Physics Letters B 772 (2017) 592–598
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Phase transitions in thick branes endorsed by entropic information
W.T. Cruz
a
, D.M. Dantas
b
, R.A.C. Correa
c,d
, C.A.S. Almeida
b,∗
a
Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE), Campus Juazeiro do Norte – 63040-540 Juazeiro do Norte, CE, Brazil
b
Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Fortaleza – CE, C.P. 6030, 60455-760, Brazil
c
UNESP, Universidade Estadual Paulista, Campus de Guaratinguetá, 12516-410, Guaratinguetá, São Paulo, Brazil
d
ITA, Instituto Tecnológico de Aeronáutica, Departamento de Física, 12228-900, São José dos Campos, São Paulo, Brazil
a r t i c l e i n f o a b s t r a c t
Article history:
Received
27 February 2017
Received
in revised form 7 July 2017
Accepted
10 July 2017
Available
online 14 July 2017
Editor:
M. Cveti
ˇ
c
Keywords:
Bloch
brane
Brane-world
models
Configurational
entropy
The so-called configurational entropy (CE) framework has proved to be an efficient instrument to study
nonlinear scalar field models featuring solutions with spatially-localised energy, since its proposal by
Gleiser and Stamapoulos. Therefore, in this work, we apply this new physical quantity in order to
investigate the properties of degenerate Bloch branes. We show that it is possible to construct a
configurational entropy measure in functional space from the field configurations, where a complete set
of exact solutions for the model studied displays both double and single-kink configurations. Our study
shows a rich internal structure of the configurations, where we observe that the field configurations
undergo a quick phase transition, which is endorsed by information entropy. Furthermore, the Bloch
configurational entropy is employed to demonstrate a high organisational degree in the structure of the
configurations of the system, stating that there is a best ordering for the solutions.
© 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
In the last years, the study of phenomenological properties in
braneworld models are increasing. We have recent works explain-
ing
anomalies in the meson B decay [1] and in the neutrinos
physics [2], performing bounds into corrections to Coulomb’s law
[3,4], into electrical conductivity [5], as also adjusting parameters
to the experimental data of the nucleon-nucleus total cross-section
of various chemical elements [6]. Applications to Myers–Perry’s
black holes [7] and results based on the observation of gravita-
tional
waves [8] are interesting issues about new insights in the
braneworld framework.
In
this context, a well-known model is the Bloch brane scenario,
proposed by Bazeia and Gomes [9]. This thick brane model is gen-
erated
by two interacting scalar fields that perform the thickness
of the model that solves several issues in the fields localisation
present in thin models [10,11], as well as in the Randall–Sundrum
models [12,13]. Moreover, the structure of this scenario is based
on domain walls, which have some interesting application in sev-
eral
branches of Physics as in high energy physics [14], cosmology
*
Corresponding author.
E-mail
addresses: wilamicruz@gmail.com (W.T. Cruz), davi@fisica.ufc.br
(D.M. Dantas),
rafael.couceiro@ufabc.edu.br (R.A.C. Correa), carlos@fisica.ufc.br
(C.A.S. Almeida).
[15,16], quantum field theory [17] and propositions about the grav-
itational
waves observation [18].
The
authors of the works [19–21] have shown the existence of
more general Bloch brane solutions in which a degeneracy parame-
ter
is responsible for the raising of two-kink solutions. That model
is the so-called degenerate Bloch brane (DBB), where the energy of
the field configuration in the superpotential is precisely the same
with regarding all parameter associated with the domain wall [19].
So, we have the formation of a double brane structure with a split-
ting
effect that is magnified by the approaching of the degeneracy
parameter to a critical value.
This
transition from single-kink solution to double-kink (or
multi-kink) solutions have some physical implications. The multi-
kinks
appear in dispersive non-linear system, where single-kinks
are no more stables [22]. Ref. [23] shows the appearance of
double-kink soliton in the sine-Gordon model under the pertur-
bation
of a space-dependent force. The experimental application of
multi-kink concepts arises, among other, in the mobility hystere-
sis
in a damped driven commensurable chain of atoms [24] and
in arrays of Josephson junctions [25]. Specifically in the context of
braneworlds, the presence of the massive resonant Kaluza–Klein
modes is dependent upon transition parameter. A resonant KK
mode is an extradimensional massive mode of a field with a fi-
nite
lifetime, which can bring some interesting phenomenology to
braneworlds branch [1,4,26–28]. The study of resonances for grav-
ity
and fermions in the symmetric and asymmetric cases of the
http://dx.doi.org/10.1016/j.physletb.2017.07.020
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© 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.