Tensor network methods for the Gross–Pitaevskii equation on fine grids

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Connor, Ryan J J and Duncan, Callum W and Daley, Andrew J (2026) Tensor network methods for the Gross–Pitaevskii equation on fine grids. New Journal of Physics, 28 (2). 023203. ISSN 1367-2630 (https://doi.org/10.1088/1367-2630/ae2b05)

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Abstract

The Gross–Pitaevskii equation and its generalisations to dissipative and dipolar gases have been very useful in describing dynamics of cold atomic gases, as well as polaritons and other nonlinear systems. For some of these applications the numerically accessible grid spacing can become a limiting factor, especially in describing turbulent dynamics and short-range effects of dipole-dipole interactions. We explore the application of tensor networks to these systems, where (in analogy to related work in fluid and plasma dynamics), they allow for physically motivated data compression that makes simulations possible on large spatial grids which would be unfeasible with direct numerical simulations. Analysing different non-equilibrium cases involving vortex formation, we find that these methods are particularly efficient, especially in combination with a matrix product operator representation of the quantum Fourier transform, which enables a spectral approach to calculation of both equilibrium states and time-dependent dynamics. The efficiency of these methods has interesting physical implications for the structure in the states that are generated by these dynamics, and provides a path to describe cold gas experiments that are challenging for existing methods.

ORCID iDs

Connor, Ryan J J, Duncan, Callum W ORCID logoORCID: https://orcid.org/0000-0003-3625-9842 and Daley, Andrew J ORCID logoORCID: https://orcid.org/0000-0001-9005-7761;
  • Item type:Article
    ID code:95654
    Dates:
    Date
    Event
    26 February 2026
    Published
    10 December 2025
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:26 Feb 2026 09:42
    Last modified:06 Mar 2026 01:47
    URI:https://strathprints.strath.ac.uk/id/eprint/95654
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