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  • richardmitnick 1:23 pm on April 17, 2014 Permalink | Reply
    Tags: , Duke Physics   

    From Duke Physics: “Another Outstanding Fermion Sign Problem Solved” 

    Duke Bloc
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    Duke University

    Second year graduate student Emilie Huffman and Prof. Shailesh Chandrasekharan have recently solved an outstanding sign problem that had remained unsolved for almost 30 yrs.

    Sign problems arise when one tries to design Monte Carlo methods to compute quantum amplitudes in quantum many body physics. Although [Richard] Feynman taught us how one can compute such amplitudes by summing over an exponentially large number of classical paths, to perform such a sum exactly is almost always impossible in realistic physical systems. Most analytic calculations involve a “perturbative” expansion in which one argues that only a few diagrams contribute. Unfortunately, one needs to sum an incredibly large number of diagrams before an accurate answer can be found in many interesting strongly correlated quantum systems.

    In thermal equilibrium, the exponential sum can sometimes be viewed as a classical statistical mechanics problem and Monte Carlo methods can be used to perform the sum. However, the statistical Boltzmann weight can be negative or even complex due to quantum mechanics and in such cases the probability distribution to sample the classical configurations is unclear. A bad choice can lead to wrong results since one is sampling a non-representative set of configurations. This is the so called sign problem, which has hindered progress in our understanding of many strongly interacting fermionic quantum field theories.

    Prof. Chandrasekharan’s research focuses on solving sign problems. His research has shown that some sign problems are solvable if one is clever in grouping fermion world lines into what he calls fermion bags. If the fermions interact with bosons, the solution may also require the use of world line variables to represent bosons. Both relativistic and non-relativistic problems are solvable using this approach. The recent work is an extension of these ideas to a different class of problems.

    The new progress is based on an interesting compact formula in quantum many body physics, derived by Huffman. This formula seems to have remained unappreciated by the quantum Monte Carlo community. When combined with the fermion bag idea, the formula solves the sign problem in a class of lattice field theories involving massless fermions. Since electrons hopping on a honeycomb lattice produce such fermions at low energies, the progress will help us study quantum critical behavior in graphene inspired lattice models.

    The breakthrough achieved in the current work overcomes another important barrier. Traditionally, many sign problems are solvable when there is pairing between an even number of species of fermions. The recent work of Huffman and Chandrasekharan show that pairing can occur between particles and holes. This pairing is hidden in traditional formulations with an odd number of fermion species, but the fermion bag approach helps to uncover it. Hence we can now solve some models with an odd number of fermion species.

    See the full article here.

    Younger than most other prestigious U.S. research universities, Duke University consistently ranks among the very best. Duke’s graduate and professional schools — in business, divinity, engineering, the environment, law, medicine, nursing and public policy — are among the leaders in their fields. Duke’s home campus is situated on nearly 9,000 acres in Durham, N.C, a city of more than 200,000 people. Duke also is active internationally through the Duke-NUS Graduate Medical School in Singapore, Duke Kunshan University in China and numerous research and education programs across the globe. More than 75 percent of Duke students pursue service-learning opportunities in Durham and around the world through DukeEngage and other programs that advance the university’s mission of “knowledge in service to society.”

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  • richardmitnick 8:52 am on July 19, 2013 Permalink | Reply
    Tags: , Duke Physics, , ,   

    From Duke Physics: “New Results from T2K Conclusively Show Muon Neutrinos Transform to Electron Neutrinos!” 

    Duke Physics

    July 19th, 2013

    “Today at the European Physical Society meeting in Stockholm, the international T2K collaboration announced definitive observation of muon neutrino to electron neutrino transformation. In 2011, the collaboration announced the first indication of this process, a new type of neutrino oscillation. At that time, there was less than a 1% chance that the result could have been due to a statistical fluctuation. Today, with 3.5 times more data, this transformation is firmly established. The probability that a random statistical fluctuations alone would produce the observed excess of electron neutrinos is less than one in a trillion. Stated in language of statistics, a statistical fluctuation is ruled out at the 7.5 sigma level; this is above the 5 sigma threshold particle physicists use to claim discoveries.

    A 3D view of a candidate electron-neutrino event in the Super-Kamiokande detector.

    This T2K observation is the first of its kind in that an explicit appearance of a unique flavor of neutrino at a detection point is unequivocally observed from a different flavor of neutrino at its production point. The T2K experiment expects to collect 10 times more data in the near future, including data with antineutrino beam for studies of CP violation in neutrinos.

    Professors Kate Scholberg and Chris Walter have been working on the Super-K or T2K experiment for over 15 years. Other current members include Postdocs Tarek Akiri and Alex Himmel along with graduate student Taritree Wongjirad. Recent past members include former graduate student Josh Albert and former postdoc Roger Wendell who is now a faculty member at the University of Tokyo.”

    See the full article here.

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