Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase space formulation of density operator for non-Hermitian
  Hamiltonians and its application in quantum theory of decay   The Wigner-Weyl transform and phase space formulation of a density matrix
approach are applied to a non-Hermitian model which is quadratic in positions
and momenta. We show that in the presence of a quantum environment or
reservoir, mean lifetime and decay constants of quantum systems do not
necessarily take arbitrary values, but could become functions of energy
eigenvalues and have a discrete spectrum. It is demonstrated also that a
constraint upon mean lifetime and energy appears, which is used to derive the
resonance conditions at which long-lived states occur. The latter indicate that
quantum dissipative effects do not always lead to decay but, under certain
conditions, can support stability of a system.

3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg