Maximal Speed for Macroscopic Particle Transport in the Bose-Hubbard Model

Area of Science:

• Quantum physics
• Condensed matter physics
• Many-body systems

Background:

• The Lieb-Robinson bound sets maximal propagation speeds in quantum spin systems.
• General bounds are lacking for bosonic lattice gases due to unbounded interactions.

Purpose of the Study:

• Establish a general ballistic upper bound for macroscopic particle transport.
• Address the challenge of unbounded local interactions in bosonic systems.
• Resolve a longstanding open problem regarding quantum dynamics.

Main Methods:

• Rigorous mathematical proof.
• Control of time evolution using adiabatic spacetime localization observables.
• Application of iterative differential inequalities.

Main Results:

• First general ballistic upper bound for particle transport in the Bose-Hubbard model.
• The bound applies to a broad class of initial states, including Mott states.
• The result extends to Bose-Hubbard-type models on various lattices.

Conclusions:

• This work provides a crucial theoretical tool for understanding quantum transport in bosonic systems.
• The established bound offers new insights into the dynamics of quantum gases.
• Resolves a key challenge in the quantum dynamics of lattice models.