arXiv subjects

A. P. C. Malbouisson

Publications and source records attributed to A. P. C. Malbouisson.

72 records · Page 4Linked to original sources

arXiv2002

Storage of energy in confined quantum systems

Using the non-perturbative method of {\it dressed} states introduced in previous publications [N.P.Andion, A.P.C. Malbouisson and A. Mattos Neto, J.Phys.{\bf A34}, 3735, (2001); G. Flores-Hidalgo, A.P.C. Malbouisson, Y.W. Milla, Phys. Rev. A, {\bf 65}, 063314 (2002)], we study the evolution of a confined quantum mechanical system embedded in a {\it ohmic} environment. Our approach furnishes a theoretical mechanism to control inhibition of the decay of excited quantum systems in cavities, in both weak and strong coupling regimes.

quant-ph↗

arXiv2002

Superconducting transition temperature in thin films

By considering the Ginzburg-Landau model, compactified in one of the spatial dimensions, and using a modified Matsubara formalism, we determine the dependence of the superconducting transition temperature (T_c) of a film as a function of its thickness (L). We show that T_c is a decreasing linear function of L^{-1}, as has been found experimentally. The critical thickness for the suppression of superconductivity is expressed in terms of the Ginzburg-Landau parameters.

cond-mat.soft↗

arXiv2002

Stability of excited atoms in small cavities

We consider a system consisting of an atom in the approximation of a harmonic oscillator of frequency $\barω$, coupled to the scalar potential inside a spherical reflecting cavity of radius R. We use {\it dressed} states introduced in a previous publication [Andion, Malbouisson and Matos Neto, J. Phys. A34, 3735 (2001)], which allow a non-perturbative unified description of the atom radiation process, in both cases, of a finite or an arbitrarily large cavity. We perform a study of the energy distribution in a small cavity, with the initial condition that the atom is in the first excited state and we conclude for the quasi-stability of the excited atom. For instance, for a frequency $\barω$ of the order $\barω\sim 4.00\times 10^{14}/s$ (in the visible red), starting from the initial condition that the atom is in the first excited level, we find that for a cavity with diameter $2R\sim 1.0\times 10^{-6}m$, the probability that the atom be at any time still in the first excited level, will be of the order of 97%. For a typical microwave frequency $\barω\sim 2,00\times 10^{10}/s$ we find stability in the first excited state also of the order of 97% for a cavity radius $R\sim 1.4\times 10^{-2}m$.

physics.atom-ph↗

arXiv2002

Spontaneous Symmetry Breaking in Compactified $λϕ^4$ Theory

We consider the massive vector $N$-component $(λϕ^{4})_{D}$ theory in Euclidian space and, using an extended Matsubara formalism we perform a compactification on a $d$-dimensional subspace, $d\leq D$. This allows us to treat jointly the effect of temperature and spatial confinement in the effective potential of the model, setting forth grounds for an analysis of phase transitions driven by temperature and spatial boundary. For $d=2$, which corresponds to the heated system confined between two parallel planes (separation $L$), we obtain, in the large $N$ limit at one-loop order, formulas for temperature- and boundary-dependent mass and coupling constant. The equation for the critical curve in the $β\times L$ plane is also derived.

hep-th↗

arXiv2002

Dressed States Approach to Quantum Systems

Using the non-perturbative method of {\it dressed} states previously introduced in JPhysA, we study effects of the environment on a quantum mechanical system, in the case the environment is modeled by an ensemble of non interacting harmonic oscillators. This method allows to separate the whole system into the {\it dressed} mechanical system and the {\it dressed} environment, in terms of which an exact, non-perturbative approach is possible. When applied to the Brownian motion, we give explicit non-perturbative formulas for the classical path of the particle in the weak and strong coupling regimes. When applied to study atomic behaviours in cavities, the method accounts very precisely for experimentally observed inhibition of atomic decay in small cavities PhysLA, physics0111042.

quant-ph↗

arXiv2001

Boundary dependence of the coupling constant and the mass in the vector N-component $(λϕ^{4})_{D}$ theory

Using the Matsubara formalism, we consider the massive $(λϕ^{4})_{D}$ vector $N$-component model in the large $N$ limit, the system being confined between two infinite paralell planes. We investigate the behavior of the coupling constant as a function of the separation $L$ between the planes. For the Wick-ordered model in $D = 3$ we are able to give an exact formula to the $L$-dependence of the coupling constant. For the non-Wick-ordered model we indicate how expressions for the coupling constant and the mass can be obtained for arbitrary dimension $D$ in the small-$L$ regime. Closed exact formulas for the $L$-dependent renormalized coupling constant and mass are obtained in $D = 3$ and their behaviors as functions of $L$ are displayed. We are also able to obtainn in generic dimension $D$, an equation for the critical value of $L$ corresponding to a second order phase transition in terms of the Riemann $zeta$-function. In $D = 3$ a renormalization is done and an explicit formula for the critical $L$ is given.

cond-mat.stat-mech↗

arXiv2001

Fermionic determinant with a linear domain wall in 2+1 dimensions

We consider a Dirac field in 2+1 Euclidean dimensions, in the presence of a linear domain wall defect in its mass, and a constant electromagnetic field. We evaluate the exact fermionic determinant for the situation where the defect is assumed to be rectilinear, static, and the gauge field is minimally coupled to the fermions. We discuss the dependence of the result on the (unique) independent geometrical parameter of this system, namely, the relative orientation of the wall and the direction of the external field. We apply the result for the determinant to the evaluation of the vacuum energy.

hep-th↗

arXiv2000

An Exact Approach to the Oscillator Radiation Process in an Arbitrarily Large Cavity

Starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius $R$, we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the confined solution. From a mathematical point of view we show that this way of facing the problem is not equivalent to consider the system {\it a} {\it priori} embedded in infinite space. In particular, the matrix elements of the transformation turning the system to principal axis, do not tend to distributions in the limit of an arbitrarily large sphere as it should be the case if the two procedures were mathematically equivalent. Also, we introduce "dressed" coordinates which allow an exact description of the oscillator radiation process for any value of the coupling, strong or weak. In the case of weak coupling, we recover from our exact expressions the well known decay formulas from perturbation theory.

physics.atom-ph↗

arXiv1999

A Non-perturbative Solution of the Zero-Dimensional lambda phi^4 Field Theory

We have done a study of the zero-dimensional $λϕ^{4}$ model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for $Re(λ)>0$. Secondly, an analytic continuation of the partition function for $Re(λ)<0$ is performed, and we obtain an expression defined in the complex coupling constant plane $λ$, for $|arg λ|<π$. Consequently, the partition function understood as an analytic continuation is defined for all values of $λ$, except for a branch cut along the real negative $λ$ axis. We also evaluate the partition function on perturbative grounds, using the Borel summation technique and we found that in the common domain of validity for $Re(λ)>0$, it coincides precisely with the exact expression.

hep-th↗

arXiv1999

Critical properties of the topological Ginzburg-Landau model

We consider a Ginzburg-Landau model for superconductivity with a Chern-Simons term added. The flow diagram contains two charged fixed points corresponding to the tricritical and infrared stable fixed points. The topological coupling controls the fixed point structure and eventually the region of first order transitions disappears. We compute the critical exponents as a function of the topological coupling. We obtain that the value of the $ν$ exponent does not vary very much from the XY value, $ν_{XY}=0.67$. This shows that the Chern-Simons term does not affect considerably the XY scaling of superconductors. We discuss briefly the possible phenomenological applications of this model.

cond-mat.supr-con↗

arXiv1998

The thermal coupling constant and the gap equation in the $λϕ^{4}_{D}$ model

By the concurrent use of two different resummation methods, the composite operator formalism and the Dyson-Schwinger equation, we re-examinate the behavior at finite temperature of the O(N)-symmetric $λϕ^{4}$ model in a generic D-dimensional Euclidean space. In the cases D=3 and D=4, an analysis of the thermal behavior of the renormalized squared mass and coupling constant are done for all temperatures. It results that the thermal renormalized squared mass is positive and increases monotonically with the temperature. The behavior of the thermal coupling constant is quite different in odd or even dimensional space. In D=3, the thermal coupling constant decreases up to a minimum value diferent from zero and then grows up monotonically as the temperature increases. In the case D=4, it is found that the thermal renormalized coupling constant tends in the high temperature limit to a constant asymptotic value. Also for general D-dimensional Euclidean space, we are able to obtain a formula for the critical temperature of the second order phase transition. This formula agrees with previous known values at D=3 and D=4.

hep-th↗

arXiv1997

A note on the phase transition in a topologically massive Ginzburg-Landau theory

We consider the phase transition in a model which consists of a Ginzburg-Landau free energy for superconductors including a Chern-Simons term. The mean field theory of Halperin, Lubensky and Ma [Phys. Rev. Lett. 32, 292 (1974)] is applied for this model. It is found that the topological mass, $θ$, drives the system into different regimes of phase transition. For instance, there is a $θ_{c}$ such that for $θ<θ_{c}$ a fluctuation induced first order phase transition occurs. On the other hand, for $θ>θ_{c}$ only the second order phase transition exists. The 1-loop renormalization group analysis gives further insight to this picture. The fixed point structure exhibits tricritical and second order fixed points.

cond-mat.supr-con↗

arXiv1997

Dimensional reduction of the chiral-continous Gross-Neveu model

We study the finite-temperature phase transition of the generalized Gross-Neveu model with continous chiral symmetry in $2 < d \leq 4$ euclidean dimensions. The critical exponents are computed to the leading order in the $1/N$ expansion at both zero and finite temperatures. A dimensionally reduced theory is obtained after the introduction of thermal counterterms necessary to cancel thermal divergences that arise in the limit of high temperature. Although at zero temperature we have an infinitely and continously degenerate vacuum state, we show that at finite temperature this degeneracy is discrete and, depending on the values of the bare parameters, we may have either total or partial restoration of symmetry. Finally we determine the universality class of the reduced theory by a simple analysis of the infrared structure of thermodynamic quantities computed using the reduced action as starting point.

hep-th↗

arXiv1997

One-loop dimensional reduction of the linear sigma model

We perform the dimensional reduction of the linear $σ$ model at one-loop level. The effective potential of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group equation which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum unstability of the model for large N.

hep-th↗

arXiv1996

Analytic regularization of the Yukawa Model at Finite Temperature

We analyse the one-loop fermionic contribution for the scalar effective potential in the temperature dependent Yukawa model. In order to regularize the model a mix between dimensional and analytic regularization procedures is used. We find a general expression for the fermionic contribution in arbitrary spacetime dimension. It is found that in D=3 this contribution is finite.

hep-th↗

arXiv1996

Critical Fluctuations in Topologically Massive Superconductors

We consider a topologically massive Ginzburg-Landau model of superconductivity. In the context of a mean field calculation, we show that there is an increase in the critical temperature driven by the topological term. It is shown that this effect persists even if we take into account the critical fluctuations. The renormalization group analysis gives further insight on this behavior. The fixed point structure is such that the critical exponents tend to their mean field values for very large values of the topological mass. In this sense, the topological term stabilizes the critical fluctuations of the order parameter.

cond-mat↗

arXiv1995

On the finite temperature $λφ^{4}$ and Gross-Neveu models. Is there a first order phase transition in $(λφ^{4})_{D=3}$?

We study the behavior of two diferent models at finite temperature in a $D$-dimensional spacetime. The first one is the $λφ^{4}$ model and the second one is the Gross-Neveu model. Using the one-loop approximation we show that in the $λφ^{4}$ model the thermal mass increase with the temperature while the thermal coupling constant decrese with the temperature. Using this facts we establish that in the $(λφ^{4})_{D=3}$ model there is a temperature $β^{-1}_{\star}$ above which the system can develop a first order phase transition, where the origin corresponds to a metastable vacuum. In the massless Gross-Neveu model, we demonstrate that for $D=3$ the thermal correction to the coupling constant is zero. For $D\neq 3$ our results are inconclusive. Pacs numbers: 11.10.Ef, 11.10.Gh

hep-th↗

arXiv1995

A non-perturbative approach to the Coleman- Weinberg mechanism in massless scalar QED

We rederive non-perturbatively the Coleman-Weinberg expression for the effective potential for massless scalar QED. Our result is not restricted to small values of the coupling constants. This shows that the Coleman- Weinberg result can be established beyond the range of validity of perturbation theory. Also, we derive it in a manifestly renormalization group invariant way. It is shown that with the derivation given no Landau ghost singularity arises. The finite temperature case is discussed. Pacs number: 11.10.Ef,11.10.Gh.

hep-th↗