Probability Distributions of Random Electromagnetic Fields in the Presence of a Semi-Infinite Isotropic Medium

Using a TE/TM decomposition for an angular plane-wave spectrum of free random electromagnetic waves and matched boundary conditions, we derive the probability density function for the energy density of the vector electric field in the presence of a semi-infinite isotropic medium. The theoretical analysis is illustrated with calculations and results for good electric conductors and for a lossless dielectric half-space. The influence of the permittivity and conductivity on the intensity, random polarization, statistical distribution and standard deviation of the field is investigated, both for incident plus reflected fields and for refracted fields. External refraction is found to result in compression of the fluctuations of the random field.Comment: 23 pages, 11 figures, accepted for publication in Radio Scienc

Probability Distribution of the Quality Factor of a Mode-Stirred Reverberation Chamber

We derive a probability distribution, confidence intervals and statistics of the quality (Q) factor of an arbitrarily shaped mode-stirred reverberation chamber, based on ensemble distributions of the idealized random cavity field with assumed perfect stir efficiency. It is shown that Q exhibits a Fisher-Snedecor F-distribution whose degrees of freedom are governed by the number of simultaneously excited cavity modes per stir state. The most probable value of Q is between a fraction 2/9 and 1 of its mean value, and between a fraction 4/9 and 1 of its asymptotic (composite Q) value. The arithmetic mean value is found to always exceed the values of all other theoretical metrics for centrality of Q. For a rectangular cavity, we retrieve the known asymptotic Q in the limit of highly overmoded regime.Comment: accepted for publication in IEEE Trans. Electromagn. Compat., 201

Money demand and financial liberalization in Mexico: A cointegration approach

This paper examines the long run dynamics of Mexico’s money demand using Johansen’s cointegration approach with different specifications. The empirical evidence indicates that real balances, real income and the interest rate are cointegrated in all subperiods. The findings suggest that recent changes in economic policy through financial liberalization affected money demand functions; this due to the fact that income elasticity fell down during the transition through the subperiods, but simultaneously this did not affect the functional stability. The cointegrated coefficient on currency-money ratio (M0/M1) suggests that when the ratio falls, the demand for money falls too. Nevertheless, this last evidence is statistically weak. In addition, it was determined that alternative equations are not better than the conventional ones.Money demand, financial liberalization, cointegration, error correction mechanism, currency-money ratio, Mexico

Mexican Real Wages Before the Revolution: A Reappraisal

Seminal literature has documented broadly the living conditions of Mexican workers before the Revolution of 1910. Various authors argue that a continuous deterioration of real wages in the preceding years of the Mexican revolution contributed to the social unrest that lead to the armed conflict. Yet, most of the quantitative evidence has focused on aggregate estimates overlooking the regional wage dynamics. Through regional historical data, this article reevaluates quantitatively the patterns of Mexican regional real wages providing new estimates for the period 1877-c.1910. The analysis reveals that a divergent pattern between sectors and regions emerged during these years. However, the study also shows that in general, locally-adjusted regional real wages remained relatively stable throughout the period

Demanda de dinero y liberalizacion financiera en Mexico: Un enfoque de cointegracion

This paper examines the long run dynamics of Mexico’s money demand using Johansen’s cointegration approach with different specifications. The empirical evidence indicates that real balances, real income and the interest rate are cointegrated in all subperiods. The findings suggest that recent changes in economic policy through financial liberalization affected money demand functions; this due to the fact that income elasticity fell down during the transition through the subperiods, but simultaneously this did not affect the functional stability. The cointegrated coefficient on currency-money ratio (M0/M1) suggests that when the ratio falls, the demand for money falls too. Nevertheless, this last evidence is statistically weak. In addition, it was determined that alternative equations are not better than the conventional ones

Demanda de dinero y liberalizacion financiera en Mexico: Un enfoque de cointegracion

This paper examines the long run dynamics of Mexico’s money demand using Johansen’s cointegration approach with different specifications. The empirical evidence indicates that real balances, real income and the interest rate are cointegrated in all subperiods. The findings suggest that recent changes in economic policy through financial liberalization affected money demand functions; this due to the fact that income elasticity fell down during the transition through the subperiods, but simultaneously this did not affect the functional stability. The cointegrated coefficient on currency-money ratio (M0/M1) suggests that when the ratio falls, the demand for money falls too. Nevertheless, this last evidence is statistically weak. In addition, it was determined that alternative equations are not better than the conventional ones

Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion

We show that the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion enables the generation of entangled Hermite-Gaussian modes. We derive an analytical expression for the two-photon state in terms of these modes and show that there are restrictions on both the parity and order of the down-converted Hermite-Gaussian fields. Using these results, we show that the two-photon state is indeed entangled in Hermite-Gaussian modes. We propose experimental methods of creating maximally-entangled Bell states and non-maximally entangled pure states of first order Hermite-Gaussian modes.Comment: 9 pages, 4 figures. Corrections made as per referee comments, references updated. Submitted PR

Nonstationary random acoustic and electromagnetic fields as wave diffusion processes

We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as an ideal incoherent and statistically homogeneous isotropic random scalar or vector field, respectively. A physical model is constructed showing that the field dynamics can be characterized as a generalized diffusion process. The Langevin--It\^{o} and Fokker--Planck equations are derived and their associated statistics and distributions for the complex analytic field, its magnitude and energy density are computed. The energy diffusion parameter is found to be proportional to the square of the ratio of the standard deviation of the source field to the characteristic time constant of the dynamic process, but is independent of the initial energy density, to first order. The energy drift vanishes in the asymptotic limit. The time-energy probability distribution is in general not separable, as a result of nonstationarity. A general solution of the Fokker--Planck equation is obtained in integral form, together with explicit closed-form solutions for several asymptotic cases. The findings extend known results on statistics and distributions of quasi-stationary ideal random fields (pure diffusions), which are retrieved as special cases.Comment: 54 pages, 8 figures, to appear in J. Phys. A: Math. Theo