Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantization of Time in Dynamic Barrier Tunnelling   In the B\"uttiker-Landauer perturbation approach to electron tunnelling,
through a time-modulated rectilinear potential barrier, the Tien-Gordon
identity was invoked, together with its infinite energy spectrum. Here, an
exact treatment is presented which is based on the temporal wave-function
matching procedure, that led to a finite energy spectrum. In seeking the
condition governing the time evolution of the tunnelling process, the Euler
formula provided the crucial ingredient for time quantization, which
discretised the continuous time in the oscillating barrier potential and energy
harmonic equations. As a result, a finite system of inelastic scattering
channels was created. When an electron entered the elastic channel, it was
scattered, instantaneously, into finite neighbouring energy-level scattering
channels, by absorption (emission) of photon energy from (to) the oscillating
field, during the transit period across the dynamic barrier. The absorption and
emission times of barrier traversal, T_+ and T_-, respectively, were derived
for the low and high frequency regimes of the barrier oscillations.
Calculations revealed that in the low (high) frequency situation T_+= T_- (T_+<
T_-).

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The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: q-fin