217 research outputs found

### Analytic Studies of Static and Transport Properties of (Gauged) Skyrmions

We study static and transport properties of Skyrmions living within a finite
spatial volume in a flat (3+1)-dimensional spacetime. In particular, we derive
an explicit analytic expression for the compression modulus corresponding to
these Skyrmions living within a finite box and we show that such expression can
produce a reasonable value. The gauged version of these solitons can be also
considered. It is possible to analyze the order of magnitude of the
contributions to the electrons conductivity associated to the interactions with
this Baryonic environment. The typical order of magnitude for these
contributions\ to conductivity can be compared with the experimental values of
the conductivity of layers of Baryons.Comment: Latex2e source file, 30 pages, 7 figures, accepted for publication in
European Physical Journal

### Cosmological Solutions in Multiscalar Field Theory

We consider a cosmological model with two scalar fields minimally coupled to
gravity which have a mixed kinetic term. Hence, Chiral cosmology is included in
our analysis. The coupling function and the potential function, which depend on
one of the fields, characterize the model we study. We prove the existence of
exact solutions that are of special interest for the cosmological evolution.
Furthermore, we provide with a methodology that relates the scale factor
behaviour to the free functions characterizing the scalar field kinetic term
coupling and potential. We derive the necessary conditions that connect these
two functions so that the relative cosmological solutions can be admitted. We
find that unified dark matter and dark energy solutions are allowed by the
theory in various scenarios involving the aforementioned functions.Comment: 15 pages, 3 figures, Latex2e source file, revised to agree with the
accepted EPJC versio

### Wheeler-DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology

Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi
Class A cosmologies. In particular, we consider General Relativity, minimally
coupled scalar field gravity and Hybrid Gravity as paradigmatic examples of the
approach. Several invariant solutions are determined and classified according
to the form of the scalar field potential. The approach gives rise to a
suitable method to select classical solutions and it is based on the first
principle of the existence of symmetries.Comment: 17 page

### Integrability and chemical potential in the (3+1)-dimensional Skyrme model

Using a remarkable mapping from the original (3+1)dimensional Skyrme model to
the Sine-Gordon model, we construct the first analytic examples of Skyrmions as
well as of Skyrmions--anti-Skyrmions bound states within a finite box in 3+1
dimensional flat space-time. An analytic upper bound on the number of these
Skyrmions--anti-Skyrmions bound states is derived. We compute the critical
isospin chemical potential beyond which these Skyrmions cease to exist. With
these tools, we also construct topologically protected time-crystals:
time-periodic configurations whose time-dependence is protected by their
non-trivial winding number. These are striking realizations of the ideas of
Shapere and Wilczek. The critical isospin chemical potential for these
time-crystals is determined.Comment: 15 pages; 1 figure; a discussion on the closeness to the topological
bound as well as some clarifying comments on the semi-classical quantization
have been included. Relevant references have been added. Version accepted for
publication on Physics Letters

### Scalar-Tensor Gravity Cosmology: Noether symmetries and analytical solutions

In this paper, we present a complete Noether Symmetry analysis in the
framework of scalar-tensor cosmology. Specifically, we consider a non-minimally
coupled scalar field action embedded in the FLRW spacetime and provide a full
set of Noether symmetries for related minisuperspaces. The presence of
symmetries implies that the dynamical system becomes integrable and then we can
compute cosmological analytical solutions for specific functional forms of
coupling and potential functions selected by the Noether Approach.Comment: 9 pages, accepted for publication by Phys. Rev.

### On the Hojman conservation quantities in Cosmology

We discuss the application of the Hojman's Symmetry Approach for the
determination of conservation laws in Cosmology, which has been recently
applied by various authors in different cosmological models. We show that
Hojman's method for regular Hamiltonian systems, where the Hamiltonian function
is one of the involved equations of the system, is equivalent to the
application of Noether's Theorem for generalized transformations. That means
that for minimally-coupled scalar field cosmology or other modified theories
which are conformally related with scalar-field cosmology, like $f(R)$ gravity,
the application of Hojman's method provide us with the same results with that
of Noether's theorem. Moreover we study the special Ansatz. $\phi\left(
t\right) =\phi\left( a\left( t\right) \right)$, which has been introduced for
a minimally-coupled scalar field, and we study the Lie and Noether point
symmetries for the reduced equation. We show that under this Ansatz, the
unknown function of the model cannot be constrained by the requirement of the
existence of a conservation law and that the Hojman conservation quantity which
arises for the reduced equation is nothing more than the functional form of
Noetherian conservation laws for the free particle. On the other hand, for
$f(T)$ teleparallel gravity, it is not the existence of Hojman's conservation
laws which provide us with the special function form of $f(T)$ functions, but
the requirement that the reduced second-order differential equation admits a
Jacobi Last multiplier, while the new conservation law is nothing else that the
Hamiltonian function of the reduced equation.Comment: 6 pages; minor corrections; accepted for publication by Physics
Letters B. arXiv admin note: substantial text overlap with arXiv:1503.0846

### Lie symmetries of (1+2) nonautonomous evolution equations in Financial Mathematics

We analyse two classes of $(1+2)$ evolution equations which are of special
interest in Financial Mathematics, namely the Two-dimensional Black-Scholes
Equation and the equation for the Two-factor Commodities Problem. Our approach
is that of Lie Symmetry Analysis. We study these equations for the case in
which they are autonomous and for the case in which the parameters of the
equations are unspecified functions of time. For the autonomous Black-Scholes
Equation we find that the symmetry is maximal and so the equation is reducible
to the $(1+2)$ Classical Heat Equation. This is not the case for the
nonautonomous equation for which the number of symmetries is submaximal. In the
case of the two-factor equation the number of symmetries is submaximal in both
autonomous and nonautonomous cases. When the solution symmetries are used to
reduce each equation to a $(1+1)$ equation, the resulting equation is of
maximal symmetry and so equivalent to the $(1+1)$ Classical Heat Equation.Comment: 15 pages, 1 figure, to be published in Mathematics in the Special
issue "Mathematical Finance

- â€¦