Generalized Schrieffer-Wolff Formalism for Dissipative Systems

Abstract

We present a formalized perturbation theory for Markovian open systems in the language of a generalized Schrieffer-Wolff (SW) transformation. A non-unitary rotation decouples the unper- turbed steady states from all fast degrees of freedom, in order to obtain an effective Liouvillian, that reproduces the exact low excitation spectrum of the system. The transformation is derived in a constructive way, yielding a perturbative expansion of the effective Liouville operator. The presented formalism realizes an adiabatic elimination of fast degrees of freedom to arbitrary orders in the perturbation. We exemplarily employ the SW formalism to two generic open systems and discuss general properties of the different orders of the perturbation.

11 pages, 1 figure

References in corpus (9)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
• Dissipative Phase Transition in Central Spin Systems
• Effective operator formalism for open quantum systems
• Quantum memories based on engineered dissipation
• Kondo Quantum Criticality of Magnetic Adatoms in Graphene
• Vibrational Sidebands and Kondo-effect in Molecular Transistors
• Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions
• Dissipation-driven quantum phase transitions in collective spin systems

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