Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perspective: Numerically "exact" approach to open quantum dynamics: The
  hierarchical equations of motion (HEOM)   An open quantum system refers to a system that is further coupled to a bath
system consisting of surrounding radiation fields, atoms, molecules, or
proteins. The bath system is typically modeled by an infinite number of
harmonic oscillators. This system-bath model can describe the time-irreversible
dynamics through which the system evolves toward a thermal equilibrium state at
finite temperature. In nuclear magnetic resonance and atomic spectroscopy,
dynamics can be studied easily by using simple quantum master equations under
the assumption that the system-bath interaction is weak (perturbative
approximation) and the bath fluctuations are very fast (Markovian
approximation). However, such approximations cannot be applied in chemical
physics and biochemical physics problems, where environmental materials are
complex and strongly coupled with environments. The hierarchical equations of
motion (HEOM) can describe numerically "exact" dynamics of a reduced system
under nonperturbative and non-Markovian system--bath interactions, which has
been verified on the basis of exact analytical solutions (non-Markovian tests)
with any desired numerical accuracy. The HEOM theory has been used to treat
systems of practical interest, in particular to account for various linear and
nonlinear spectra in molecular and solid state materials, to evaluate charge
and exciton transfer rates in biological systems, to simulate resonant
tunneling and quantum ratchet processes in nanodevices, and to explore quantum
entanglement states in quantum information theories. This article, presents an
overview of the HEOM theory, focusing on its theoretical background and
applications, to help further the development of the study of open quantum
dynamics.

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The categories of this paper are: eess
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The categories of this paper are: econ
37
The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
1
The categories of this paper are: cs