On the theory of high-velocity particles: A comment

Edward R. Floyd

M. Popović‐Božić

Daniel A. Roberts, Brian G. Swingle

As experiments are increasingly able to probe the quantum dynamics of systems with many degrees of freedom, it is interesting to probe fundamental bounds on the dynamics of quantum information. We elaborate on the relationship between one such bound-the Lieb-Robinson bound-and the butterfly effect in strongly coupled quantum systems. The butterfly effect implies the ballistic growth of local operators in time, which can be quantified with the "butterfly" velocity v_{B}. Similarly, the Lieb-Robinson velocity places a state-independent ballistic upper bound on the size of time evolved operators in nonrelativistic lattice models. Here, we argue that v_{B} is a state-dependent effective Lieb-Robinson velocity. We study the butterfly velocity in a wide variety of quantum field theories using holography and compare with free-particle computations to understand the role of strong coupling. We find that v_{B} remains constant or decreases with decreasing temperature. We also comment on experimental prospects and on the relationship between the butterfly velocity and signaling.

Laurens Vanderstraeten

М. В. Давидович

Some paradoxes are discussed concerning the interpretation of the passage of particles and electromagnetic waves (pulses) across potential barriers and through nonuniform media, in particular, those with frequency dispersion and therefore dissipation. It is emphasized that a rigorous nonstationary approach does not entail any supraluminal velocities for the transfer of physical substances, although supraluminal velocities are indeed possible for several kinematically defined velocities, e.g., for the group velocity.

Sudipta Das