Maximal Speed of Quantum Propagation

Abstract

For Schroedinger equations with both time-independent and time-dependent Kato potentials, we give a simple proof of the maximal speed bound. The latter states that the probability to find the quantum system outside the ball of radius proportional to the time lapsed decays as an inverse power of time. We give an explicit expression for the constant of proportionality in terms of the maximal energy available to the initial condition. For the time-independent part of the interaction, we require neither decay at infinity nor smoothness.

arXiv commentMinor changes to the presentation and the proof of Theorem 2.1

References in corpus (3)

• An improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
• Improving the Lieb-Robinson bound for long-range interactions
• Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in ${\mathbb{R}}^d$

Cited by in corpus (6)

• Speed limits and locality in many-body quantum dynamics
• Maximal speed for macroscopic particle transport in the Bose-Hubbard model
• On Lieb-Robinson bounds for the Bose-Hubbard model
• On Lieb-Robinson bounds for a class of continuum fermions
• Locality bounds for quantum dynamics at low energy
• Differential Equations of Quantum Mechanics