Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time irreversibility in the quantum systems with infinite number of
  particles   The time irreversible evolution of quantum systems with infinite number of
particles (QSINP) was studied within a newly constructed algebraic framework.
The QSINP could be described by the quantum infinite lattice field. The
*-Algebra R is the set of all dynamic variables of the QSINP, in which a
special addition and multiplication operations were defined. The full pure
state vector (FPSV) \rho, the pure state vector {\rho_f} and the equivalent
relations within them are also well defined. The set of all pure state vectors,
which are equivalent to the FPSV \rho, is a Hilbert Space {H_\rho}, if the
addition, the inner product and the norm were defined in it. The set of all
linear transformation {N_\rho} on {H_\rho} is isomorphic to R, and
{{N_\rho},{H_\rho}} is the representation of R, associated with \rho. The
*-Algebra R has infinitely many non-equivalent irreducible GNS constructions
(representations), associated with different nonequivalent FPSVs respectively.
  It is proved that, the dynamical motions of the QSINP is totally within the
GNS construction associated with the initial pure state vector; However, the
time reversal transformation makes the initial FPSV and its corresponding
dynamical evolution into another non-equivalent GNS construction. Therefore,
within the GNS construction associated with the FPSV, the dynamics of the QSINP
is time irreversible.
  Finally, due to the Liouville operator has real continuous spectrum within
the GNS construction, the longtime asymptotic solution of Liouville equation in
the GNS construction could be treated by the formal scattering theory. The
Master equation with dissipative term was obtained, which is formally
irrelevant of the initial state and the corresponding GNS construction. This
master equation could be regarded as the evolution equation of the QSINP on R.

19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat