Capturing exponential variance using polynomial resources: applying tensor networks to nonequilibrium stochastic...

Area of Science:

• Statistical physics
• Computational physics

Background:

• Estimating expected values in nonequilibrium processes often requires extensive sampling, especially for high-variance observables.
• High variance necessitates a large number of samples, increasing computational cost and time.

Purpose of the Study:

• To introduce a sampling-free method for efficiently estimating expected values in nonequilibrium stochastic processes.
• To demonstrate the capability of tensor network compression in handling high variances.

Main Methods:

• Utilizing tensor network compression to avoid direct sampling.
• Applying the method to systems of various geometries and dimensions.
• Focusing on the high-variance observable e^{-βW}, related to Jarzynski's equality.

Main Results:

• Tensor network compression efficiently captures high variances without sampling.
• The method's accuracy matches or exceeds sampling methods requiring exponentially larger sample sizes.
• Exact and efficient capture of the e^{-βW} observable is achieved.

Conclusions:

• Tensor network compression provides a powerful and efficient alternative to sampling for nonequilibrium systems.
• This method significantly reduces computational resources for high-variance observables.
• The technique shows promise for advancing studies in statistical physics and related fields.