Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Star-unitary transformations. From dynamics to irreversibility and
  stochastic behavior   We consider a simple model of a classical harmonic oscillator coupled to a
field. In standard approaches Langevin-type equations for {\it bare} particles
are derived from Hamiltonian dynamics. These equations contain memory terms and
are time-reversal invariant. In contrast the phenomenological Langevin
equations have no memory terms (they are Markovian equations) and give a time
evolution split in two branches (semigroups), each of which breaks time
symmetry. A standard approach to bridge dynamics with phenomenology is to
consider the Markovian approximation of the former. In this paper we present a
formulation in terms of {\it dressed} particles, which gives exact Markovian
equations. We formulate dressed particles for Poincar\'e nonintegrable systems,
through an invertible transformation operator $\Lam$ introduced by Prigogine
and collaborators. $\Lam$ is obtained by an extension of the canonical
(unitary) transformation operator $U$ that eliminates interactions for
integrable systems. Our extension is based on the removal of divergences due to
Poincar\'e resonances, which breaks time-symmetry. The unitarity of $U$ is
extended to ``star-unitarity'' for $\Lam$. We show that $\Lam$-transformed
variables have the same time evolution as stochastic variables obeying Langevin
equations, and that $\Lam$-transformed distribution functions satisfy exact
Fokker-Planck equations. The effects of Gaussian white noise are obtained by
the non-distributive property of $\Lam$ with respect to products of dynamical
variables. Therefore our method leads to a direct link between dynamics of
Poincar\'e nonintegrable systems, probability and stochasticity.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas