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Nuclear Theory·nucl-th

Thursday·February 13, 2020

6 papers—2 primary·4 cross-listed

All6Primary2Cross-lists4
  1. 01

    [Submitted on 12 Feb 2020]

    Hydrodynamics of massive particles with spin 1/2

    Wojciech Florkowski

    The formulation of relativistic hydrodynamics for massive particles with spin 1/2 is shortly reviewed. The proposed framework is based on the Wigner function treated in a semi-classical approximation or, alternatively, on a classical treatment of spin 1/2. Several theoretical issues regarding the choice of the energy-momentum and spin tensors used to construct the hydrodynamic framework with spin are discussed in parallel.

    Comments:
    contribution to QM2019 Proceedings
    Subjects:
    Nuclear Theory (nucl-th)
    arXiv:
    2002.04823 [pdf]
    NPA(2021)·1 citation
  2. 02

    [Submitted on 12 Feb 2020]

    Symmetry reduction of tensor networks in many-body theory I. Automated symbolic evaluation of algebra

    Alexander Tichai🇩🇪 · Roland Wirth🇺🇸 · Julien Ripoche🇫🇷 · Thomas Duguet🇫🇷

    The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angular-momentum, i.e. , quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angular-momentum reduction is presented. Taking the symmetry-unrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to demonstrate the generality of the approach and to highlight the potential impact on the many-body community.

    Comments:
    24 pages, 4 figures, accompanying source code available at github.com/radnut/amc
    Subjects:
    Nuclear Theory (nucl-th); Computational Physics (physics.comp-ph)
    arXiv:
    2002.05011 [pdf]
    EPJA(2020)·23 citations

Affiliations

first authorsco-authorsvia INSPIRE