Asymptotically Decreasing Lieb-Robinson Velocity for a Class of Dissipative Quantum Dynamics

TL;DR

This paper investigates how the speed of information spread in certain dissipative quantum systems decreases over time, showing that the velocity can become zero, which differs from previous reversible models.

Contribution

It introduces a time-dependent Lieb-Robinson velocity for dissipative quantum dynamics, revealing decay towards zero, unlike prior models that assumed constant velocity.

Findings

Velocity of information propagation decreases over time

Velocity can become zero in some cases

Revisits exponential clustering in Markovian dynamics

Abstract

We study the velocity of the propagation of information for a class of local dissipative quantum dynamics. This finite velocity is expressed by the so-called Lieb-Robinson bound. Besides the properties of the already studied dynamics, we consider an additional relation that expresses the propagation of certain subspaces. The previously derived bounds did not reflect the dissipative character of the dynamics and yielded the same result as for the reversible case. In this article, we show that for this class the velocity of propagation of information is time dependent and decays in time towards a smaller velocity. In some cases the velocity becomes zero. At the end of the article, the exponential clustering theorem of general frustration free local Markovian dynamics is revisited.