Schrödinger bridges for systems of interacting particles

Area of Science:

• Statistical Mechanics
• Quantum Mechanics
• Optimal Transport Theory

Background:

• The Schrödinger bridge problem determines the most probable path between two probability distributions.
• Existing solutions are limited to noninteracting particle systems (simple Brownian evolution).
• The problem is mathematically linked to entropy-regularized optimal transport.

Purpose of the Study:

• To generalize the Schrödinger bridge problem to systems of interacting particles.
• To develop a computational framework for analyzing the dynamics of interacting systems.

Main Methods:

• Derivation of novel equations for forward and backward single-particle "wave functions."
• Extension of optimal transport principles to interacting particle systems.

Main Results:

• The derived equations enable the computation of the most probable single-particle probability evolution.
• Successfully generalized the Schrödinger bridge framework to handle particle interactions.

Conclusions:

• The new method provides a powerful tool for studying complex systems with interacting particles.
• This work bridges the gap between optimal transport theory and the dynamics of interacting quantum or classical systems.