Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heisenberg Picture for Open Quantum Systems   In this note, we develop a framework to describe open quantum systems in the
Heisenberg picture, i.e., via time evolving operator algebras. We point out the
incompleteness of the previous proposals in this regard. We argue that a
complete Heisenberg picture for an open quantum system involves multiple image
Heisenberg operators for each system observable. For a given system observable,
the number of such image operators is equal to the dimension of the environment
Hilbert space. We derive a perturbative expression, accurate upto arbitrary
orders in the system environment coupling, for these image operators in terms
of a single one point operator. This expression depends non-linearly on the
state of the environment. This perturbative expression can equivalently be
thought of as deforming the operator product on the Hilbert space of the open
quantum system. In the Markovian limit, the one point operator evolves by an
adjoint Lindblad equation. We illustrate these ideas using a simple spin
system.

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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nlin