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Francisco Peña

Publications and source records attributed to Francisco Peña.

16 recordsLinked to original sources
arXiv2026

Bound-State Spectra of a Lifshitz-Type Dirac Equation in (2+1) Dimensions

We investigate a Dirac-type equation in $(2+1)$ dimensions modified by Lifshitz spatial derivatives with dynamical exponent $z=2$, focusing on the spectral properties of bound-states under radial confinement. Analytical solutions are obtained for constant backgrounds, hard-wall confinement, and harmonic potentials, while logarithmic confinement is treated numerically via the Numerov method and complemented by a semiclassical WKB analysis. The resulting spectra exhibit characteristic scaling laws governed by the Lifshitz parameter $b$, including $E - M \propto b/R_0^2$ for hard-wall confinement, $E - M \propto \sqrt{2b}\,ω$ for harmonic trapping, and $E - M \sim α\ln\sqrt{b}$ in the semiclassical regime of logarithmic confinement, where $M$ is a mass scale. These results provide a consistent characterization of how higher-order spatial derivatives modify the energy spectra in two-dimensional Dirac systems and may be relevant for effective descriptions of materials with quadratic low-energy dispersion, such as bilayer graphene and related anisotropic 2D systems.

cond-mat.str-el↗
arXiv2021

Influence of the four-fermion interactions in (2+1)D massive electrons system

The description of the electromagnetic interaction in two-dimensional Dirac materials, such as graphene and transition-metal dichalcogenides, in which electrons move in the plane and interact via virtual photons in 3d, leads naturally to the emergence of a projected non-local theory, called pseudo-quantum electrodynamics (PQED), as an effective model suitable for describing electromagnetic interaction in these systems. In this work, we investigate the role of a complete set of four-fermion interactions in the renormalization group functions when we coupled it with the anisotropic version of massive PQED, where we take into account the fact that the Fermi velocity is not equal to the light velocity. We calculate the electron self-energy in the dominant order in the $1/N$ expansion in the regime where $m ^ 2 \ll p ^ 2$. We show that the Fermi velocity renormalization is insensitive to the presence of quartic fermionic interactions, whereas the renormalized mass may have two different asymptotic behaviors at the high-density limit, which means a high-energy scale.

hep-th↗
arXiv2020

Dynamical Mass Generation in Pseudo Quantum Electrodynamics with Gross-Neveu Interaction at finite temperature

We study the dynamical mass generation in Pseudo Quantum Electrodynamics (PQED) coupled to the Gross-Neveu (GN) interaction, in (2+1) dimensions, at both zero and finite temperatures. We start with a gapless model and show that, under particular conditions, a dynamically generated mass emerges. In order to do so, we use a truncated Schwinger-Dyson equation, at the large-N approximation, in the imaginary-time formalism. In the instantaneous-exchange approximation (the static regime), we obtain two critical parameters, namely, the critical number of fermions $N_c(T)$ and the critical coupling constant $α_c(T)$ as a function of temperature and of the cutoff $Λ$, which must be provided by experiments. In the dynamical regime, we find an analytical solution for the mass function $Σ(p,T)$ as well as a zero-external momentum solution for $p=0$. We compare our analytical results with numerical tests and a good agreement is found.

hep-th↗
arXiv2020

Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions

Recently the renormalization of the band gap $m$, in both WSe$_2$ and MoS$_2$, has been experimentally measured as a function of the carrier concentration $n$. The main result establishes a decreasing of hundreds of meV, in comparison with the bare band gap, as the carrier concentration increases. These materials are known as transition metal dichalcogenides and their low-energy excitations are, approximately, described by the massive Dirac equation. Using Pseudo Quantum Electrodynamics (PQED) to describe the electromagnetic interaction between these quasiparticles and from renormalization group analysis, we obtain that the renormalized mass describes the band gap renormalization with a function given by $m(n)/m_0=(n/n_0)^{C_λ/2}$, where $m_0=m(n_0)$ and $C_λ$ is a function of the coupling constant $λ$. We compare our theoretical results with the experimental findings for WSe$_2$ and MoS$_2$, and we conclude that our approach is in agreement with these experimental results for reasonable values of $λ$. In addition we introduced a Gross-Neveu (GN) interaction which could simulate an disorder/impurity-like microscopic interaction. In this case, we show that there exists a critical coupling constant, namely, $λ_c \approx 0,66$ in which the beta function of the mass vanishes, providing a stable fixed point in the ultraviolet limit. For $λ>λ_c$, the renormalized mass decreases while for $λ<λ_c$ it increases with the carrier concentration.

