Markovian and non-Markovian dynamics from probability amplitudes perspective

TL;DR

This paper investigates the dynamics of open quantum spin chains with complex interactions, analyzing how probability amplitudes and non-Markovianity depend on three-spin interactions using fermionization and trace distance methods.

Contribution

It introduces a novel analysis of Markovian and non-Markovian dynamics in spin chains with three-spin interactions, highlighting the role of probability amplitudes in determining system behavior.

Findings

Non-Markovian dynamics involve multiple fluctuating probability amplitudes.

Markovian dynamics occur when all but one probability amplitude vanish.

The type of three-spin interaction influences the degree of non-Markovianity.

Abstract

One-spin and two-spin in a thermodynamic limit spin-1/2 chain as open quantum systems are considered. The dynamics of system is generated by XX Heisenberg interaction and three-spin interaction (TSI) among all the nearest three spins in the chain. Two variety Hamiltonians of the three-spin interaction are considered. Using the fermionization technique and calculating the trace distance, non-Markovianity as a function of the TSI is evaluated, and the results for the two different open quantum systems are compared. In addition, the time behavior of the probability amplitudes are studied. The results show that if all probability amplitudes except one of them will almost vanish after some time, the dynamics of the open quantum system will be Markovian. In the non-Markovian dynamics, more than one of the probability amplitudes fluctuate in time and will never reach zero value.