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Quantum Many-Body Dynamics of Trapped Bosons with the MCTDHB Package: Towards New Horizons with Novel Physics

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Abstract

The MCTDHB package has been applied to study the physics of trapped interacting many-boson systems by solving the underlying time-dependent (as well as the time-independent) many-boson Schrödinger equation. Here we report on four studies where novel physical ideas and phenomena have been proposed and discovered: (a) Universality of the fragmentation dynamics in double wells – at long propagation times properties of the evolving system saturate to some asymptotic values; (b) Novel many-body spectral features in trapped systems – the newly-developed linear-response theory on-top of MCTDHB predicts the existence of low-lying excitations not described so far by the standard theory even in harmonic potentials; (c) Efficient protocol to control the many-particle tunneling dynamics to open space, by combining the effects of a threshold potential and inter-particle interaction; (d) Physics behind the formation of patterns in the ground states of trapped bosonic systems with strong finite- and long-range repulsive interactions and the origin of their dynamical stability. From the perspective of the required computational resources and numerical algorithms applied, each of these numerically-demanding studies has challenged different aspects of computational physics and mathematics: Long-time propagation – stability of the numerical methods used to integrate the MCTDHB equations-of-motion; Control of the tunneling dynamics – a very detailed study where an interplay of the parameters controlling the decay by tunneling dynamics is accompanied by a long-time propagation on huge spatial grids, which are needed to simulate open systems; Excited states of many-body systems – construction and diagonalization of complex non-hermitian linear-response matrices; Finite- and long-range interactions in 1D, 2D, and 3D setups – efficient methods and techniques for evaluation of involved high-dimensional integrals. Implications and further perspectives and future plans are briefly discussed and addressed.

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Authors and Affiliations

  1. Theoretische Chemie, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120, Heidelberg, Germany

    Shachar Klaiman, Lorenz S. Cederbaum & Alexej I. Streltsov

  2. Condensed Matter Theory and Quantum Computing Group, Departement für Physik, Universität Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland

    Axel U. J. Lode

  3. Department of Physics, Stanford University, Stanford, CA, 94305, USA

    Kaspar Sakmann

  4. Laboratory of Information Technologies, Joint Institute for Nuclear Research, Joliot-Curie 6, Dubna, Russia

    Oksana I. Streltsova

  5. Department of Physics, University of Haifa at Oranim, Tivon, 36006, Israel

    Ofir E. Alon

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  1. Shachar Klaiman
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  2. Axel U. J. Lode
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  3. Kaspar Sakmann
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  4. Oksana I. Streltsova
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  6. Lorenz S. Cederbaum
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Correspondence to Alexej I. Streltsov .

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  1. Zentrum für Informationsdienste und Hochleistungsrechnen (ZIH), Technische Universität Dresden, Dresden, Germany

    Wolfgang E. Nagel

  2. Abteilung für Angewandte Mathematik, Universität Freiburg, Freiburg, Germany

    Dietmar H. Kröner

  3. HöchstleistungsrechenzentrumStuttgart (HLRS), Universität Stuttgart, Stuttgart, Germany

    Michael M. Resch

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Klaiman, S. et al. (2015). Quantum Many-Body Dynamics of Trapped Bosons with the MCTDHB Package: Towards New Horizons with Novel Physics. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering ‘14. Springer, Cham. https://doi.org/10.1007/978-3-319-10810-0_5

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