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E. S. Moreira Jr

Publications and source records attributed to E. S. Moreira Jr.

13 recordsLinked to original sources
arXiv2024

Blackbody heat capacity at constant pressure

At first glance, the title of this work seems to be improper. And the reason is well known. Since blackbody pressure depends only on temperature, one cannot take the derivative of the thermodynamic quantities with respect to one of them, keeping the other constant. That is, the heat capacity at constant pressure, $C_{P}$, as well as, the coefficient of thermal expansion, $α$, and the isothermal compressibility, $κ_{T}$, are ill-defined quantities. This work will show that when the perfect conducting nature of the walls of a blackbody cavity is taken into account, $C_{P}$, $α$ and $κ_{T}$ are in fact well defined, and they are related by the usual thermodynamic relations, as expected. Two geometries will be considered, namely, a spherical shell and a cubic box. It will be shown that $C_{P}$, $α$ and $κ_{T}$ depend very much on the geometry of the cavity. Issues regarding thermodynamic stability will be addressed, revealing that they also depend on the cavity's geometry. It is argued that these findings may be amenable to experimental verification.

cond-mat.stat-mech↗
arXiv2023

Boundary effects on the thermal stability of a black hole at the centre of a conducting spherical shell

This paper reports calculations and analysis of the effects of a perfect conducting wall of a very large spherical shell on the stable thermodynamic equilibrium of a black hole sitting at the centre of the shell which is filled with Electromagnetic blackbody radiation. A parallel is drawn with the case where electromagnetic is replaced by scalar blackbody radiation with Dirichlet or Neumann boundary conditions on the wall. It is found that the value of the shell radius above which only blackbody radiation remains in stable thermodynamic equilibrium can be considerably affected by vacuum polarization due to the presence of the wall.

gr-qc↗
arXiv2023

Thermodynamics of a charged relativistic ideal Boltzmann gas

This paper presents a toy model of a charged relativistic classical gas in flat spacetime of an arbitrary number of dimensions equipped with some ``pair production'' mechanism. Working with the microcanonical ensemble, the charge is taken to be conserved in contrast with the total number of ``particles'' plus ``antiparticles'' which varies with temperature $T$. Thermodynamics of the classical gas is detailed studied in the nonrelativistic ($Mc^{2}\gg kT$) as well as in the ultrarelativistic ($Mc^{2}\ll kT$) regimes. It is shown that, although we are dealing with classical distributions, at the ultrarelativistic regime the behavior of the gas is Planckian. We also compare the thermodynamics of the toy model with that of quantum gases.

cond-mat.stat-mech↗
arXiv2020

Ambiguities in the local thermal behavior of the scalar radiation in one-dimensional boxes

This paper reports certain ambiguities in the calculation of the ensemble average $\left $ of the stress-energy-momentum tensor of an arbitrarily coupled massless scalar field in one-dimensional boxes in flat spacetime. The study addresses a box with periodic boundary condition (a circle) and boxes with reflecting edges (with Dirichlet's or Neumann's boundary conditions at the endpoints). The expressions for $\left $ are obtained from finite-temperature Green functions. In an appendix, in order to control divergences typical of two dimensions, these Green functions are calculated for related backgrounds with arbitrary number of dimensions and for scalar fields of arbitrary mass, and specialized in the text to two dimensions and for massless fields. The ambiguities arise due to the presence in $\left $ of double series that are not absolutely convergent. The order in which the two associated summations are evaluated matters, leading to two different thermodynamics for each type of box. In the case of a circle, it is shown that the ambiguity corresponds to the classic controversy in the literature whether or not zero mode contributions should be taken into account in computations of partition functions. In the case of boxes with reflecting edges, it results that one of the thermodynamics corresponds to a total energy (obtained by integrating the non homogeneous energy density over space) that does not depend on the curvature coupling parameter $ξ$ as expected; whereas the other thermodynamics curiously corresponds to a total energy that does depend on $ξ$. Thermodynamic requirements (such as local and global stability) and their restrictions to the values of $ξ$ are considered.

hep-th↗
arXiv2019

Thermodynamics of the scalar radiation in the presence of a reflecting plane wall

This paper investigates further how the presence of a single reflecting plane wall modifies the usual Planckian forms in the thermodynamics of the massless scalar radiation in $N$-dimensional Minkowski spacetime. This is done in a rather unconventional way by integrating the energy density over space to obtain the internal energy and from that the Helmholtz free energy. The reflecting wall is modelled by assuming the Dirichlet or the Neumann boundary conditions on the wall. It is found that when $N>2$ integration over space eliminates dependence on the curvature coupling parameter $ξ$. Unexpectedly though, when $N=2$, the internal energy and the corresponding thermodynamics turn out to be dependent on $ξ$. For instance, the correction to the two-dimensional Planckian heat capacity is $\mp ξk_{B}$ (minus for Dirichlet, plus for Neumann). Other aspects of this dependence on $ξ$ are also discussed. Results are confronted with those in the literature concerning related setups of reflecting walls (such as slabs) where conventional (i.e., global) approaches to obtain thermodynamics have been used.

hep-th↗
arXiv2015

Local thermal behaviour of a massive scalar field near a reflecting wall

The mean square fluctuation and the expectation value of the stress-energy-momentum tensor of a neutral massive scalar field at finite temperature are determined near an infinite plane Dirichlet wall, and also near an infinite plane Neumann wall. The flat background has an arbitrary number of dimensions and the field is arbitrarily coupled to the vanishing curvature. It is shown that, unlike vacuum contributions, thermal contributions are free from boundary divergences, and that the thermal behaviour of the scalar field near a Dirichlet wall differs considerably from that near a Neumann wall. Far from the wall the study reveals a local version of dimensional reduction, namely, corrections to familiar blackbody expressions are linear in the temperature, with the corresponding coefficients given only in terms of vacuum expectation values in a background with one less dimension. It is shown that such corrections are "classical" (i.e., not dependent on Planck's constant) only if the scalar field is massless. A natural conjecture that arises is that the "local dimensional reduction" is universal since it operates for massless and massive fields alike and regardless of the boundary conditions.

hep-th↗
arXiv2015

Hot scalar radiation setting bounds on the curvature coupling parameter

This paper addresses the interplay between vacuum and thermal local averages for massless scalar radiation near a plane wall of a large cavity where the Dirichlet boundary condition is assumed to hold. The main result is that stable thermodynamic equilibrium is possible only if the curvature coupling parameter is restricted to a certain range. In more than three spacetime dimensions such a range contains the conformal coupling, but it does not contain the minimal coupling. Since this same range for possible values of the curvature coupling parameter also applies to massive scalar radiation, it may be relevant in settings where arbitrarily coupled scalar fields are present.

gr-qc↗
arXiv2012

Gravitational spectral shift caused by Casimir stresses

The linearized Einstein field equations with the renormalized stress tensor of a massless quantum scalar field as source are solved in the 4-dimensional spacetime near an infinite plane boundary. The motion of particles and light is investigated disclosing a variety of effects. For instance, it is shown that light rays initially parallel to the boundary do not bend. On the other hand, under the same initial conditions, particles will be affected by the presence of the quantum field, being accelerated toward the plane boundary or departing from it depending on the value of the curvature coupling parameter ξ. It is suggested that ξ can be set by measuring the spectral deviation of a light ray travelling perpendicularly to the boundary.

hep-th↗
arXiv2009

Quantum and Classical Statistical Mechanics of a Class of non-Hermitian Hamiltonians

This paper investigates the thermodynamics of a large class of non-Hermitian, $PT$-symmetric oscillators, whose energy spectrum is entirely real. The spectrum is estimated by second-order WKB approximation, which turns out to be very accurate even for small quantum numbers, and used to generate the quantum partition function. Graphs showing the thermal behavior of the entropy and the specific heat, at all regimes of temperature, are given. To obtain the corresponding classical partition function it turns out to be necessary in general to integrate over a complex "phase space". For the wrong-sign quartic, whose equivalent Hermitian Hamiltonian is known exactly, it is demonstrated explicitly how this formulation arises, starting from the Hermitian case.

quant-ph↗
arXiv2001

Classical self-forces in a space with a dispiration

We derive the gravitational and electrostatic self-energies of a particle at rest in the background of a cosmic dispiration (topological defect), finding that the particle may experience potential steps, well potentials or potential barriers depending on the nature of the interaction and also on certain properties of the defect. The results may turn out to be useful in cosmology and condensed matter physics.

gr-qc↗
arXiv1999

Ambiguity in the evaluation of the effective action on the cone

An ambiguity in the computation of the one-loop effective action for fields living on a cone is illustrated. It is shown that the ambiguity arises due to the non-commutativity of the regularization of ultraviolet and (conical) boundary divergencies.

hep-th↗