arXiv subjects

Freddy P. Zen

Publications and source records attributed to Freddy P. Zen.

At least 37 records · Page 2Linked to original sources

arXiv2015

Spin glass behavior of the antiferromagnetic Heisenberg model on scale free network

Randomness and frustration are considered to be the key ingredients for the existence of spin glass (SG) phase. In a canonical system, these ingredients are realized by the random mixture of ferromagnetic (FM) and antiferromagnetic (AF) couplings. The study by Bartolozzi {\it et al.} [Phys. Rev. B{\bf 73}, 224419 (2006)] who observed the presence of SG phase on the AF Ising model on scale free network (SFN) is stimulating. It is a new type of SG system where randomness and frustration are not caused by the presence of FM and AF couplings. To further elaborate this type of system, here we study Heisenberg model on AF SFN and search for the SG phase. The canonical SG Heisenberg model is not observed in $d$-dimensional regular lattices for ($d \leq 3$). We can make an analogy for the connectivity density ($m$) of SFN with the dimensionality of the regular lattice. It should be plausible to find the critical value of $m$ for the existence of SG behaviour, analogous to the lower critical dimension ($d_l$) for the canonical SG systems. Here we study system with $m=2,3,4$ and $5$. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter. We observed SG phase for each value of $m$ and estimated its corersponding critical temperature.

cond-mat.dis-nn↗

arXiv2015

Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity

We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to write operators acting on spin network states in (2+1)-dimensional loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional intrinsic, and 2-dimensional extrinsic curvatures.

gr-qc↗

arXiv2014

Vanishing Dimensions in Four Dimensional Cosmology with Nonminimal Derivative Coupling of Scalar Field

We discussed a mechanism that allows the universe to start from lower dimension ($d < 4$) in its very early era and evolves to four dimension at the end of the process. The mechanism is generated by a nonminimal derivative coupling of scalar field, where derivative terms of the scalar field coupled to curvature tensor. We solve the Einstein equations for a limit of large and nearly constant Hubble parameter and analyze the evolution of the Hubble parameter in this limit. The lower-dimensionality in early universe has advantages in the context of unification theory.

physics.gen-ph↗

arXiv2014

Cosmological Model with Nonminimal Derivative Coupling of Scalar Fields in Five Dimensions

We study a nonminimal derivative coupling (NMDC) of scalar field, where the scalar field is coupled to curvature tensor in the five dimensional universal extra dimension model. We apply the Einstein equation and find its solution. First, we consider a special case of pure free scalar field without NMDC and we find that for static extradimension, the solution is equivalent to the standard cosmology with stiff matter. For a general case of pure free scalar field with NMDC, we find that the de Sitter solution is the solution of our model. For this solution, the scalar field evolves linearly in time. In the limit of small Hubble parameter, the general case give us the same solution as in the pure free scalar field. Finally, we perform a dynamical analysis to determine the stability of our model. We find that the extradimension, if it exist, can not be static and always shrinks with the expansion of four dimensional spacetime.

gr-qc↗

arXiv2014

How many quanta are there in a quantum spacetime?

Following earlier insights by Livine and Terno, we develop a technique for describing quantum states of the gravitational field in terms of coarse grained spin networks. We show that the number of nodes and links and the values of the spin depend on the observables chosen for the description of the state. Hence the question in the title of this paper is ill posed, unless further information about what is been measured is given.

gr-qc↗

arXiv2013

Some Aspects of Spherical Symmetric Extremal Dyonic Black Holes in 4d N=1 Supergravity

In this paper we study several aspects of extremal spherical symmetric black hole solutions of four dimensional N=1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region the complex scalars are fixed and regular which can be viewed as the critical points of the black hole and the scalar potentials with vanishing scalar charges. It follows that the asymptotic geometries are of a constant and non-zero scalar curvature which are generally not Einstein. These spaces could also correspond to the near horizon geometries which are the product spaces of a two anti-de Sitter surface and the two sphere if the value of the scalars in both regions coincides. In addition, we prove the local existence of non-trivial radius dependent complex scalar fields which interpolate between the horizon and the asymptotic region. We finally give some simple ${\lC}^{n}$-models with both linear superpotential and gauge couplings.

hep-th↗

arXiv2013

Bosonic Part of 4d N=1 Supersymmetric Gauge Theory with General Couplings: Local Existence

In this paper, we prove the local existence of the bosonic part of N=1 supersymmetric gauge theory in four dimensions with general couplings. We start with the Lagrangian of the vector and chiral multiplets with general couplings and scalar potential turned on. Then, for the sake of simplicity, we set all fermions vanish at the level of equations of motions, so we only have the bosonic parts of the theory. We apply Segal's general theory to show the local existence of solutions of equations of motions by taking Kahler potential to be bounded above by U(n) symmetric Kahler potential and the first derivative of gauge couplings to be at most linear growth functions.

math-ph↗

arXiv2011

Rise or sink: spherical intruder in density frequency dependence static granular fluid

A simple model for intruder in vibrating granular bed is constructed by introducing a term that governs frequency dependent granular bed density. Varying the vibrating frequency will drive the buoyant force acting on the intruder by the granular bed. Swapped regions of rising and sinking intruder compared to other reported result have bee found.

cond-mat.soft↗

arXiv2011

N=1 Supergravity BPS Domain Walls on Kähler-Ricci Soliton

This paper provides a study of some aspects of flat and curved BPS domain walls together with their Lorentz invariant vacua of four dimensional chiral N=1 supergravity. The scalar manifold can be viewed as a one-parameter family of Kähler manifolds generated by a Kähler-Ricci flow equation. Consequently, a vacuum manifold characterized by $(m,λ)$ where $m$ and $λ$ are the dimension and the index of the manifold, respectively, does deform with respect to the flow parameter related to the geometric soliton. Moreover, one has to carry out the renormalization group analysis to verify the existence of such a vacuum manifold in the ultraviolet or infrared regions. At the end, we discuss a simple model with linear superpotential on U(n) symmetric Kähler-Ricci orbifolds.

hep-th↗

arXiv2010

Kaluza-Klein two-brane-worlds cosmology at low energy

We study two $(4+n)$-dimensional branes embedded in $(5+n)$-dimensional spacetime. Using the gradient expansion approximation, we find that the effective theory is described by $(4+n)$-dimensional scalar-tensor gravity with a specific coupling function. Based on this theory we investigate the Kaluza-Klein two-brane-worlds cosmology at low energy, in both the static and the nonstatic internal dimensions. In the case of the static internal dimensions, the effective gravitational constant in the induced Friedmann equation depends on the equations of state of the brane matter, and the dark radiation term naturally appears. In the nonstatic case we take a relation between the external and internal scale factors of the form $b(t)=a^γ(t)$ in which the brane world evolves with two scale factors. In this case, the induced Friedmann equation on the brane is modified in the effective gravitational constant and the term proportional to $a^{-4β}$. For dark radiation, we find $γ=-2/(1+n)$. Finally, we discuss the issue of conformal frames which naturally arises with scalar-tensor theories. We find that the static internal dimensions in the Jordan frame may become nonstatic in the Einstein frame.

hep-th↗

arXiv2009

Cosmological evolution of interacting dark energy in Lorentz violation

The cosmological evolution of an interacting scalar field model in which the scalar field interacts with dark matter, radiation, and baryon via Lorentz violation is investigated. We propose a model of interaction through the effective coupling $\barβ$. Using dynamical system analysis, we study the linear dynamics of an interacting model and show that the dynamics of critical points are completely controlled by two parameters. Some results can be mentioned as follows. Firstly, the sequence of radiation, the dark matter, and the scalar field dark energy exist and baryons are sub dominant. Secondly, the model also allows the possibility of having a universe in the phantom phase with constant potential. Thirdly, the effective gravitational constant varies with respect to time through $\barβ$. In particular, we consider a simple case where $\barβ$ has a quadratic form and has a good agreement with the modified $Λ$CDM and quintessence models. Finally, we also calculate the first post--Newtonian parameters for our model.

hep-th↗

arXiv2009

Modified Gravitational Equations on Braneworld with Lorentz Invariant Violation

The modified gravitational equations to describe a four-dimensional braneworld in the case with the Lorentz invariant violation in a bulk spacetime is presented. It contains a trace part of the brane energy-momentum tensor and the coefficients of all terms describe the Lorentz violation effects from the bulk spacetime. As an application, we apply this formalism to study cosmology. In respect to standard effective Friedmann equations on the brane, Lorentz invariance violation in the bulk causes a modification of this equations that can lead to significant physical consequences. In particular, the effective Friedmann equation on the brane explicitly depends on the equation of state of the brane matter and the Lorentz violating parameters. We show that the components of five-dimensional Weyl curvature are related to the matter on brane even at low energies. We also find that the constraints on the theory parameters are depend on the equation of state of the energy components of the brane matter. Finally, the stability of the model depend on the specific choices of initial conditions and the parameters $β_i$.

hep-th↗

arXiv2009

Deformation of Curved BPS Domain Walls and Supersymmetric Flows on 2d Kähler-Ricci Soliton

We consider some aspects of the curved BPS domain walls and their supersymmetric Lorentz invariant vacua of the four dimensional N=1 supergravity coupled to a chiral multiplet. In particular, the scalar manifold can be viewed as a two dimensional Kähler-Ricci soliton generating a one-parameter family of Kähler manifolds evolved with respect to a real parameter, $τ$. This implies that all quantities describing the walls and their vacua indeed evolve with respect to $τ$. Then, the analysis on the eigenvalues of the first order expansion of BPS equations shows that in general the vacua related to the field theory on a curved background do not always exist. In order to verify their existence in the ultraviolet or infrared regions one has to perform the renormalization group analysis. Finally, we discuss in detail a simple model with a linear superpotential and the Kähler-Ricci soliton considered as the Rosenau solution.

hep-th↗

arXiv2008

Kaehler-Ricci Flow, Morse Theory, and Vacuum Structure Deformation of N=1 Supersymmetry in Four Dimensions

We address some aspects of four dimensional chiral N=1 supersymmetric theories on which the scalar manifold is described by Kähler geometry and can further be viewed as Kähler-Ricci soliton generating a one-parameter family of Kähler geometries. All couplings and solutions, namely the BPS domain walls and their supersymmetric Lorentz invariant vacua turn out to be evolved with respect to the flow parameter related to the soliton. Two models are discussed, namely N=1 theory on Kähler-Einstein manifold and U(n) symmetric Kähler-Ricci soliton with positive definite metric. In the first case we find that the evolution of the soliton causes topological change and correspondingly, modifies the Morse index of the nondegenerate vacua realized in the parity transformation of the Hessian matrix of the scalar potential after hitting singularity, which is natural in the global theory and for nondegenerate Minkowskian vacua of the local theory. However, such situation is not trivial in anti de Sitter (AdS) vacua. In an explicit model, we find that this geometric (Kähler-Ricci) flow can also change the index of the vacuum before and after singularity. Finally in the second case, since around the origin the metric is diffeomorphic to $ {\mathrm{\lC P}}^{n -1}$, we have to consider it in the asymptotic region. Our analysis shows that no index modification of vacua is present in both global and local theories.

hep-th↗

arXiv2008

BPS Domain Walls and Vacuum Structure of N=1 Supergravity Coupled to a Chiral Multiplet

We study BPS domain walls of N=1 supergravity coupled to a chiral multiplet and their Lorentz invariant vacua which can be viewed as critical points of BPS equations and the scalar potential. Supersymmetry further implies that gradient flows of BPS equations controlled by a holomorphic superpotential and the Kaehler geometry are unstable near local maximum of the scalar potential, whereas they are stable around local minimum and saddles of the scalar potential. However, the analysis using RG flows shows that such gradient flows do not always exist particularly in infrared region.

hep-th↗

arXiv2008

Attractor Solutions in Lorentz Violating Scalar-Vector-Tensor Theory

We investigate properties of attractors for scalar field in the Lorentz violating scalar-vector-tensor theory of gravity. In this framework, both the effective coupling and potential functions determine the stabilities of the fixed points. In the model, we consider the constants of slope of the effective coupling and potential functions which lead to the quadratic effective coupling vector with the (inverse) power-law potential. For the case of purely scalar field, there are only two stable attractor solutions in the inflationary scenario. In the presence of a barotropic fluid, the fluid dominated solution is absent. We find two scaling solutions: the kinetic scaling solution and the scalar field scaling solutions. We show the stable attractors in regions of ($γ$, $ξ$) parameter space and in phase plane plot for different qualitative evolutions. From the standard nucleosynthesis, we derive the constraints for the value of the coupling parameter.

hep-th↗

arXiv2007

Astrophysical Condition on the attolensing as a possible probe for a modified gravity theory

We investigate the wave effect in the gravitational lensing by a black hole with very tiny mass less than 10^-19 solar mass, which is called attolensing, motivated by a recent report that the lensing signature might be a possible probe of a modified gravity theory in the braneworld scenario. We focus on the finite source size effect and the effect of the relative motion of the source to the lens, which are influential to the wave effect in the attolensing. Astrophysical condition that the lensed interference signature can be a probe of the modified gravity theory is demonstrated. The interference signature in the microlensing system is also discussed.

astro-ph↗

arXiv2007

Some Impacts of Lorentz Violation on Cosmology

The impact of Lorentz violation on the dynamics of a scalar field is investigated. In particular, we study the dynamics of a scalar field in the scalar-vector-tensor theory where the vector field is constrained to be unity and time like. By taking a generic form of the scalar field action, a generalized dynamical equation for the scalar-vector-tensor theory of gravity is obtained to describe the cosmological solutions. We present a class of exact solutions for an ordinary scalar field or phantom field corresponding to a power law coupling vector and the Hubble parameter. As the results, we find a constant equation of state in de Sitter space-time and power law expansion with the quadratic of coupling vector, while a dynamic equation of state is obtained for $n> 2$. Then, we consider the inflationary scenario based on the Lorentz violating scalar-vector-tensor theory of gravity with general power-law coupling vector and two typical potentials: inverse power-law and power-law potentials. In fact, both the coupling vector and the potential models affect the dynamics of the inflationary solutions. Finally, we use the dynamical system formalism to study the attractor behavior of a cosmological model containing a scalar field endowed with a quadratic coupling vector and a chaotic potential.

hep-th↗