hep-th↗
arXiv2016

Regular Charged Black Holes, Quasilocal Energy and Energy Conditions

We revisit the relationship of inequality between the gravitational field energy and the Komar charge, both quantities evaluated at the event horizon, for static and spherically symmetric regular black hole solutions obtained with nonlinear electrodynamics. We found a way to characterize these regular black hole solutions by the energy conditions that they satisfy. In particular, we show the relation between the direction of the inequality and the energy condition that satisfy the regular black hole solutions.

gr-qc↗
arXiv2015

Bulk-Boundary interaction and the second law in Hořava-Lifshitz cosmology

By defining $Q$ as a function which realizes the energy transference between the bulk and the boundary of spacetime, as we interprete it here in the framework of Hořava-Lifshitz (HL) cosmology, flat case, we discuss the validity of the second law of thermodynamics in the light of the sign changes of $Q$ (changes in the direction of energy transference) and its consequences through the cosmic evolution, in particular, whether the thermal equilibrium between bulk and boundary is reached or not. Additionally, we discuss possible phase transitions experienced by the bulk and the boundary (seen as sign changes in their heat capacities) through the cosmic evolution. The energy density in the bulk is modeled under an holographic perspective. As far as we know, currently there is not observational data on bulk-boundary interaction.

gr-qc↗
arXiv2015

Chiral-Symmetry Breaking in Pseudo Quantum Electrodynamics at Finite Temperature

We use the Schwinger-Dyson equations in the presence of a thermal bath, in order to study chiral symmetry breaking in a system of massless Dirac fermions interacting through pseudo quantum electrodynamics (PQED3), in (2+1) dimensions. We show that there is a critical temperature $T_c$, below which chiral symmetry is broken, and a corresponding mass gap is dynamically generated, provided the coupling is above a certain, temperature dependent, critical value $α_c$. The ratio between the energy gap and the critical temperature for this model is estimated to be $2 π$. These results are confirmed by analytical and numerical investigations of the Schwinger-Dyson equation for the electron. In addition, we calculate the first finite-temperature corrections to the static Coulomb interaction. The relevance of this result in the realm of condensed matter systems, like graphene, is briefly discussed.

hep-th↗
arXiv2015

Holographic energy density on Hořava-Lifshitz cosmology

In Hořava-Lifshitz cosmology we use the holographic Ricci-like cut-off for the energy density proposed by L. N. Granda and A. Oliveros and under this framework we study, through the cosmic evolution at late times, the sign change in the amount of non-conservation energy ($Q$) present in this cosmology. We revise the early stage (curvature-dependent) of this cosmology, where a term reminiscent of stiff matter is the dominant, and in this stage we find a power-law solution for the cosmic scale factor although $ω=-1$. Late and early phantom schemes are obtained without requiring $ω<-1$. Nevertheless, these schemes are not feasible according to what is shown in this paper. We also show that $ ω=-1$ alone does not imply a de Sitter phase in the present cosmology. Thermal aspects are revised by considering the energy interchange between the bulk and the spacetime boundary and we conclude that there is no thermal equilibrium between them. Finally, a ghost scalar graviton (extra degree of freedom in HL gravity) is required by the observational data.

hep-th↗
arXiv2014

DGP Cosmological model with generalized Ricci dark energy

The braneworld model proposed by Dvali, Gabadadze and Porrati (DGP) leads to an accelerated universe without cosmological constant or other form of dark energy for the positive branch $(ε=+1)$. For the negative branch $(ε=-1)$ we have investigated the behavior of a model with an holographic Ricci-like dark energy and dark matter, where the IR cutoff takes the form $αH^2 + β\dot{H}$, being $H$ the Hubble parameter and $α$, $β$ positive constants of the model. We perform an analytical study of the model in the late-time dark energy dominated epoch, where we obtain a solution for $r_cH(z)$, where $r_c$ is the leakage scale of gravity into the bulk, and conditions for the negative branch on the holographic parameters $α$ and $β$, in order to hold the conditions of weak energy and accelerated universe. On the other hand, we compare the model versus the late-time cosmological data using the latest type Ia supernova sample of the Joint Light-curve Analysis (JLA), in order to constraint the holographic parameters in the negative branch, as well as $r_cH_0$ in the positive branch, where $H_0$ is the Hubble constant. We find that the model has a good fit to the data and that the most likely values for $(r_cH_0, α, β)$ lie in the permitted region found from an analytical solution in a dark energy dominated universe. We give a justification to use holographic cut-off in 4D for the dark energy in the 5 dimensional DGP model. Finally, using the Bayesian Information Criterion we find that this model it is disfavored compared with the flat $Λ$CDM model.

