Capturing Exponential Variance Using Polynomial Resources: Applying Tensor Networks to Nonequilibrium Stochastic Processes
Abstract
Estimating the expected value of an observable appearing in a nonequilibrium stochastic process usually involves sampling. If the observable's 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 highvariance observable e^{β W} , motivated by Jarzynski's equality, with W the work done quenching from equilibrium at inverse temperature β , is exactly and efficiently captured by tensor networks.
 Publication:

Physical Review Letters
 Pub Date:
 March 2015
 DOI:
 10.1103/PhysRevLett.114.090602
 arXiv:
 arXiv:1410.3319
 Bibcode:
 2015PhRvL.114i0602J
 Keywords:

 05.70.Ln;
 03.67.Mn;
 05.10.a;
 05.40.a;
 Nonequilibrium and irreversible thermodynamics;
 Entanglement production characterization and manipulation;
 Computational methods in statistical physics and nonlinear dynamics;
 Fluctuation phenomena random processes noise and Brownian motion;
 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 7 pages, 3 figures, including supplemental material