Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-linear quantum effects in electromagnetic radiation of a vortex
  electron   There is a controversy of how to interpret interactions of electrons with a
large spatial coherence with light and matter. When such an electron emits a
photon, it can do so either as if its charge were confined to a point within a
coherence length, the region where a square modulus of a wave function
$|\psi|^2$ is localized, or as a continuous cloud of space charge spread over
it. This problem was addressed in a recent study R.~Remez, et al., Phys. Rev.
Lett. {\bf 123}, 060401 (2019) where a conclusion was drawn in favor of the
first (point) interpretation. Here we argue that there is an alternative
explanation for the measurements reported in that paper, which relies on purely
classical arguments and does not allow one to refute the second interpretation.
We propose an experiment of Smith-Purcell radiation from a non-relativistic
vortex electron carrying orbital angular momentum, which can unambiguously lead
to the opposite conclusion. Beyond the paraxial approximation, the vortex
packet has a non-point electric quadrupole moment, which grows as the packet
spreads and results in a non-linear $L^3$-growth of the radiation intensity
with the length $L$ of the grating when $L$ is much larger than the packet's
Rayleigh length. Such a non-linear effect has never been observed for single
electrons and, if detected, it would be a hallmark of the non-point nature of
charge in a wave packet. Thus, two views on $|\psi|^2$ are complementary to
each other and an electron radiates either as a point charge or as a continuous
charge flow depending on the experimental conditions and on its quantum state.
Our conclusions hold for a large class of non-Gaussian packets and emission
processes for which the radiation formation length can exceed the Rayleigh
length, such as Cherenkov radiation, transition radiation, diffraction
radiation, and so forth.

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The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga