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A. E. Santana

Publications and source records attributed to A. E. Santana.

At least 37 records · Page 2Linked to original sources
arXiv2013

Dynamics and physical interpretation of quasi-stationary states in systems with long-range interactions

Although the Vlasov equation is used as a good approximation for a sufficiently large $N$, Braun and Hepp have showed that the time evolution of the one particle distribution function of a $N$ particle classical Hamiltonian system with long range interactions satisfies the Vlasov equation in the limit of infinite $N$. Here we rederive this result using a different approach allowing a discussion of the role of inter-particle correlations on the system dynamics. Otherwise for finite N collisional corrections must be introduced. This has allowed the a quite comprehensive study of the Quasi Stationary States (QSS) but many aspects of the physical interpretations of these states remain unclear. In this paper a proper definition of timescale for long time evolution is discussed and several numerical results are presented, for different values of $N$. Previous reports indicates that the lifetimes of the QSS scale as $N^{1.7}$ or even the system properties scales with $\exp(N)$. However, preliminary results presented here shows indicates that time scale goes as $N^2$ for a different type of initial condition. We also discuss how the form of the inter-particle potential determines the convergence of the $N$-particle dynamics to the Vlasov equation. The results are obtained in the context of following models: the Hamiltonian Mean Field, the Self Gravitating Ring Model, and a 2-D Systems of Gravitating Particles. We have also provided information of the validity of the Vlasov equation for finite $N$, i. e.\ how the dynamics converges to the mean-field (Vlasov) description as $N$ increases and how inter-particle correlations arise.

cond-mat.stat-mech↗
arXiv2013

The Noncommutative Harmonic Oscillator based in Simplectic Representation of Galilei Group

In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schrödinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using the group theory approach as a guide a physical consistent theory in phase space is constructed. The state is described by a quasi-probability amplitude that is in association with the Wigner function. The 3D harmonic oscillator and the noncommutative oscillator are studied in phase space as an application, and the Wigner function associated to both cases are determined.

math-ph↗
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

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

Teleparallel formalism of galilean gravity

A pseudo-Riemannian manifold is introduced, with light-cone coordinates in (4+1) dimensional space-time, to describe a Galilei covariant gravity. The notion of 5-bein and torsion are developed and a galilean version of teleparallelism is constructed in this manifold. The formalism is applied to two spherically symmetric configurations. The first one is an ansatz which is inferred by following the Schwarzschild solution in general relativity. The second one is a solution of galilean covariant equations. In addition, this Galilei teleparallel approach provides a prescription to couple the 5-bein field to the galilean covariant Dirac field.

gr-qc↗
arXiv2010

Casimir Effect at finite temperature for the Kalb-Ramond field

We use the thermofield dynamics (TFD) formalism to obtain the energy-momentum tensor for the Kalb-Ramond (KR) field in a topology $% S^{1}\times S^{1}\times R^{2}$. The compactification is carried out by a generalized TFD-Bogoliubov transformation that is used to define a renormalized energy-momentum tensor. The expressions for the Casimir energy and pressure at finite temperature are then derived. A comparative analysis with the electromagnetic case is developed, and the results may be important for applications, as in cuprate superconductivity, for instance.

hep-th↗
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

Non-linear Liouville and Shrödinger equations in phase space

Unitary representations of the Galilei group are studied in phase space, in order to describe classical and quantum systems. Conditions to write in general form the generator of time translation and Lagrangians in phase space are then established. In the classical case, Galilean invariance provides conditions for writing the Liouville operator and Lagrangian for non-linear systems. We analyze, as an example, a generalized kinetic equation where the collision term is local and non-linear. The quantum counter-part of such unitary representations are developed by using the Moyal (or star) product. Then a non-linear Schrödinger equation in phase space is derived and analyzed. In this case, an association with the Wigner formalism is established, which provides a physical interpretation for the formalism.

hep-th↗
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

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.

hep-th↗
arXiv2009

Galilean Covariance and the Gravitational Field

The paper is concerned with the development of a gravitational field theory having locally a covariant version of the Galilei group. We show that this Galilean gravity can be used to study the advance of perihelion of a planet, following in parallel with the result of the (relativistic) theory of general relativity in the post-Newtonian approximation.

gr-qc↗
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↗
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↗
arXiv2006

Noncommutative Geometry and Symplectic Field Theory

In this work we study representations of the Poincare group defined over symplectic manifolds, deriving the Klein-Gordon and the Dirac equation in phase space. The formalism is associated with relativistic Wigner functions; the Noether theorem is derived in phase space and an interacting field, including a gauge field, approach is discussed.

hep-th↗
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↗