Exponential concentration of fluctuations in mean-field boson dynamics

TL;DR

This paper proves that in mean-field boson systems, the probability of particles outside the condensate decays exponentially, improving upon previous polynomial bounds for a wide class of interactions.

Contribution

It establishes exponential decay bounds for fluctuations in mean-field boson dynamics, extending results to models with both bounded and unbounded interactions.

Findings

Exponential decay of fluctuations in boson systems.

Applicable to models with bounded and unbounded interactions.

Strengthens previous polynomial bounds on excitations.

Abstract

We study the mean-field dynamics of a system of $N$ interacting bosons starting from an initially condensated state. For a broad class of mean-field Hamiltonians, including models with arbitrary bounded interactions and models with unbounded interaction potentials, we prove that the probability of having $n$ particles outside the condensate decays exponentially in $n$ for any finite evolution time. Our results strengthen previously known bounds that provide only polynomial control on the probability of having $n$ excitations.