Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Taming Hamiltonian systems with balanced loss and gain via Lorentz
  interaction : General results and a case study with Landau Hamiltonian   The kinetic energy term of Hamiltonian systems with balanced loss and gain is
not semi-positive-definite, leading to instabilities at the classical as well
quantum level. It is shown that an additional Lorentz interaction in the
Hamiltonian allows the kinetic energy term to be semi-positive-definite and
thereby, improving the stability properties of the system. Further, a
consistent quantum theory admitting bound states may be obtained on the real
line instead of Stoke wedges on the complex plane. The Landau Hamiltonian in
presence of balanced loss and gain is considered for elucidating the general
result. The kinetic energy term is semi-positive-definite provided the
magnitude of the applied external magnetic field is greater than the magnitude
of the `analogous magnetic field' due to the loss gain terms. It is shown that
the classical particle moves on an elliptical orbit with a cyclotron frequency
that is less than its value in absence of the loss-gain terms. The quantum
system share the properties of the standard Landau Hamiltonian, but, with the
modified cyclotron frequency. It is shown that the Hall current has
non-vanishing components along the direction of the external uniform electric
field and to its transverse direction. The Pauli equation in presence of
balanced loss and gain is shown to be supersymmetric.

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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
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The categories of this paper are: physics
32
The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: nlin
23
The categories of this paper are: solv-int