Uncovering some causal relationships between productivity growth and the structure of economic fluctuations: a tentative survey

This paper discusses recent theoretical and empirical work on the interactions between growth and business cycles. One may distinguish two very different types of approaches to the problem of the influence of macroeconomic fluctuations on long-run growth. In the first type of approach, which relies on learning by doing mechanisms or aggregate demand externalities, productivity growth and direct production activities are complements. An expansion therefore has a positive long-run effect on total factor productivity. In the second type of approach, hereafter labeled 'opportunity cost or 'learning-by-doing', productivity growth and production activities are substitutes. The opportunity cost of some productivity improving activities falls in a recession, which has a long-run positive impact on output. This does not mean, however, that recessions should on average last longer or be more frequent, since the expectation of future recessions reduces today's incentives for productivity growth. We also briefly discuss some empirical work which is mildly supportive of the opportunity cost approach, while showing that it can be reconciled with the observed pro-cyclical behavior of measured total factor productivity. We also describe some theoretical work on the effects of growth on business cycles

Heat transport in SrCu_2(BO_3)_2 and CuGeO_3

In the low dimensional spin systems $SrCu_2(BO_3)_2$ and $CuGeO_3$ the thermal conductivities along different crystal directions show pronounced double-peak structures and strongly depend on magnetic fields. For $SrCu_2(BO_3)_2$ the experimental data can be described by a purely phononic heat current and resonant scattering of phonons by magnetic excitations. A similar effect seems to be important in $CuGeO_3$, too but, in addition, a magnetic contribution to the heat transport may be present.Comment: 4 pages, 2 figures; appears in the proceedings of the SCES2001 (Physica B

On the soliton width in the incommensurate phase of spin-Peierls systems

We study using bosonization techniques the effects of frustration due to competing interactions and of the interchain elastic couplings on the soliton width and soliton structure in spin-Peierls systems. We compare the predictions of this study with numerical results obtained by exact diagonalization of finite chains. We conclude that frustration produces in general a reduction of the soliton width while the interchain elastic coupling increases it. We discuss these results in connection with recent measurements of the soliton width in the incommensurate phase of CuGeO_3.Comment: 4 pages, latex, 2 figures embedded in the tex

Geometric Exponents, SLE and Logarithmic Minimal Models

In statistical mechanics, observables are usually related to local degrees of freedom such as the Q < 4 distinct states of the Q-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit, these models are described by rational conformal field theories, namely the minimal models M(p,p') for suitable p, p'. More generally, as in stochastic Loewner evolution (SLE_kappa), one can consider observables related to nonlocal degrees of freedom such as paths or boundaries of clusters. This leads to fractal dimensions or geometric exponents related to values of conformal dimensions not found among the finite sets of values allowed by the rational minimal models. Working in the context of a loop gas with loop fugacity beta = -2 cos(4 pi/kappa), we use Monte Carlo simulations to measure the fractal dimensions of various geometric objects such as paths and the generalizations of cluster mass, cluster hull, external perimeter and red bonds. Specializing to the case where the SLE parameter kappa = 4p'/p is rational with p < p', we argue that the geometric exponents are related to conformal dimensions found in the infinitely extended Kac tables of the logarithmic minimal models LM(p,p'). These theories describe lattice systems with nonlocal degrees of freedom. We present results for critical dense polymers LM(1,2), critical percolation LM(2,3), the logarithmic Ising model LM(3,4), the logarithmic tricritical Ising model LM(4,5) as well as LM(3,5). Our results are compared with rigourous results from SLE_kappa, with predictions from theoretical physics and with other numerical experiments. Throughout, we emphasize the relationships between SLE_kappa, geometric exponents and the conformal dimensions of the underlying CFTs.Comment: Added reference

Temperature and magnetic field dependence of the lattice constant in spin-Peierls cuprate CuGeO_3 studied by capacitance dilatometry in fields up to 16 Tesla

We present high resolution measurements of the thermal expansion coefficient and the magnetostriction along the a-axis of CuGeO_3 in magnetic fields up to 16 Tesla. From the pronounced anomalies of the lattice constant a occurring for both temperature and field induced phase transitions clear structural differences between the uniform, dimerized, and incommensurate phases are established. A precise field temperature phase diagram is derived and compared in detail with existing theories. Although there is a fair agreement with the calculations within the Cross Fisher theory, some significant and systematic deviations are present. In addition, our data yield a high resolution measurement of the field and temperature dependence of the spontaneous strain scaling with the spin-Peierls order parameter. Both the zero temperature values as well as the critical behavior of the order parameter are nearly field independent in the dimerized phase. A spontaneous strain is also found in the incommensurate high field phase, which is significantly smaller and shows a different critical behavior than that in the low field phase. The analysis of the temperature dependence of the spontaneous strain yields a pronounced field dependence within the dimerized phase, whereas the temperature dependence of the incommensurate lattice modulation compares well with that of the dimerization in zero magnetic field.Comment: 25 pages, 15 Figs., to appear in Phys. Rev. B55 (Vol.5

Stochastic Reaction-diffusion Equations Driven by Jump Processes

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.Comment: See journal reference for teh final published versio