Quantum dynamics in a tiered non-Markovian environment
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We introduce a new analytical method for studying the open quantum systems problem of a discrete system weakly coupled to an environment of harmonic oscillators. Our approach is based on a phase space representation of the density matrix for a system coupled to a two-tiered environment. The dynamics of the system and its immediate environment are resolved in a non-Markovian way, and the environmental modes of the inner environment can themselves be damped by a wider 'universe'. Applying our approach to the canonical cases of the Rabi and spin-boson models we obtain new analytical expressions for an effective thermalization temperature and corrections to the environmental response functions as direct consequences of considering such a tiered environment. A comparison with exact numerical simulations confirms that our approximate expressions are remarkably accurate, while their analytic nature offers the prospect of deeper understanding of the physics which they describe. A unique advantage of our method is that it permits the simultaneous inclusion of a continuous bath as well as discrete environmental modes, leading to wide and versatile applicability.
Fruchtman , A , Lovett , B W , Benjamin , S C & Gauger , E M 2015 , ' Quantum dynamics in a tiered non-Markovian environment ' New Journal of Physics , vol 17 . DOI: 10.1088/1367-2630/17/2/023063
New Journal of Physics
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This work was supported by the Leverhulme Trust, EPSRC under platform grant EP/J015067/1, and the National Research Foundation and Ministry of Education, Singapore. BWL thanks the Royal Society for a University Research Fellowship. EMG acknowledges support from the RSE/Scottish Government.
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