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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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Optimal Sampling of Dynamical Large Deviations in Two Dimensions via Tensor Networks.

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Area of Science:

  • Statistical mechanics
  • Complex systems dynamics
  • Computational physics

Background:

  • Dynamical activity in statistical models is crucial for understanding complex systems.
  • Large deviation statistics help characterize rare events and phase transitions.
  • Projected entangled-pair states (PEPS) offer a powerful tensor network approach for quantum and classical systems.

Purpose of the Study:

  • To calculate large deviation statistics of dynamical activity in 2D lattice models.
  • To investigate phase transitions between active and inactive dynamical phases.
  • To develop and apply PEPS for efficient sampling of rare dynamical trajectories.

Main Methods:

  • Utilized projected entangled-pair states (PEPS) for numerical simulations.
  • Analyzed the 2D East model and 2D symmetric simple exclusion process (SSEP) with open boundaries.
  • Implemented a trajectory sampling scheme based on PEPS to access rare events.

Main Results:

  • Identified phase transitions in dynamical activity at long times for both models.
  • Characterized the 2D East model transition as first-order.
  • Found indications of a second-order transition for the 2D SSEP.
  • Demonstrated PEPS' capability for direct rare trajectory sampling.

Conclusions:

  • PEPS are effective for studying large deviation statistics and phase transitions in dynamical systems.
  • The developed methods allow for direct investigation of rare events in complex systems.
  • Future extensions can explore rare events at finite times.