Simulation of Supersymmetric Models with a Local Nicolai Map

We study the numerical simulation of supersymmetric models having a local Nicolai map. The mapping can be regarded as a stochastic equation and its numerical integration provides an algorithm for the simulation of the original model. In this paper, the method is discussed in details and applied to examples in 0+1 and 1+1 dimensions.Comment: 18 pages, REVTeX + 2 PostScript figure

Perturbative and Numerical Methods for Stochastic Nonlinear Oscillators

Interferometric gravitational wave detectors are devoted to pick up the effect induced on masses by gravitational waves. The variations of the length dividing two mirrors is measured through a laser interferometric technique. The Brownian motion of the masses related to the interferometer room temperature is a limit to the observation of astrophysical signals. It is referred to as thermal noise and it affects the sensitivity of both the projected and the future generation interferometers. In this paper we investigate the relevance of small non-linear effects and point out their impact on the sensitivity curve of interferometric gravitational wave detectors (e.g. VIRGO, LIGO, GEO, ...) through perturbative methods and numerical simulations. We find that in the first order approximation the constants characterizing the power spectrum density (PSD) are renormalized but it retains its typical shape. This is due to the fact that the involved Feynman diagrams are of tadpole type. Higher order approximations are required to give rise to up-conversion effects. This result is predicted by the perturbative approach and is in agreement with the numerical results obtained by studying the system's non-linear response by numerically simulating its dynamics.Comment: 12 pages, REVTeX + 7 PostScript figure

Radiative Correction Effects of a Very Heavy Top

If the top is very heavy, m_t >> M_Z, the dominant radiative correction effects in all electroweak precision tests can be exactly characterized in terms of two quantities, the rho-parameter and the GIM violating Z -> b bbar coupling. These quantities can be computed using the Standard Model Lagrangian with vanishing gauge couplings. This is done here up to two loops for arbitrary values of the Higgs mass.Comment: 9 pages, report IFUP-TH 20/9

The b -> s gamma decay revisited

In this work we compute the leading logarithmic corrections to the b -> s gamma decay in a dimensional scheme which does not require any definition of the gamma5 matrix. The scheme does not exhibit unconsistencies and it is therefore a viable alternative to the t'Hooft Veltman scheme, particularly in view of the next-to-leading computation. We confirm the recent results of Ciuchini et al.Comment: 11 pages RevTeX + 2 EPSF figures, report IFUP-TH 2/94, HUTP-93/A038. PostScript file or hardcopy available from the authors upon reques

Lattice energy-momentum tensor with Symanzik improved actions

We define the energy-momentum tensor on lattice for the $\lambda \phi^4$ and for the nonlinear $\sigma$-model Symanzik tree-improved actions, using Ward identities or an explicit matching procedure. The resulting operators give the correct one loop scale anomaly, and in the case of the sigma model they can have applications in Monte Carlo simulations.Comment: Self extracting archive fil

The Kramers equation simulation algorithm I. Operator analysis

Using an operatorial formalism, we study the Kramers equation and its applications to numerical simulations. We obtain classes of algorithms which may be made precise at every desired order in the time step $\epsilon$ and with a set of free parameters which can be used to reduce autocorrelations. We show that it is possible to use a global Metropolis test to restore Detailed Balance.Comment: 32 pages, REVTeX 3.0, IFUP-TH-2

Discrete sine transform for multi-scale realized volatility measures

In this study we present a new realized volatility estimator based on a combination of the multi-scale regression and discrete sine transform (DST) approaches. Multi-scale estimators similar to that recently proposed by Zhang (2006) can, in fact, be constructed within a simple regression-based approach by exploiting the linear relation existing between the market microstructure bias and the realized volatilities computed at different frequencies. We show how such a powerful multi-scale regression approach can also be applied in the context of the Zhou [Nonlinear Modelling of High Frequency Financial Time Series, pp. 109–123, 1998] or DST orthogonalization of the observed tick-by-tick returns. Providing a natural orthonormal basis decomposition of observed returns, the DST permits the optimal disentanglement of the volatility signal of the underlying price process from the market microstructure noise. The robustness of the DST approach with respect to the more general dependent structure of the microstructure noise is also shown analytically. The combination of the multi-scale regression approach with DST gives a multi-scale DST realized volatility estimator similar in efficiency to the optimal Cramer–Rao bounds and robust against a wide class of noise contamination and model misspecification. Monte Carlo simulations based on realistic models for price dynamics and market microstructure effects show the superiority of DST estimators over alternative volatility proxies for a wide range of noise-to-signal ratios and different types of noise contamination. Empirical analysis based on six years of tick-by-tick data for the S&P 500 index future, FIB 30, and 30 year U.S. Treasury Bond future confirms the accuracy and robustness of DST estimators for different types of real data

The Kramers equation simulation algorithm II. An application to the Gross-Neveu model

We continue the investigation on the applications of the Kramers equation to the numerical simulation of field theoretic models. In a previous paper we have described the theory and proposed various algorithms. Here, we compare the simplest of them with the Hybrid Monte Carlo algorithm studying the two-dimensional lattice Gross-Neveu model. We used a Symanzik improved action with dynamical Wilson fermions. Both the algorithms allow for the determination of the critical mass. Their performances in the definite phase simulations are comparable with the Hybrid Monte Carlo. For the two methods, the numerical values of the measured quantities agree within the errors and are compatible with the theoretical predictions; moreover, the Kramers algorithm is safer from the point of view of the numerical precision.Comment: 20 pages + 1 PostScript figure not included, REVTeX 3.0, IFUP-TH-2

Scaling, asymptotic scaling and Symanzik improvement. Deconfinement temperature in SU(2) pure gauge theory

We report on a high statistics simulation of SU(2) pure gauge field theory at finite temperature, using Symanzik action. We determine the critical coupling for the deconfinement phase transition on lattices up to 8 x 24, using Finite Size Scaling techniques. We find that the pattern of asymptotic scaling violation is essentially the same as the one observed with conventional, not improved action. On the other hand, the use of effective couplings defined in terms of plaquette expectation values shows a precocious scaling, with respect to an analogous analysis of data obtained by the use of Wilson action, which we interpret as an effect of improvement.Comment: 43 pages ( REVTeX 3.0, self-extracting shell archive, 13 PostScript figs.), report IFUP-TH 21/93 (2 TYPOS IN FORMULAS CORRECTED,1 CITATION UPDATED,CITATIONS IN TEXT ADDED