various defect energies are related to areas enclosed by contours joining heteroclinic points of the area-preserving map generated by the conditions of mechanical equilibrium.     

Hierarchical models and chaotic spin glasses

Renormalization-group studies in position space have led to the discovery of hierarchical models which are exactly solvable, exhibiting nonclassical critical behavior at finite temperature. Position-space renormalization-group approximations that had been widely and successfully used are in fact alternatively applicable as exact solutions of hierarchical models, this realizability guaranteeing important physical requirements. For example, a hierarchized version of the Sierpiriski gasket is presented, corresponding to a renormalization-group approximation which has quantitatively yielded the multicritical phase diagrams of submonolayers on graphite. Hierarchical models are now being studied directly as a testing ground for new concepts. For example, with the introduction of frustration, chaotic renormalization-group trajectories were obtained for the first time. Thus, strong and weak correlations are randomly intermingled at successive length scales, and a new microscopic picture and mechanism for a spin glass emerges. An upper critical dimension occurs via a boundary crisis mechanism in cluster-hierarchical variants developed to have well-behaved susceptibilities.     

Exactly solvable models showing chaotic behavior

Several examples of the one-dimensional mapping which are exactly solvable and show chaotic behaviour are presented. The importance of the accuracy of the numerical calculation is stressed.     

Scaling behavior of one-dimensional weakly disordered models

The density of states and various characteristic lengths of one-dimensional tight-binding models and disordered harmonic chains are calculated in the limit of weak disorder at the band edge of the ordered system. The density of states and a localization length of the one-dimensional Anderson model were already calculated by Derrida and Gardner; we recover their results. For the tight-binding models with off-diagonal disorder our results are in agreement with numerical calculations of Krey.     

Resistance of one-dimensional chains in Kronig-Penny-like models

We give the formula for the resistance of one-dimensional chains of arbitrary δ-potentials without finding electron eigenfunctions. We have analyzed the main consequences of this formula, and the distribution functions of resistances are also determined.     

Classification of quantum degenerate regimes in one-dimensional Bose gases

In this paper we address the different regimes of quantum degeneracy in a one-dimensional Bose gas taking into consideration some parameters that are readily accessible in the experiment. We pay particular attention to the tunability of the trap anisotropy and the number of particles in the system.     

Coarsening process in one-dimensional surface growth models

Surface growth models may give rise to instabilities with mound formation whose typical linear size L increases with time (coarsening process). In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (corresponding to model B of dynamics): coarsening is known to be logarithmic in the absence of noise ( L(t) ∼ ln t) and to follow a power law ( L(t) ∼t ^1/3) when noise is present. If the surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stages of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster : if α is the exponent describing the steepening of the maximal slope M of mounds ( M ^α∼L) we find that L(t) ∼t ⁿ: n is equal to for 1≤α≤2 and it decreases from to for α≥2, according to n = α/(5α - 2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t) ∼t ^1/4, irrespectively of α. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model α = 1, both in the absence and in the presence of noise. Received 28 September 2001 and Received in final form 21 November 2001     

Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models

The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of correlation functions are closed, are considered. A transfer matrix method is used to find the static solution. It is seen that this transfer matrix can be obtained in a closed form, if the reaction rates satisfy certain conditions. We call such models superautonomous. Possible static phase transitions of such models are investigated. At the end, as an example of superautonomous models, a nonuniform voter model is introduced, and solved explicitly.     

Competition and cooperation in one-dimensional stepping-stone models

Mutualism is a major force driving evolution and sustaining ecosystems. Although the importance of spatial degrees of freedom and number fluctuations is well known, their effects on mutualism are not fully understood. With range expansions of microbes in mind, we show that, even when mutualism confers a selective advantage, it persists only in populations with high density and frequent migrations. When these parameters are reduced, mutualism is generically lost via a directed percolation (DP) process, with a phase diagram strongly influenced by an exceptional symmetric DP (DP2) transition.     

Effective one-dimensional models from matrix product states

In this paper we present a method for deriving effective one-dimensional models based on the matrix product state formalism. It exploits translational invariance to work directly in the thermodynamic limit. We show, how a representation of the creation operator of single quasi-particles in both real and momentum space can be extracted from the dispersion calculation. The method is tested for the analytically solvable Ising model in a transverse magnetic field. Properties of the matrix product representation of the creation operator are discussed and validated by calculating the one-particle contribution to the spectral weight. Results are also given for the ground state energy and the dispersion.     

Front propagation in certain one-dimensional exclusion models

Recent results on two interacting particle systems on are summarized, the asymmetric simple exclusion process and the branching exclusion process.