Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-adjoint Lyapunov variables, temporal ordering and irreversible
  representations of Schroedinger evolution   In non relativistic quantum mechanics time enters as a parameter in the
Schroedinger equation. However, there are various situations where the need
arises to view time as a dynamical variable. In this paper we consider the
dynamical role of time through the construction of a Lyapunov variable - i.e.,
a self-adjoint quantum observable whose expectation value varies monotonically
as time increases. It is shown, in a constructive way, that a certain class of
models admit a Lyapunov variable and that the existence of a Lyapunov variable
implies the existence of a transformation mapping the original quantum
mechanical problem to an equivalent irreversible representation. In addition,
it is proved that in the irreversible representation there exists a natural
time ordering observable splitting the Hilbert space at each t>0 into past and
future subspaces.

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The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: econ
14
The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org