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Complex Poles (complex + pole)

Distribution by Scientific Domains
Engineering50%

Selected Abstracts

Positive width function and energy indeterminacies in ammonia molecule

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 8 2007
Theodosios G. Douvropoulos
A recently published methodology based on the semiclassical path integral theory was applied in a double well structure and gave the analytic form of the system's Green's function. This type of potential can describe the ammonia molecule as far as the motion of the nitrogen atom perpendicular to the hydrogen plane is discussed. Because of the fact that a double well describes a bound system and correspondingly stationary states (constructed by the symmetric and antisymmetric superposition of the eigenstates of the two unperturbed wells), it was expected that the energy spectrum would be real, in a form of doublets due to the splitting effect that takes place. However, the result was a pair of complex poles, which had a clearly positive imaginary part for each member. The present work explains the role of the imaginary parts of the complex poles as the decay rate of quantities defined as the energy indeterminacies, which are directly related to the fact that energy is not well determined in a classically forbidden region of motion. These quantities come as a function of (d,)/dE, which is the derivative of the classical action inside the potential barrier, with respect to energy. The major contribution comes from the turning points, and then the imaginary parts are responsible, not only for the conservation of energy, but for the correct sign of time as well. In this way, a different approach for the tunneling process is adopted, in which the entry or exit of the particle from the potential barrier takes place inside a neighborhood of the turning point, as though the latter was broadened and fluctuating. The magnitude of the previously mentioned decay rate is equal to ,/,, where , is the frequency of the classical oscillations inside one well. In contrast, the inversion frequency is generated by the part of the complex pole that is unrelated to (d,)/dE and is much smaller in magnitude than the classical frequency, since it is given as ,/, exp(,,). In this way, the period of the energy fluctuations is much smaller than the internal period of the system produced by the oscillating communication of the two classically allowed regions of motion. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]

Simulation of general linear dielectric properties in TLM

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5-6 2002
John Paul
Abstract The simulation of linear dispersive dielectric materials in time-domain TLM requires the inclusion of frequency-dependent material properties in the scattering process. For media having frequency dependencies described by a single pole or a pair of complex poles, for example Debye, Drude or Lorentz, it is straightforward to develop individual algorithms on a case-by-case basis. However, this approach lacks generality and when applied to the modelling of media displaying more complicated frequency dependencies, somewhat lengthy calculations need to be evaluated each time a new material is required. To address this difficulty, this paper describes methods for obtaining the iteration algorithm for general linear isotropic dielectric media. The results obtained using different ,,-transform methods are compared and an example of a frequency-dependent structure is simulated. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Positive width function and energy indeterminacies in ammonia molecule

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 8 2007
Theodosios G. Douvropoulos
A recently published methodology based on the semiclassical path integral theory was applied in a double well structure and gave the analytic form of the system's Green's function. This type of potential can describe the ammonia molecule as far as the motion of the nitrogen atom perpendicular to the hydrogen plane is discussed. Because of the fact that a double well describes a bound system and correspondingly stationary states (constructed by the symmetric and antisymmetric superposition of the eigenstates of the two unperturbed wells), it was expected that the energy spectrum would be real, in a form of doublets due to the splitting effect that takes place. However, the result was a pair of complex poles, which had a clearly positive imaginary part for each member. The present work explains the role of the imaginary parts of the complex poles as the decay rate of quantities defined as the energy indeterminacies, which are directly related to the fact that energy is not well determined in a classically forbidden region of motion. These quantities come as a function of (d,)/dE, which is the derivative of the classical action inside the potential barrier, with respect to energy. The major contribution comes from the turning points, and then the imaginary parts are responsible, not only for the conservation of energy, but for the correct sign of time as well. In this way, a different approach for the tunneling process is adopted, in which the entry or exit of the particle from the potential barrier takes place inside a neighborhood of the turning point, as though the latter was broadened and fluctuating. The magnitude of the previously mentioned decay rate is equal to ,/,, where , is the frequency of the classical oscillations inside one well. In contrast, the inversion frequency is generated by the part of the complex pole that is unrelated to (d,)/dE and is much smaller in magnitude than the classical frequency, since it is given as ,/, exp(,,). In this way, the period of the energy fluctuations is much smaller than the internal period of the system produced by the oscillating communication of the two classically allowed regions of motion. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]

A parameter-reduced volterra model for dynamic RF power amplifier modeling based on orthonormal basis functions

INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 6 2007
M. Isaksson
Abstract A nonlinear dynamic behavioral model for radio frequency power amplifiers is presented. It uses orthonormal basis functions, Kautz functions, with complex poles that are different for each nonlinear order. It has the same general properties as Volterra models, but the number of parameters is significantly smaller. Using frequency weighting the out-of-band model error can be reduced. Using experimental data it was found that the optimal poles were the same for different input powers and for the different nonlinear orders. The optimal poles were also the same for direct and inverse models, which could be explained theoretically to be a general property of nonlinear systems with negligible linear memory effects. The model can be used as either a direct or inverse model with the same model error for power amplifiers with negligible linear memory effects. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007. [source]