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#### BetheSF: Efficient computation of the exact tagged-particle propagator in single-file systems via the Bethe eigenspectrum

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##### Citation

Lapolla, A., & Godec, A. (2021). BetheSF: Efficient computation of the exact tagged-particle
propagator in single-file systems via the Bethe eigenspectrum.* Computer Physics Communications,*
*258*: 107569. doi:10.1016/j.cpc.2020.107569.

Cite as: http://hdl.handle.net/21.11116/0000-0007-1370-5

##### Abstract

Single-file diffusion is a paradigm for strongly correlated classical stochastic many-body dynamics and has widespread applications in soft condensed matter and biophysics. However, exact results for single-file systems are sparse and limited to the simplest scenarios. We present an algorithm for computing the non-Markovian time-dependent conditional probability density function of a tagged-particle in a single-file of particles diffusing in a confining external potential. The algorithm implements an eigenexpansion of the full interacting many-body problem obtained by means of the coordinate Bethe ansatz. While formally exact, the Bethe eigenspectrum involves the generation and evaluation of permutations, which becomes unfeasible for single-files with an increasing number of particles . Here we exploit the underlying exchange symmetries between the particles to the left and to the right of the tagged-particle and show that it is possible to reduce the complexity of the algorithm from the worst case scenario down to . A C++ code to calculate the non-Markovian probability density function using this algorithm is provided. Solutions for simple model potentials are readily implemented including single-file diffusion in a flat and a ‘tilted’ box, as well as in a parabolic potential. Notably, the program allows for implementations of solutions in arbitrary external potentials under the condition that the user can supply solutions to the respective single-particle eigenspectra.