Efficient Quasi Monte Carlo methods and their application in Quantum Field Theory

• Applicants: Privatdozent Dr. Karl Jansen; Professorin Dr. Caren Tischendorf, since 5/2016
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Mathematics
• Term: from 2013 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 248869916

• Final Report Year: 2018

Final Report Abstract

During this project and in very close collaboration between physicists and mathematicians, we were able to develop a number of mathematical and algorithmic tools to solve models of high energy physics. These methods comprise Quasi Monte Carlo techniques, iterative numerical integration, effective dimension reduction and new integration rules showing polynomial exactness. This toolbox of new methods is extremely valuable to address problems in the future. Investigations of models in high energy physics in higher dimensions are still under study even beyond the funding period. In fact, very signifcant significant progress in this direction has been made recently and we expect to publish results from these investigations very soon. For the development of such a toolbox of new methods and the very successful interaction between theoretical physicists from high energy physics and applied mathematicians the funding of the DFG has been indispensable. This support has established a very productive cooperation, which is still running and continued in new projects.

Publications

• A first look at quasi-Monte Carlo for lattice field theory problems. J. Phys. Conf. Ser. 454 (2013) 012043
  K. Jansen, H. Leövey, A. Nube, A. Griewank, M. Müller-Preussker
  (See online at https://doi.org/10.1088/1742-6596/454/1/012043)
• Applicability of Quasi-Monte Carlo for lattice systems. PoS LATTICE2013 (2014) 040
  A. Ammon, T. Hartung, K. Jansen, H. Leövey, A. Griewank, M. Müller-Preussker
  
• Quasi-Monte Carlo methods for lattice systems: a first look. Comput. Phys. Commun. 185 (2014) 948-959
  K. Jansen, H. Leövey, A. Ammon, A. Griewank, M. Müller-Preussker
  (See online at https://doi.org/10.1016/j.cpc.2013.10.011)
• Derivative Based Quasi-Monte Carlo Construction and Sensitivity Estimations. Dissertation, Humboldt-Universität zu Berlin (2015)
  Hernan Leövey
  
• Quasi-Monte Carlo methods for linear two-stage stochastic programming problems. Mathematical Programming 151 (2015) 315
  H. Leövey and W. Römisch
  (See online at https://doi.org/10.1007/s10107-015-0898-x)
• New polynomially exact integration rules on U{N) and SU(N). PoS LATTICE2016 (2016) 334
  A. Ammon, T. Hartung, K. Jansen, H. Leövey, Julia Volmer
  (See online at https://doi.org/10.22323/1.256.0334)
• On the efficient numerical solution of lattice systems with low-order couplings. Comput. Phys. Commun. 198 (2016) 71-81
  A. Ammon, A. Genz, T. Hartung, K. Jansen, H. Leövey, J. Volmer
  (See online at https://doi.org/10.1016/j.cpc.2015.09.004)
• Overcoming the sign problem in one-dimensional QCD by new integration rules with polynomial exactness. Phys. Rev. D94 (2016) no. 11, 114508
  A. Ammon, T. Hartung, K. Jansen, H. Leövey, J. Volmer
  (See online at https://doi.org/10.1103/PhysRevD.94.114508)
• Derivative-Based Global Sensitivity Analysis: Upper Bounding of Sensitivites in Seismic-Hazard Assessment Using Automatic Differentiation. Bulletin of the Seismological Society of America 107 (2017) 984
  C. Molkenthin, F. Scherbaum, A. Griewank, H. Leövey, S. Kucherenko, F. Cotton
  (See online at https://doi.org/10.1785/0120160185)