Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenization procedure for a metamaterial and local violation of the
  second principle of thermodynamics   Classical theory of crystals states that a medium to be considered
homogeneous must satisfy the following requirements: a) the dimension of the
elementary cell must be much smaller than the incident wavelength; b) the
sample must contain a large number of elementary cells, i.e. it must be
macroscopic with respect to wavelength. Under these conditions, macroscopic
quantities can be introduced in order to describe the optical response of the
medium. We analytically demonstrate that for a symmetric elementary cell those
requirements can be relaxed, and it is possible to assign a permittivity and a
permeability to a composite structure, even if the metamaterial cannot be
considered homogeneous under the requirements stated above. However, the
effective permittivity and permeability in some cases may give rise to
unphysical, effective behaviors inside the medium, notwithstanding the fact
that they satisfy requirements like being Kramers-Kronig pairs, for example,
and are consistent with all the linear properties outside the structure (i.e.
reflection, transmission, and absorption at all frequencies). In some
situations the medium is assigned a magnetic response even though the medium is
not magnetically active. In particular, we demonstrate that the homogenization
procedure can lead to a medium that locally violates the second principle of
thermodynamics. We also show that, in the non-homogeneous regime, it is not
possible to describe the nonlinear behavior of the structure using an effective
parameters approach, despite the possibility to assign an effective linear
refractive index.

11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat