Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On causality, apparent 'superluminality' and reshaping in barrier
  penetration   We consider tunnelling of a non-relativistic particle across a potential
barrier. It is shown that the barrier acts as an effective beam splitter which
builds up the transmitted pulse from the copies of the initial envelope shifted
in the coordinate space backwards relative to the free propagation. Although
along each pathway causality is explicitly obeyed, in special cases reshaping
can result an overall reduction of the initial envelope, accompanied by an
arbitrary coordinate shift. In the case of a high barrier the delay amplitude
distribution (DAD) mimics a Dirac $\delta$-function, the transmission amplitude
is superoscillatory for finite momenta and tunnelling leads to an accurate
advancement of the (reduced) initial envelope by the barrier width. In the case
of a wide barrier, initial envelope is accurately translated into the complex
coordinate plane. The complex shift, given by the first moment of the DAD,
accounts for both the displacement of the maximum of the transmitted
probability density and the increase in its velocity. It is argued that
analysing apparent 'superluminality' in terms of spacial displacements helps
avoid contradiction associated with time parameters such as the phase time.

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The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex