arXiv subjects

J. M. C. Malbouisson

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

At least 37 records · Page 2Linked to original sources

arXiv2009

Renormalized coordinate approach to the thermalization process

We consider a particle in the harmonic approximation coupled linearly to an environment. modeled by an infinite set of harmonic oscillators. The system (particle--environment) is considered in a cavity at thermal equilibrium. We employ the recently introduced notion of renormalized coordinates to investigate the time evolution of the particle occupation number. For comparison we first present this study in bare coordinates. For a long ellapsed time, in both approaches, the occupation number of the particle becomes independent of its initial value. The value of ocupation number of the particle is the physically expected one at the given temperature. So we have a Markovian process, describing the particle thermalization with the environment. With renormalized coordinates no renormalization procedure is required, leading directly to a finite result.

quant-ph↗

arXiv2008

Thermalization process in bare and dressed coordinate approaches

We consider a particle in the approximation of a harmonic oscillator, coupled linearly to a field modeling an environment. The field is described by an infinite set of harmonic oscillators, and the system (particle--field) is considered in a cavity at thermal equilibrium. We employ the notions of bare and dressed coordinates to study the time evolution of the occupation number. With dressed coordinates no renormalization procedure is required, leading directly to a finite result. In particular, for a large time, the occupation number of the particle becomes independent of its initial value. So we have a Markovian process, describing the particle thermalization with the environment.

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

Classical behavior of deformed sine-Gordon models

In this work we deform the phi^4 model with distinct deformation functions, to propose a diversity of sine-Gordon-like models. We investigate the proposed models and we obtain all the topological solutions they engender. In particular, we introduce non-polynomial potentials which support some exotic two-kink solutions.

nlin.PS↗

arXiv2007

Maximum Entanglement in Squeezed Boson and Fermion States

A class of squeezed boson and fermion states is studied with particular emphasis on the nature of entanglement. We first investigate the case of bosons, considering two-mode squeezed states. Then we construct the fermion version to show that such states are maximum entangled, for both bosons and fermions. To achieve these results, we demonstrate some relations involving squeezed boson states. The generalization to the case of fermions is made by using Grassmann variables.

quant-ph↗

arXiv2007

Conditional displacement operator for traveling fields

We show that the conditional displacement operator $\hat{U}_{CD}=\exp [\hat{b}^{\dagger}\hat{b}(β\hat{a}^{\dagger}-β^{\ast}\hat{a})]$ acting upon an arbitrary state of traveling waves can be well approximated by the action of a Kerr medium placed between two beam splitters whose respective second ports are fed by highly excited coherent states. Applications to the generation of nonclassical states and measurement of Wigner function of arbitrary states are also considered.

quant-ph↗

arXiv2005

Critical behaviour of the compactified $λϕ^4$ theory

We investigate the critical behaviour of the $N$-component Euclidean $λϕ^4$ model at leading order in $\frac{1}{N}$-expansion. We consider it in three situations: confined between two parallel planes a distance $L$ apart from one another, confined to an infinitely long cylinder having a square cross-section of area $A$ and to a cubic box of volume $V$. Taking the mass term in the form $m_{0}^2=α(T - T_{0})$, we retrieve Ginzburg-Landau models which are supposed to describe samples of a material undergoing a phase transition, respectively in the form of a film, a wire and of a grain, whose bulk transition temperature ($T_{0}$) is known. We obtain equations for the critical temperature as functions of $L$ (film), $A$ (wire), $V$ (grain) and of $T_{0}$, and determine the limiting sizes sustaining the transition.

math-ph↗

arXiv2004

Thermofield Dynamics and Casimir Effect for Fermions

A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons (J. C. da Silva, A. Matos Neto, F. C. Khanna and A. E. Santana, Phys. Rev. A 66 (2002) 052101), and is based on the thermofield dynamics approach. We analyse the energy-momentum tensor for the Casimir effect of a free massless fermion field in a $d$-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a 3-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic boc changes sign and estimate its value when the edge of the cybe is of the order of confining lengths for baryons.

hep-th↗

arXiv2004

Boundary behaviour of the four-point function in the 3-dimensional Gross-Neveu model

We consider the $N$-components 3-dimensional massive Gross-Neveu model compactified in one spatial direction, the system being constrained to a slab of thickness $L$. We derive a closed formula for the renormalized $L$-dependent four-point function at vanishing external momenta in the large-N limit (the effective coupling constant), using bag-model boundary conditions. For values of the fixed coupling constant in absence of boundaries $λ\geq λ_c \simeq 19.16$, we obtain small-distance asymptotic freedom (for $L \to 0$) and a singularity for a length $L^{(c)}$ such that $2.07 m^{-1} < L^{(c)} \lesssim 2.82 m^{-1}$, $m$ being the fermionic mass. Taking for $m$ an average of the masses of the quarks composing the proton, we obtain a "confining" length $L^{(c)}_p$ which is comparable with an estimated proton diameter.

hep-ph↗

arXiv2004

New results for deformed defects

We extend a deformation prescription recently introduced and present some new soluble nonlinear problems for kinks and lumps. In particular, we show how to generate models which present the basic ingredients needed to give rise to dimension bubbles. Also, we show how to deform models which possess lumplike solutions, to get to new models that support kinklike solutions.

hep-th↗

arXiv2003

New soluble nonlinear models for scalar fields

We extend a deformation prescription recently introduced and present some new soluble nonlinear problems for kinks and lumps. In particular, we show how to generate models which present the basic ingredients needed to give rise to "dimension bubbles," having different macroscopic space dimensions on the interior and the exterior of the bubble surface. Also, we show how to deform a model possessing lumplike solutions, relevant to the discussion of tachyonic excitations, to get a new one having topological solutions.

hep-th↗

arXiv2003

Nonclassical degree of states of single and bipartite systems

We consider experimental routes to determine the nonclassical degree of states of a field mode. We adopt a distance-type criterium based on the Hilbert-Schmidt metric to quantify the nonclassicality. The concept of nonclassical degree is extended for states of bipartite systems, allowing us to discuss a possible connection between nonclassicality and entanglement measures.

quant-ph↗

arXiv2003

Confinement in the 3-dimensional Gross-Neveu model

We consider the $N$-components 3-dimensional massive Gross-Neveu model compactified in one spatial direction, the system being constrained to a slab of thickness $L$. We derive a closed formula for the effective renormalized $L$-dependent coupling constant in the large-N limit, using bag-model boundary conditions. For values of the fixed coupling constant in absence of boundaries $λ\geq λ_c \simeq 19.16$, we obtain ultra-violet asymptotic freedom (for $L \to 0$) and confinement for a length $L^{(c)}$ such that $2.07 m^{-1} < L^{(c)} \lesssim 2.82 m^{-1}$, $m$ being the fermionic mass. Taking for $m$ an average of the masses of the quarks composing the proton, we obtain a confining legth $L^{(c)}_p$ which is comparable with an estimated proton diameter.

hep-th↗

arXiv2003

Large-N transition temperature for superconducting films in a magnetic field

We consider the $N$-component Ginzburg-Landau model in the large $N$ limit, the system being embedded in an external constant magnetic field and confined between two parallel planes a distance $L$ apart from one another. On physical grounds, this corresponds to a material in the form of a film in the presence of an external magnetic field. Using techniques from dimensional and $zeta$-function regularization, modified by the external field and the confinement conditions, we investigate the behavior of the system as a function of the film thickness $L$. This behavior suggests the existence of a minimal critical thickness below which superconductivity is suppressed.

cond-mat.supr-con↗

arXiv2002

Deformed Defects

We introduce a method to obtain deformed defects starting from a given scalar field theory which possesses defect solutions. The procedure allows the construction of infinitely many new theories that support defect solutions, analytically expressed in terms of the defects of the original theory. The method is general, valid for both topological and non-topological defects, and we show how it extends to quantum mechanics, and how it works when the scalar field couples to fermions. We illustrate the general procedure with several examples, which support kink-like or lump-like defects.

hep-th↗

arXiv2002

On the measure of nonclassicality of field states

The degree of nonclassicality of states of a field mode is analysed considering both phase-space and distance-type measures of nonclassicality. By working out some general examples, it is shown explicitly that the phase-space measure is rather sensitive to superposition of states, with finite superpositions possessing maximum nonclassical depth (the highest degree of nonclassicality) irrespective to the nature of the component states. Mixed states are also discussed and examples with nonclassical depth varying between the minimum and the maximum allowed values are exhibited. For pure Gaussian states, it is demonstrated that distance-type measures based on the Hilbert-Schmidt metric are equivalent to the phase-space measure. Analyzing some examples, it is shown that distance-type measures are efficient to quantify the degree of nonclassicality of non-Gaussian pure states.

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

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↗