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Archive of Highlights Highlights Vol. 50 No. 3 - Highlights Geometry of quantum evolution in a nonequilibrium environment (Vol. 50, No. 3)

Geometry of quantum evolution in a nonequilibrium environment (Vol. 50, No. 3)

Geometry of quantum evolution in a nonequilibrium environment
Effective geometric phase Φe(t) as a function of evolution time t for different values of a with θ = π/2 in (a) the Markovian dynamics region with ν =0.5λ and κ = λ and (b) the non-Markovian dynamics region with ν =2λ and κ = λ (the solid and dashed lines are plotted for a>0and a< 0, respectively)

The geometric effect of quantum dynamical evolution has potential applications in studying quantum phase transition and realizing geometric quantum computation. Due to the fact that a quantum system unavoidably interacts with its environments and undergoes decoherence, much extensive attention has been paid to theoretical investigations on the geometric dynamical evolution in open quantum systems under nonunitary dynamics. The investigation on the geometry in the dynamical evolution of an open quantum system is crucial for further understanding the origins of decoherence, quantum-classical transition and so on.

There are many significant situations where the nonequilibrium feature of the environment becomes dominant. In these situations, the statistical properties of the environmental noise are nonstationary, corresponding physically to impulsively excited phonons of the environment in certain nonequilibrium states initially. We show that the renormalization of the intrinsic energy of the system, namely, the frequency shift induced by the nonequilibrium feature of the environment has a significant impact on the geometry of quantum dynamical evolution.

X. Cai, R. Men, Y. Zhang and L. Wang, Geometry of quantum evolution in a nonequilibrium environment, EPL 125, 30007 (2019)
[Abstract]