Adiabatic approximation in open quantum systems

By Marcelo S. Sarandy, Daniel A. Lidar. 2004

156 citations recorded by the source corpus.

We generalize the standard quantum adiabatic approximation to the case of open quantum systems. We define the adiabatic limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of independently evolving Jordan blocks. We then establish validity and invalidity conditions for this approximation and discuss their applicability to superoperators changing slowly in time. As an example, the adiabatic evolution of a two-level open system is analyzed.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/0ff2b7f0c778dbdb79b4b010303081ffaad68ad6

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Dynamics of non-Markovian open quantum systems (2015, methodology): “(69) [and hence (65)], using either projection methods or a perturbative expansion, leads one to conclude that it is also valid for timedependent HS (Amin, 2009; Amin et al., 2008; Breuer, 2004; Sarandy and Lidar, 2005; de Vega et al., 2010).”
Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories (2020, background): “To every Lindblad master equation corresponds a nonHermitian Liouvillian superoperator L which can display Liouvillian exceptional points (LEPs) [12, 23, 46–52].”
Geometry and Response of Lindbladians (2015, background): “We do not make the adiabatic approximation to HðsÞ [and, later, LðsÞ [179]] since it is not sufficient for the adiabatic theorem to hold; see Ref.”
Fast-forward of adiabatic dynamics in quantum mechanics (2009, background): “A (2010) 466, 1135–1154 doi:10.1098/rspa.2009.0446 Published online 25 November 2009 Fast-forward of adiabatic dynamics in quantum mechanics”
Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps (2019, background): “Since the Liouvillian is a non-Hermitian matrix, it too can exhibit EPs [37–44].”