arXiv subjects

E. Cavalcanti

Publications and source records attributed to E. Cavalcanti.

7 recordsLinked to original sources

arXiv2024

Instantons and transseries of the Mathieu potential deformed by a $\mathcal{PT}$-symmetry parameter

We investigate the non-perturbative effects of a deformation of the Mathieu differential equation consistent with $\mathcal{PT}$ symmetry. First, we develop a connection between the non-Hermitian and Hermitian scenarios by a reparameterization in the complex plane, followed by a restriction of the $\mathcal{PT}$ deformation parameter. The latter is responsible for preserving the information about $\mathcal{PT}$ symmetry when we choose to work in the Hermitian scenario. We note that this factor is present in all non-perturbative results and in the transseries representation of the deformed Mathieu partition function that we have obtained. In quantum mechanics, we found that the deformation parameter of $\mathcal{PT}$ symmetry has an effect on the real instanton solution for the deformed Mathieu potential in the Hermitian scenario. As its value increases, the non-Hermiticity factor makes it smoother for the instanton to pass from one minimum to another, that is, it modifies the instanton width. The explanation for this lies in the fact that the height of the potential barrier decreases as we increase the value of the deformation parameter. We present how this effect extends to the multi-instanton level and to the bounce limit of an instanton-anti-instanton pair. As an application of the obtained results, we show that the equation of motion under a tilted version of the potential in the Hermitian scenario compares to the resistively shunted junction (RSJ) model for the Josephson junction.

hep-th↗

arXiv2022

Quantum forces in cavities

We present an alternative route to investigate quantum forces in a cavity, for both a free scalar field and a free fermionic field. Considering a generalized Matsubara procedure, we compute the quantum pressure on the boundaries of a compactified space in a thermal bath. Also, considering both periodic and antiperiodic boundary conditions in the cavity, we discuss the attractive or repulsive character of the quantum forces. Our results highlight the relevance and interdisciplinarity of the generalized Matsubara procedure as a theoretical platform to manage quantum phenomena in nontrivial topologies.

quant-ph↗

arXiv2022

Energy levels for $\mathcal{PT}$-symmetric deformation of the Mathieu equation

We propose a non-Hermitian deformation of the Mathieu equation that preserves $\mathcal{PT}$ symmetry and study its spectrum and the transition from $\mathcal{PT}$-unbroken to $\mathcal{PT}$-broken phases. We show that our model not only reproduces behaviors expected by the literature but also indicates the existence of a richer structure for the spectrum. We also discuss the influence of the boundary condition and the model parameters in the exceptional line that marks the $\mathcal{PT}$ breaking.

quant-ph↗

arXiv2019

The effect of boundary conditions on dimensionally reduced field-theoretical models at finite temperature

Here we understand \textit{dimensional reduction} as a procedure to obtain an effective model in $D-1$ dimensions that is related to the original model in $D$ dimensions. To explore this concept we use both a self-interacting fermionic model and self-interacting bosonic model. Furthermore, in both cases, we consider different boundary conditions in space: periodic, antiperiodic, Dirichlet and Neumann. For bosonic fields, we get the so defined dimensional reduction. Taking the simple example of a quartic interaction, we obtain that the boundary condition (periodic, Dirichlet, Neumann) influence the new coupling of the reduced model. For fermionic fields, we get the curious result that the model obtained reducing from $D$ dimensions to $D-1$ dimensions is distinguishable from taking into account a fermionic field originally in $D-1$ dimensions. Moreover, when one considers antiperiodic boundary condition in space (both for bosons or fermions) it is found that the dimensional reduction is not allowed.

hep-th↗

arXiv2018

Dimensional reduction of a finite-size scalar field model at finite temperature

We investigate the process of dimensional reduction of one spatial dimension in a thermal scalar field model defined in $D$ dimensions (inverse temperature and $D-1$ spatial dimensions). We obtain that a thermal model in $D$ dimensions with one of the spatial dimensions having a finite size $L$ is related to the finite temperature model with just $D-1$ spatial dimensions and no finite size. Our results are obtained for one-loop calculations and for any dimension $D$. For example, in $D=4$ we have a relationship between a thin film with thickness $L$ at finite temperature and a surface at finite temperature. We show that, although a strict dimensional reduction is not allowed, it is possible to define a valid prescription for this procedure.

hep-th↗

arXiv2018

Impact of unitarization on the $J/ψ$-light meson cross section

Hidden charm mesons continue playing an essential role as relevant probes to understand the evolution of partonic matter. It is expected that the charmonia that survived the quark-gluon plasma phase suffer collisions with other particles composing the hadronic matter. In this work, we intend to contribute on this subject by presenting an updated study about the interactions of $J/ψ$ with surrounding hadronic medium. The meson-meson interactions are described with a $SU(4)$ effective Lagrangian, and within the framework of unitarized coupled channel amplitudes projected onto s-wave. The symmetry is explicitly broken to $SU(3)$ by suppression of the interactions driven by charmed mesons. We calculate the cross sections for $J/ψ$ scattering by light pseudoscalar mesons ($π, K, η$) and vector mesons ($ρ, K^\ast, ω$), as well as their inverse processes. Keeping the validity of this present approach in the low CM energy range, the most relevant channels are evaluated and a comparison of the findings with existing literature is performed.

hep-ph↗

arXiv2017

Properties of size-dependent models having quasiperiodic boundary conditions

Boundary conditions effects are explored for size-dependent models in thermal equilibrium. Scalar and fermionic models are used for $D=1+3$ (films), $D=1+2$ (hollow cylinder) and $D=1+1$ (ring). For all models a minimal length is found, below which no thermally-induced phase transition occurs. Using quasiperiodic boundary condition controlled by a contour parameter $θ$ ($θ=0$ is a periodic boundary condition and $θ=1$ is an antiperiodic condition) it results that the minimal length depends directly on the value of $θ$. It is also argued that this parameter can be associated to an Aharonov-Bohm phase.

hep-th↗