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J. M. C. Malbouisson

Publications and source records attributed to J. M. C. Malbouisson.

At least 19 recordsLinked to original sources
arXiv2014

Quantum field theory on toroidal topology: algebraic structure and applications

The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particles physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matted physics.

hep-th↗
arXiv2014

Realization of the Noncommutative Seiberg-Witten Gauge Theory by Fields in Phase Space

Representations of the Poincaré symmetry are studied by using a Hilbert space with a phase space content. The states are described by wave functions ( quasi amplitudes of probability) associated with Wigner functions (quasi probability density). The gauge symmetry analysis provides a realization of the Seiberg-Witten gauge theory for noncommutative fields.

hep-th↗
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

Deformation method for generalized Abelian Higgs-Chern-Simons models

We present an extension of the deformation method applied to self-dual solutions of generalized Abelian Higgs-Chern-Simons models. Starting from a model defined by a potential $V(| ϕ|)$ and a non-canonical kinetic term $ω(| ϕ|) | D_μϕ|^2$ whose analytical domain wall solutions are known, we show that this method allows to obtain an uncountable number of new analytical solutions of new models defined by other functions $\widetilde{V}$ and $\widetildeω$. We present some examples of deformation functions leading to new families of models and their associated analytic solutions.

hep-th↗
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↗
arXiv2012

Phase transition in the massive Gross-Neveu model in toroidal topologies

We use methods of quantum field theory in toroidal topologies to study the $N$-component $D$-dimensional massive Gross-Neveu model, at zero and finite temperature, with compactified spatial coordinates. We discuss the behavior of the large-$N$ coupling constant ($g$), investigating its dependence on the compactification length ($L$) and the temperature ($T$). For all values of the fixed coupling constant ($λ$), we find an asymptotic-freedom type of behavior, with $g\to 0$ as $L\to 0$ and/or $T\to \infty$. At T=0, and for $λ\geq λ_{c}^{(D)}$ (the strong coupling regime), we show that, starting in the region of asymptotic freedom and increasing $L$, a divergence of $g$ appears at a finite value of $L$, signaling the existence of a phase transition with the system getting spatially confined. Such a spatial confinement is destroyed by raising the temperature. The confining length, $L_{c}^{(D)}$, and the deconfining temperature, $T_{d}^{(D)}$, are determined as functions of $λ$ and the mass ($m$) of the fermions, in the case of $D=2,3,4$. Taking $m$ as the constituent quark mass ($\approx 350\: MeV$), the results obtained are of the same order of magnitude as the diameter ($\approx 1.7 fm$) and the estimated deconfining temperature ($\approx 200\: MeV$) of hadrons.

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

Multi-sine-Gordon Models

This work deals with the presence of defect structures in generalized sine-Gordon models. The models are described by periodic potentials, with substructure having one, two, three or more distinct topological sectors, with multiplicity one, two, three or more, respectively. The investigation takes advantage of the deformation procedure introduced in previous work, which is used to introduce the new models, and to study all the defect structures they may comprise.

hep-th↗
arXiv2011

Quantum fields in toroidal topology

The standard representation of c*-algebra is used to describe fields in compactified space-time dimensions characterized by topologies of the type $ Γ_{D}^{d}=(\mathbb{S}^{1})^{d}\times \mathbb{M}^{D-d}$. The modular operator is generalized to introduce representations of isometry groups. The Poincaré symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space-time, that follows as a generalization of the Fourier-integral representation of the propagator at finite temperature. An important result is that the $2\times2$ representation of the real time formalism is not needed. The end result on calculating observables is described as a condensate in the ground state. We analyze initially the free Klein-Gordon and Dirac fields, and then formulate non-abelian gauge theories in $Γ_{D}^{d}$. Using the S-matrix, the decay of particles is calculated in order to show the effect of the compactification.

hep-th↗
arXiv2011

Finite-size effects on the phase diagram of difermion condensates in two-dimensional four-fermion interaction models

We investigate finite-size effects on the phase structure of chiral and difermion condensates at finite temperature and density in the framework of the two-dimensional large-$N$ Nambu-Jona-Lasinio model. We take into account size-dependent effects by making use of $zeta$-function and compactification methods. The thermodynamic potential and the gap equations for the chiral and difermion condensed phases are then derived in the mean-field approximation. Size-dependent critical lines separating the different phases are obtained considering anti-periodic boundary conditions for the spatial coordinate.

hep-th↗
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

Phase transition in the 3-D massive Gross-Neveu model

We consider the 3-dimensional massive Gross-Neveu model at finite temperature as an effective theory for strong interactions. Using the Matsubara imaginary time formalism, we derive a closed form for the renormalized $T$-dependent four-point function. This gives a singularity, suggesting a phase transition. Considering the free energy we obtain the $T$-dependent mass, which goes to zero for some temperature. These results lead us to the conclusion that there is a second-order phase transition.

hep-th↗
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↗
arXiv2010

Thermal Effects on the Stability of Excited Atoms in Cavities

An atom, coupled linearly to an environment, is considered in a harmonic approximation in thermal equilibrium inside a cavity. The environment is modeled by an infinite set of harmonic oscillators. We employ the notion of dressed states to investigate the time evolution of the atom initially in the first excited level. In a very large cavity (free space) for a long elapsed time, the atom decays and the value of its occupation number is the physically expected one at a given temperature. For a small cavity the excited atom never completely decays and the stability rate depends on temperature.

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↗
arXiv2009

Finite-size effects on the chiral phase diagram of four-fermion models in four dimensions

We study the size dependence of the dynamical symmetry breaking in the four-dimensional Nambu-Jona-Lasinio model. We show that the presence of boundaries reduces the chiral breaking region, and this effect is strengthened for a larger number of compactified dimensions. A critical value for the length of the compactified dimensions exists, below which the dynamical symmetry breaking is not possible. Considering finite temperature and chemical potential, the chiral phase structure for the system with compactified dimensions is obtained. A gradual decreasing of the chiral breaking region with increasing of chemical potential is found. Also, at fixed chemical potential, the decreasing of the size of the system changes the order of the chiral phase transition.

hep-th↗
arXiv2009

Dimensional renormalizability in compactified spaces

We first briefly review some aspects of the techniques of dealing with ultraviolet divergences in Feynman amplitudes in an Euclidian $D$-dimensional space-time. Next we consider compactification of a $d$-dimensional ($d\leq D$) subspace. This includes effects of temperature and of compactification of $d-1$ spatial coordinates. Then we show how dimensional renormalization can be implemented for a field theory defined on this Euclidian space-time with a compactified subspace.

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