Information and Particle Propagation Bounds for Lattice Bosons Under Long-Range Interactions

Vortrag von Carla Rubiliani

Sprecher eingeladen von: Prof. Dr. Benjamin Schlein

Datum: 18.12.25  Zeit: 16.15 - 18.00  Raum: ETH HG G 19.2

In this talk, we explore locality properties of a Schrödinger-type PDE describing the dynamics of a many-body bosonic system on a finite volume lattice. Such locality properties translate into two types of propagation bounds

1. Information propagation bounds (IPB) or Lieb-Robinson bounds, which control the dynamics of local operators.
2. Particle propagation bounds (PPB), which control the dynamics of particles through the lattice.

Although the PDE under consideration is linear, we have to face two mathematical challenges. First, the dimension of the underlying Hilbert space is very high and we want to derive bounds that thermodynamically stable, i.e. are uniform in such dimension. Second, bosonic interactions are unbounded in operator norm. Thanks to a multi-scale adaptation of the ASTLO ( adiabatic space-time localisation observables) method, which allows to remove the dependence of the error term on far away particles, we establish the first thermodynamically stable bosonic PPB for a class of long-range interactions. We were also able to control higher moments of the number operator. This opens the door to proving the first thermodynamically stable IPB for such bosonic systems. Establishing these bounds for bosonic systems is a long-standing open problem due to the lack of existing methods to control the unbounded nature of the bosonic operators when deriving  IPB.