Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superconductivity in mesoscopic high-$T_{c}$ superconducting particles   Based on the Hubbard model in the framework of non-phonon kinematical
mechanism and taking into account the discreetness of an electronic energy
spectrum, the superconducting critical temperature of a mesoscopic high-$T_{c}$
sphere is analyzed as a function of doping and as a function of a particle's
radius. The critical temperature $T_{c}$ is found to be an oscillating function
of the radius of a particle. The size-dependent doping regime is revealed in
high-$T_{c}$ nanoparticles. Our analysis shows that each oscillation in $T_{c}$
corresponds to the increase of a number of the energy levels in the sphere by
one. The amplitude of oscillations of $T_{c}$ increases with decreasing $R$ and
can reach a value of 6 K for nanopartilces with sizes about 25 nm, in a good
agreement with experimental studies of YBa$_{2}$Cu$_{3}$O$_{7-\delta}$
nanoparticles.

37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin