Dynamics with a memory: non-Markovian evolution

Charlotte Bäcker, Nick Maryshchak, Walter T. Strunz

A profound understanding of decoherence and dissipation in quantum dynamics is crucial for the realistic modeling of the evolution of quantum systems. In open quantum dynamics one distinguishes between a memoryless, so-called Markovian evolution and dynamics incorporating memory effects, termed non-Markovian. In this work we study how prevalent memory effects are in the set of all such dynamics. We thus investigate how often a Markovian description is applicable. This question is approached by investigating randomly generated two-step qubit dynamics with respect to different concepts and witnesses of non-Markovianity. We observe that almost all dynamics are non-Markovian, and only a small (yet finite) fraction is Markovian. Furthermore, we study how this proportion changes when considering certain subclasses such as lower rank or mixed-unitary dynamics. Importantly, our results shed light on the relative ratios of -- and interrelations between -- the sets of dynamics that are non-Markovian with respect to different criteria. Finally, we investigate the fraction of dynamics in which the memory effects are necessarily of quantum nature and establish a connection between two recently developed concepts that characterize the quantumness of memory in non-Markovian dynamics.

Dariusz Chruściński, Andrzej Kossakowski

Doojin Kim, Balbeer Singh

We present a quantum computing framework for simulating open-quantum-system approaches based on Markovian and non-Markovian dynamics, which is relevant to heavy-ion collisions. To simulate the non-Markovian evolution on quantum computers, we introduce an auxiliary two-level pseudomode that carries the memory forward and couples to both the subsystem and the residual Markovian bath. We explicitly show that tracing out the pseudomode reproduces the non-Markovian evolution with the exact memory kernel. Moreover, in the relevant time scale hierarchy, the quantum circuit construction of the pseudomode smoothly converges to the Markovian limit. For a given bath memory kernel, our results demonstrate the feasibility of quantum simulations of both Markovian and non-Markovian dynamics, establishing a framework for future studies of hard probes such as jets, heavy quarks, and quarkonia in heavy-ion collisions.

Mark P. Davidson

Dariusz Chruściński, Andrzej Kossakowski, Saverio Pascazio

If the dynamics of an open quantum system is non-Markovian, its asymptotic state strongly depends on the initial conditions, even if the dynamics possesses an invariant state. This is the very essence of memory effects. In particular, the asymptotic state can remember and partially preserve its initial entanglement. Interestingly, even if the non-Markovian evolution relaxes to an equilibrium state, this state needs not be invariant. Therefore, the noninvariance of equilibrium becomes a clear sign of non-Markovianity.

Bassano Vacchini