Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigorous derivation of coherent resonant tunneling time and velocity in
  finite periodic systems   The velocity $v_{res}$ of resonant tunneling electrons in finite periodic
structures is analytically calculated in two ways. The first method is based on
the fact that a transmission of unity leads to a coincidence of all still
competing tunneling time definitions. Thus, having an indisputable resonant
tunneling time $\tau_{res},$ we apply the natural definition
$v_{res}=L/\tau_{res}$ to calculate the velocity. For the second method we
combine Bloch's theorem with the transfer matrix approach to decompose the wave
function into two Bloch waves. Then the expectation value of the velocity is
calculated. Both different approaches lead to the same result, showing their
physical equivalence. The obtained resonant tunneling velocity $v_{res}$ is
smaller or equal to the group velocity times the magnitude of the complex
transmission amplitude of the unit cell. Only at energies where the unit cell
of the periodic structure has a transmission of unity $v_{res}$ equals the
group velocity. Numerical calculations for a GaAs/AlGaAs superlattice are
performed. For typical parameters the resonant velocity is below one third of
the group velocity.

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The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
26
The categories of this paper are: bayes-an
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The categories of this paper are: cs
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: astro-ph