arXiv subjects

C. A. Linhares

Publications and source records attributed to C. A. Linhares.

At least 19 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

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↗

arXiv2019

Finite-volume and magnetic effects on the phase structure of the three-flavor Nambu--Jona-Lasinio model

In this work we analyze the finite-volume and magnetic effects on the phase structure of a generalized version of Nambu--Jona-Lasinio model with three quark flavors. By making use of mean-field approximation and Schwinger's proper-time method in a toroidal topology with antiperiodic conditions, we investigate the gap equation solutions under the change of the size of compactified coordinates, strength of magnetic field, temperature and chemical potential. The 't Hooft interaction contributions are also evaluated. The thermodynamic behavior is strongly affected by the combined effects of relevant variables. The findings suggest that the broken phase is disfavored due to both increasing of temperature and chemical potential, and the drop of the cubic volume of size $L$, whereas it is stimulated with the augmentation of magnetic field. In particular, the reduction of $L$ (remarkably at $L\approx 0.5 - 3 $~fm) engenders a reduction of the constituent masses for $u,d,s$-quarks through a crossover phase transition to the their corresponding current quark masses. On the other hand, the presence of a magnetic background generates greater values constituent quark masses, inducing smaller sizes and greater temperatures at which the constituent quark masses drop to the respective current ones.

hep-ph↗

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↗

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↗

arXiv2016

Casimir effect via a generalized Matsubara formalism

We investigate the Casimir effect in the context of a nontrivial topology by means of a generalized Matsubara formalism. This is performed in the context of a scalar field in $D$ Euclidean spatial dimensions with $d$ compactified dimensions. The procedure gives us the advantage of considering simultaneously spatial constraints and thermal effects. In this sense, the Casimir pressure in a heated system between two infinite planes is obtained and the results are compared with those found in the literature.

quant-ph↗

arXiv2013

Magnetic effects on spontaneous symmetry breaking/restoration in a toroidal topology

We study temperature and finite-size effects on the spontaneous symmetry breaking/restoration for a scalar field model under the influence of an external magnetic field, at finite chemical potential. We use the 2PI formalism and consider the large-$N$ limit. We find that there is a minimal size of the system to sustain the broken phase, which diminishes as the applied field increases but is independent of the chemical potential. We analyze the critical curves and show that the magnetic field enhances the broken-phase regions, while increasing the chemical potential leads to a diminishement of the critical temperature.

hep-th↗

arXiv2013

Finite-size, magnetic and chemical-potential effects on first-order phase transitions

We perform a study about effects of an applied magnetic field and a finite chemical potential on the size-dependent phase structure of a first-order transition. These effects are introduced by using methods of quantum fields defined on toroidal spaces, and we study in particular the case of two compactified dimensions, imaginary time and a spatial one (a heated film). It is found that for any value of the applied field, there is a minimal size of the system, independent of the chemical potential, below which the transition disappears.

cond-mat.stat-mech↗

arXiv2012

Spontaneous symmetry restoration in a field theory at finite chemical potential in a toroidal topology

We consider the massive vector $N$-component $(λφ^{4})_{D}$ theory defined on a Euclidean space with a toroidal topology. Using recently developed methods to perform a compactification of a $d$-dimensional subspace at finite chemical potential, we treat jointly the effects of temperature and spatial boundaries, setting forth grounds for an analysis of spontaneous symmetry restoration driven by temperature and spatial boundaries as a function of the chemical potential. We restrict ourselves to d=2, which corresponds to the heated system confined between two parallel planes (separation $L$) in dimensions D=3 and D=4. We present results, in the large-$N$ limit, which exhibit how finite size and chemical potential affect spontaneous symmetry restoration.

hep-th↗

arXiv2011

Time evolution of entangled biatomic states in a cavity

We study the time evolution of entangled states of a pair of identical atoms, considered in the harmonic approximation, coupled to an environment represented by an infinite set of free oscillators, with the whole system confined within a spherical cavity of radius $R$. Taking the center-of-mass and the relative-position coordinates, and using the dressed-state approach, we present the time evolution of some quantities measuring the entanglement, for both limits of a very large and a small cavity; the chosen examples are simple and illustrate these very distinct behaviors.

quant-ph↗

arXiv2011

A note on the infrared behavior of the compactified Ginzburg--Landau model in a magnetic field

We consider the Euclidean large-$N$ Ginzburg--Landau model in $D$ dimensions, $d$ ($d\leq D$) of them being compactified. For D=3, the system can be supposed to describe, in the cases of d=1, d=2, and d=3, respectively, a superconducting material in the form of a film, of an infinitely long wire having a rectangular cross-section and of a brick-shaped grain. We investigate the fixed-point structure of the model, in the presence of an external magnetic field. An infrared-stable fixed points is found, which is independent of the number of compactified dimensions. This generalizes previous work for type-II superconducting films

hep-th↗

arXiv2011

Infrared behavior and fixed-point structure in the compactified Ginzburg--Landau model

We consider the Euclidean $N$-component Ginzburg--Landau model in $D$ dimensions, of which $d$ ($d\leq D$) of them are compactified. As usual, temperature is introduced through the mass term in the Hamiltonian. This model can be interpreted as describing a system in a region of the $D$-dimensional space, limited by $d$ pairs of parallel planes, orthogonal to the coordinates axis $x_1,\,x_2,\,...,\,x_d$. The planes in each pair are separated by distances $L_1,\;L_2,\; ...,\,L_d$. For $D=3$, from a physical point of view, the system can be supposed to describe, in the cases of $d=1$, $d=2$, and $d=3$, respectively, a superconducting material in the form of a film, of an infinitely long wire having a retangular cross-section and of a brick-shaped grain. We investigate in the large-$N$ limit the fixed-point structure of the model, in the absence or presence of an external magnetic field. An infrared-stable fixed point is found, whether of not an external magnetic field is applied, but for different ranges of values of the space dimension $ D$.

math-ph↗

arXiv2010

Addendum: Behavior of a bipartite system in a cavity

This note is an Addendum to our previous article [Phys. Rev. A \textbf{81}, 053820 (2010)]. We show that under the assumption of a Bose-Einstein distribution for the thermal reservoir, zero-temperature properties of the entangled states considered there are not changed by heating, for temperatures up to the order of room temperatures. In this case, the system is dissipative in free space and presents stability for a small cavity, both for T=0 and for finite temperature.

quant-ph↗

arXiv2010

Behavior of a bipartite system in a cavity

We study the time evolution of a superposition of product states of two dressed atoms in a spherical cavity in the situations of an arbitrarily large cavity (free space) and of a small one. In the large-cavity case, the system dissipates, whereas, for the small cavity, the system evolves in an oscillating way and never completely decays. We verify that the von Neumann entropy for such a system does not depend on time, nor on the size of the cavity

quant-ph↗

arXiv2009

Time evolution of a two-atom dressed entangled state in a cavity

We study the time evolution of superposition of product states of two dressed atoms in a spherical cavity in the extreme situations of an arbitrarily large cavity (free space) and of a small one. In the large-cavity case, the system dissipates, whereas, for the small finite cavity, the system evolves in an oscillating way and never completely decays. We also compute the von Neumann entropy for such a system, a measurement of the degree of entanglement of the two atoms, as the superposed state evolves in time. We find that this entropy does not depend on time, nor on the size of the cavity.

quant-ph↗

arXiv2008

Time evolution of a superposition of dressed oscillator states in a cavity

Using the formalism of {\it renormalized} coordinates and \textit{dressed} states introduced in previous publications, we perform a nonperturbative study of the time evolution of a superposition of two states, the ground state and the first excited level of a harmonic oscillator, the system being confined in a perfectly reflecting cavity of radius $R$. For $R\to\infty$, we find dissipation with dominance of the interference terms of the density matrix, in both weak- and strong-coupling regimes. For small values of $R$ all elements of the density matrix present an oscillatory behavior as times goes on and the system is not dissipative. In both cases, we obtain improved theoretical results with respect to those coming from perturbation theory.

quant-ph↗

arXiv2007

Critical temperature for first-order phase transitions in confined systems

We consider the Euclidean $D$-dimensional $-λ|ϕ|^4+η|ϕ|^6$ ($λ,η>0 $) model with $d$ ($d\leq D$) compactified dimensions. Introducing temperature by means of the Ginzburg--Landau prescription in the mass term of the Hamiltonian, this model can be interpreted as describing a first-order phase transition for a system in a region of the $D$-dimensional space, limited by $d$ pairs of parallel planes, orthogonal to the coordinates axis $x_1, x_2, ..., x_d$. The planes in each pair are separated by distances $L_1, L_2, ..., L_d$. We obtain an expression for the transition temperature as a function of the size of the system, $% T_c(\{L_i\})$, $i=1, 2, ..., d$. For D=3 we particularize this formula, taking $L_1=L_2=... =L_d=L$ for the physically interesting cases $d=1$ (a film), $d=2$ (an infinitely long wire having a square cross-section), and for $d=3$ (a cube). For completeness, the corresponding formulas for second-order transitions are also presented. Comparison with experimental data for superconducting films and wires shows qualitative agreement with our theoretical expressions

cond-mat.soft↗