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Capturing exponential variance using polynomial resources: applying tensor networks to non-equilibrium stochastic processes

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 نشر من قبل Tomi Johnson
 تاريخ النشر 2014
  مجال البحث فيزياء
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Estimating the expected value of an observable appearing in a non-equilibrium stochastic process usually involves sampling. If the observables variance is high, many samples are required. In contrast, we show that performing the same task without sampling, using tensor network compression, efficiently captures high variances in systems of various geometries and dimensions. We provide examples for which matching the accuracy of our efficient method would require a sample size scaling exponentially with system size. In particular, the high variance observable $mathrm{e}^{-beta W}$, motivated by Jarzynskis equality, with $W$ the work done quenching from equilibrium at inverse temperature $beta$, is exactly and efficiently captured by tensor networks.



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