astro-ph.CO↗
arXiv2014

No stable dissipative phantom scenario in the framework of a complete cosmological dynamics

We investigate the phase space dynamics of a bulk viscosity model in the Eckart approach for a spatially flat Friedmann-Robertson-Walker universe. We have included two barotropic fluids and a dark energy component. One of the barotropic fluids is treated as an imperfect fluid having bulk viscosity, whereas the other components are assumed to behave as perfect fluids. Both barotropic fluids are identified as either radiation or dark matter. Considering that the bulk viscosity acts on either radiation or dark matter, we find that viscous phantom solutions with stable behavior are not allowed in the framework of complete cosmological dynamics. Only an almost zero value of the bulk viscosity allows a transition from a radiation-dominated to a matter-dominated epoch, which then evolves to an accelerated late time expansion, dominated by dark energy.

gr-qc↗
arXiv2013

Chern-Simons terms in Lifshitz like quantum electrodynamics

In this work the generation of generalized Chern-Simons terms in three dimensional quantum electrodynamics with high spatial derivatives is studied. We analyze the self-energy corrections to the gauge field propagator by considering an expansion of the amplitude up to third order in the external momenta. The divergences of the corrections are determined and explicit forms for the Chern-Simons terms with high derivatives are obtained. Some unusual aspects of the calculation are stressed and the existence of a smooth isotropic limit is proved. The transversality of the anisotropic gauge propagator is also discussed.

hep-th↗
arXiv2012

Γ-sign in entropic cosmology

We study a cosmology by considering entropic issues. We make a bare/effective description of the equation of state of the cosmic fluid through a bare (ω)/effective (ω_eff) conservation equation. In the bare case, where we have a non conserved equation of state for the cosmic fluid, we describe the change in the sign of the inhomogeneus term at different times of the cosmic evolution. We show that by a redefinition of the adiabatic ω-parameter we can recover the usual scheme for the cosmic evolution. In the effective case we show also that if the evolution is driven by dust or cosmological constant, the universe evolves on the thermal equilibrium. Additionally, by incorporating a quantum correction only cosmological constant can drive an evolution on thermal equilibrium.

hep-th↗
arXiv2011

Holographic dark energy in the DGP model

The braneworld model proposed by Dvali, Gabadadze and Porrati leads to an accelerated universe without cosmological constant or other form of dark energy. Nevertheless, we have investigated the consequences of this model when an holo- graphic dark energy is included, taken the Hubble scale as IR cutoff. We have found that the holographic dark energy leads to an accelerated universe flat (de Sitter like expansion) for the two branch: {\ko} = \pm1 of the DGP model. Nevertheless, in universes with no null curvature the dark energy presents an EoS corresponding to a phantom fluid during the present era and evolving to a de Sitter like phase for future cosmic time. In the special case in which the holographic parameter c is equal to one we have found a sudden singularity in closed universes. In this case the expansion is decelerating. Manuscript

gr-qc↗
arXiv2011

Fermionic and scalar fields as sources of interacting dark matter-dark energy

From a variational action with non-minimal coupling with a scalar field and classical scalar and fermionic interaction, cosmological field equations can be obtained. Imposing a FLRW metric the equations lead directly to a cosmological model consisting of two interacting fluids, where the scalar field fluid is interpreted as dark energy and the fermionic field fluid is interpreted as dark matter. Several cases were studied analytically and numerically. An important feature of the non-minimal coupling is that it allows crossing the barrier from a quintessence to phantom behavior. The insensitivity of the solutions to one of the parameters of the model permits it to find an almost analytical solution for the cosmological constant type of universe.

gr-qc↗
arXiv2005

Loop Equations in Abelian Gauge Theories

The equations obeyed by the vacuum expectation value of the Wilson loop of Abelian gauge theories are considered from the point of view of the loop-space. An approximative scheme for studying these loop-equations for lattice Maxwell theory is presented. The approximation leads to a partial difference equation in the area and length variables of the loop, and certain physically motivated ansatz is seen to reproduce the mean field results from a geometrical perspective.

hep-th↗