arXiv subjects
Publications and source records attributed to F. C. Santos.
A beautiful theorem due to J. L. F. Bertrand concerning the laws of attraction that admit bounded closed orbits for arbitrarily chosen initial conditions is translated from French into English.
Making use of the quantum correlators associated with the Maxwell field vacuum distorted by the presence of plane parallel material surfaces we derive the Casimir-Polder interaction in the presence of plane parallel conducting walls and in the presence of a conducting wall and a magnetically permeable one.
We show that in order to account for the repulsive Casimir effect in the parallel plate geometry in terms of the quantum version of the Lorentz force, virtual surface densities of magnetic charges and currents must be introduced. The quantum version of the Lorentz force expressed in terms of the correlators of the electric and magnetic fields for planar geometries yields then correctly the Casimir pressure.
We investigate the influence of a uniform magnetic field on the zero-point energy of charged fields of two types, namely, a massive charged scalar field under Dirichlet boundary conditions and a massive fermion field under MIT boundary conditions. For the first, exact results are obtained, in terms of exponentially convergent functions, and for the second, the limits for small and for large mass are analytically obtained too. Coincidence with previously known, partial result serves as a check of the procedure. For the general case in the second situation --a rather involved one-- a precise numerical analysis is performed.
We evaluate the fermionic Casimir effect associated with a massive fermion confined within a planar (d+1) dimensional slab-bag, on which MIT bag model boundary conditions of standard type, along a single spatial direction, are imposed. A simple and effective method for adding up the zero-point energy eigenvalues, corresponding to a quantum field under the influence of arbitrary boundary conditions, imposed on the field on flat surfaces perpendicular to a chosen spatial direction, is proposed. Using this procedure, an analytic result is obtained, from which small and large fermion mass limits, valid for an arbitrary number of dimensions, are derived. They match some known results in particular cases. The method can be easily extended to other configurations.
We introduce a general, simple and effective method of evaluating the zero point energy of a quantum field under the influence of arbitrary boundary conditions imposed on the field on flat surfaces perpendicular to a chosen spatial direction. As an example we apply the method to the Casimir effect associated with a massive fermion field on which MIT bag model type of boundary conditions are imposed.
It is well known that for the case of two neutral but electrically polarizable atoms the consideration or not of retardation effects on the dispersive van der Waals force between them leads essentially to different power laws for the forces; while the retarded force is proportional to $1/r^8$, where $r$ is the distance between the atoms, the non-retarded force is proportional to $1/r^7$. Here we consider the (repulsive) dispersive force between an electrically polarizable atom and a magnetically polarizable one and show that, in contrast to the previous case, a quite unexpected result appears, namely: while the retarded force is still proportional to $1/r^8$, the non-retarded force is proportional to $1/r^5$. We employ a semiclassical method based on the fluctuating dipole model for both atoms.
Using perturbative QED we show that, while the retarded dispersive force between an electrically polarizable atom and a magnetically polarizable one is proportional to $1/r^{8}$, where $r$ is the distance between the atoms, the non-retarded force is proportiaonal to $1/r^{5}$. This is a rather surprising result that should be compared with the dispersive van der Waals force between two electrically polarizable atoms, where the retarded force is also proportional to $1/r^{8}$, but the non-retarded force is proportional to $1/r^{7}$.
We evaluate the Casimir vacuum energy at finite temperature associated with the Maxwell field confined by a perfectly conducting rectangular cavity and show that an extended version of the temperature inversion symmetry is present in this system.
A method of obtaining vector constants of motion for time-independent as well as time-dependent central fields is discussed. Some well-established results are rederived in this alternative way and new ones obtained.
We apply the generalized zeta function method to compute the Casimir energy and pressure between an unusual pair of parallel plates at finite temperature, namely: a perfectly conducting plate and an infinitely permeable one. The high and low temperature limits of these quantities are discussed; relationships between high and low temperature limits are estabkished by means of a modified version of the temperature inversion symmetry.
We compute the Casimir energy between an unusual pair of parallel plates at finite temperature, namely, a perfectely conducting plate ($ε\to\infty$) and an infinitely permeable one ($μ\to\infty$) by applying the generalized zeta function method. We also compute the Casimir pressure and discuss the high and the low temperature limits.