Optimal sampling of dynamical large deviations via matrix product states

Area of Science:

• Statistical Mechanics
• Dynamical Systems Theory
• Computational Physics

Background:

• Large deviation statistics of dynamical observables are linked to spectral properties of Markov generators.
• Tensor network methods accurately compute leading eigenvalues and eigenvectors.
• Efficiently generating rare trajectories remains a challenge.

Purpose of the Study:

• To develop an efficient sampling scheme for rare trajectories.
• To leverage matrix product state approximations for this purpose.
• To closely resemble optimal (Doob) dynamics for rare event realization.

Main Methods:

• Utilizing matrix product state (MPS) approximation of the dominant eigenvector.
• Implementing an efficient sampling scheme based on MPS.
• Applying the method to lattice models: Fredrickson-Andersen, East kinetically constrained, and symmetric simple exclusion process.

Main Results:

• The proposed sampling scheme efficiently generates rare trajectories.
• The method closely mimics optimal Doob dynamics.
• Demonstrated applicability on multiple well-studied lattice models.

Conclusions:

• Matrix product state approximations offer an efficient route to sampling rare events in dynamical systems.
• The developed method provides a powerful tool for large deviation statistics.
• The approach is generalizable to higher dimensions.