Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A quantum waveguide with Aharonov Bohm magnetic field   In a previous study \cite{n} we investigate the bound states of the
Hamiltonian describing a quantum particle living on three dimensional straight
strip of width $d$. We impose the Neumann boundary condition on a disc window
of radius $a$ and Dirichlet boundary conditions on the remained part of the
boundary of the strip. We proved that such system exhibits discrete eigenvalues
below the essential spectrum for any $a>0$. In the present work we study the
effect of a magnetic filed of Aharonov-Bohm type when the magnetic field is
turned on this system. Precisely we prove that in the presence of such magnetic
filed there is some critical values of $a_0>0$, for which we have absence of
the discrete spectrum for $\displaystyle 0<\frac{a}{d}<a_0$. We give a
sufficient condition for the existence of discrete eigenvalues.

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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
11
The categories of this paper are: hep-lat