Search results for "PERTURBATION"
showing 10 items of 811 documents
Cyclicity of common slow–fast cycles
2011
Abstract We study the limit cycles of planar slow–fast vector fields, appearing near a given slow–fast cycle, formed by an arbitrary sequence of slow parts and fast parts, and where the slow parts can meet the fast parts in a nilpotent contact point of arbitrary order. Using the notion slow divergence integral, we delimit a large subclass of these slow–fast cycles out of which at most one limit cycle can perturb, and a smaller subclass out of which exactly one limit cycle will perturb. Though the focus lies on common slow–fast cycles, i.e. cycles with only attracting or only repelling slow parts, we present results that are valid for more general slow–fast cycles. We also provide examples o…
2MOLCAS as a development platform for quantum chemistry software
2004
This work presents the quantum chemistry package MOLCAS, with emphasis on its usefulness as a platform for developing new quantum chemical codes, and the reader is assumed to be familiar with such a process. The development of new codes for quantum chemistry is a time-consuming job that can be dramatically simplified by using libraries for standard problems (such as calculation of integrals), and tools to surmount computer language and operating system limitations. The MOLCAS quantum chemistry software contains modules for a variety of quantum chemical methods, such as Hartree-Fock (HF), density functional theory (DFT), coupled-cluster (CC), and multiconfigurational (MCSCF) approaches, incl…
The anomalous magnetic moment of the muon in the Standard Model
2020
We are very grateful to the Fermilab Directorate and the Fermilab Theoretical Physics Department for their financial and logistical support of the first workshop of the Muon g -2 Theory Initiative (held near Fermilab in June 2017) [123], which was crucial for its success, and indeed for the successful start of the Initiative. Financial support for this workshop was also provided by the Fermilab Distinguished Scholars program, the Universities Research Association through a URA Visiting Scholar award, the Riken Brookhaven Research Center, and the Japan Society for the Promotion of Science under Grant No. KAKEHNHI-17H02906. We thank Shoji Hashimoto, Toru Iijima, Takashi Kaneko, and Shohei Nis…
Properties of Design-Based Functional Principal Components Analysis.
2010
This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA is a dimension reduction tool which is the first step to develop model assisted approaches that can take auxiliary information into account. FPCA relies on the estimation of the eigenelements of the covariance operator which can be seen as nonlinear functionals. Adapting to our functional context the linearization technique based on the influence function developed by Deville (1999), we prove that these estimators are asymptotically design unbiased and con…
Quantum averaging for driven systems with resonances
2000
Abstract We discuss the effects of resonances in driven quantum systems within the context of quantum averaging techniques in the Floquet representation. We consider in particular iterative methods of KAM type and the extensions needed to take into account resonances. The approach consists in separating the coupling terms into resonant and nonresonant components at a given scale of time and intensity. The nonresonant part can be treated with perturbative techniques, which we formulate in terms of KAM-type unitary transformations that are close to the identity. These can be interpreted as averaging procedures with respect to the dynamics defined by effective uncoupled Hamiltonians. The reson…
Macroscopic Dynamic Effects of Migrations in Patchy Predator-prey Systems
1997
Abstract Different mechanisms at the behaviourial or physiological levels determine many properties of predator-prey systems at the population level. In this paper, we present a method of obtaining complex predator-prey dynamic models from models at a detailed, behaviourial level of description. We consider a multi-patch predator-prey model, the dynamics of which contains two time-scales: a fast one, associated with migrations between patches, and a slow one, on which interactions, reproduction and mortality occur. We use methods of perturbation theory in order to aggregate the multi-patch system into a reduced system of two differential equations for the total prey and predator populations…
Assessing covariate imbalance in meta-analysis studies.
2010
The main goal of meta-analysis is to combine data across studies or data sets to obtain summary estimates. In this paper, the novelty is to propose a statistical tool to assess a possible covariate imbalance in baseline variables to investigate similarity of trials. We conducted the detection of the covariate imbalance, first, through some graphical comparison of the empirical cumulative distribution functions or ECDFs, which are built by putting together arms or trials according to some risk factor, and second, through some non-parametric tests such as the Kolmogorov–Smirnov and the Anderson–Darling tests. To overcome the huge presence of ties, we conducted the statistical tests on perturbe…
Time-dependent perturbation treatment of independent Raman schemes
2007
The problem of a trapped ion subjected to the action of two or more independent Raman schemes is analysed through a suitable time-dependent perturbative approach based on the factorization of the evolution operator in terms of other unitary operators. We show that the dynamics of the system may be traced back to an effective Hamiltonian up to a suitable dressing. Moreover, we give the method to write the master equation corresponding to the case wherein spontaneous decays occur.
Explicit near-symplectic mappings of Hamiltonian systems with Lie-generating functions
2008
The construction of explicit near-symplectic mappings for generic Hamiltonian systems with the utilization of Lie transforms is presented. The method is mathematically rigorous and systematically extended to high order with respect to a perturbation parameter. The explicit mappings are compared to their implicit counterparts, which use mixed-variable generating functions, in terms of conservation of invariant quantities, calculation speed and accurate construction of Poincare surfaces of sections. The comparative study considers a wide range of parameters and initial conditions for which different time scales are involved due to large differences between internal and external frequencies of…
Doubling the success of quantum walk search using internal-state measurements
2015
In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it doubles the success probability of many quantum spatial search algorithms. For example, this allows Grover's unstructured search problem to be solved with certainty, rather than with probability 1/2 if only the walker's position is measured, so the additional measurement yields a search algorithm that is twice as fast as without it, on average. Thus the internal state of discrete-time quantum walks holds valuable information that can be utilized to improve a…