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arXiv · 1410.0304

Hierarchical equations for open system dynamics in fermionic and bosonic environments

Daniel Suess·Walter T. Strunz·Alexander Eisfeld
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Abstract

We present novel approaches to the dynamics of an open quantum system coupled linearly to a non-Markovian fermionic or bosonic environment. In the first approach, we obtain a hierarchy of stochastic evolution equations of the diffusion type. For the bosonic case such a hierarchy has been derived and proven suitable for efficient numerical simulations recently [arXiv:1402.4647]. The stochastic fermionic hierarchy derived here contains Grassmannian noise, which makes it difficult to simulate numerically due to its anti-commutative multiplication. Therefore, in our second approach we eliminate the noise by deriving a related hierarchy of density matrices. A similar reformulation of the bosonic hierarchy of pure states to a master equation hierarchy is also presented.

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Daniel Suess, Walter T. Strunz, Alexander Eisfeld. 2014-10-01. Hierarchical equations for open system dynamics in fermionic and bosonic environments. https://doi.org/10.1007/s10955-015-1236-7

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