Exact quantum states of a general time-dependent quadratic system from classical action

A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not change the classical equation of motion. Based on the observation by Feynman and Hibbs, the propagators (kernels) of the systems are calculated from the classical action, in terms of solutions of the classical equation of motion: two homogeneous and one particular solutions. The kernels are then used to find wave functions which satisfy the Schr\"{o}dinger equation. One of the wave functions is shown to be that of a Gaussian pure state. In every case considered, we prove that the kernel does not depend on the way of choosing the classical solutions, while the wave functions depend on the choice. The generalization which gives a rather complicated quadratic Hamiltonian is simply interpreted as acting an unitary transformation to the driven harmonic oscillator system in the Hamiltonian formulation.Comment: Submitted to Phys. Rev.

Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential

The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.Comment: Phys. Rev. A (Brief Report), in pres

Classes of exact wavefunctions for general time-dependent Dirac Hamiltonians in 1+1 dimensions

In this work we construct two classes of exact solutions for the most general time-dependent Dirac Hamiltonian in 1+1 dimensions. Some problems regarding to some formal solutions in the literature are discussed. Finally the existence of a generalized Lewis-Riesenfeld invariant connected with such solutions is discussed

Exact solvability of potentials with spatially dependent effective masses

We discuss the relationship between exact solvability of the Schroedinger equation, due to a spatially dependent mass, and the ordering ambiguity. Some examples show that, even in this case, one can find exact solutions. Furthermore, it is demonstrated that operators with linear dependence on the momentum are nonambiguous.Comment: 12 page

A finite element approach for the acoustic modelling of perforated dissipative mufflers with non-homogeneous properties

[EN] In this work, a finite element approach is presented for modeling sound propagation in perforated dissipative mufflers with non-homogeneous properties. The spatial variations of the acoustic properties can arise, for example, from uneven filling processes during manufacture and degradation associated with the flow of soot particles within the absorbent material. First, the finite element method is applied to the wave equation for a propagation medium with variable properties (outer chamber with absorbent material) and a homogeneous medium (central passage). For the case of a dissipative muffler, the characterization of the absorbent material is carried out by means of its equivalent complex density and speed of sound. To account for the spatial variations of these properties, a coordinate-dependent function is proposed for the filling density of the absorbent material. The coupling between the outer chamber and the central passage is achieved by using the acoustic impedance of the perforated central pipe, that relates the acoustic pressure jump and the normal velocity through the perforations. The acoustic impedance of the perforated central duct includes the influence of the absorbent material and therefore a spatial variation of the impedance is also taken into account. A detailed study is then presented to assess the influence of the heterogeneous properties and the perforated duct porosity on the acoustic attenuation performance of the muffler.The authors gratefully acknowledge the financial support of Ministerio de Ciencia e Innovacion and the European Regional Development Fund by means of the projects DPI2007-62635 and DPI2010-15412.Antebas, A.; Denia Guzmán, FD.; Pedrosa Sanchez, AM.; Fuenmayor Fernández, FJ. (2013). A finite element approach for the acoustic modelling of perforated dissipative mufflers with non-homogeneous properties. Mathematical and Computer Modelling. 57(7):1970-1978. https://doi.org/10.1016/j.mcm.2012.01.021S1970197857

Differential metabolism of Mycoplasma species as revealed by their genomes

The annotation and comparative analyses of the genomes of Mycoplasma synoviae and Mycoplasma hyopneumonie, as well as of other Mollicutes (a group of bacteria devoid of a rigid cell wall), has set the grounds for a global understanding of their metabolism and infection mechanisms. According to the annotation data, M. synoviae and M. hyopneumoniae are able to perform glycolytic metabolism, but do not possess the enzymatic machinery for citrate and glyoxylate cycles, gluconeogenesis and the pentose phosphate pathway. Both can synthesize ATP by lactic fermentation, but only M. synoviae can convert acetaldehyde to acetate. Also, our genome analysis revealed that M. synoviae and M. hyopneumoniae are not expected to synthesize polysaccharides, but they can take up a variety of carbohydrates via the phosphoenolpyruvate-dependent phosphotransferase system (PEP-PTS). Our data showed that these two organisms are unable to synthesize purine and pyrimidine de novo, since they only possess the sequences which encode salvage pathway enzymes. Comparative analyses of M. synoviae and M. hyopneumoniae with other Mollicutes have revealed differential genes in the former two genomes coding for enzymes that participate in carbohydrate, amino acid and nucleotide metabolism and host-pathogen interaction. The identification of these metabolic pathways will provide a better understanding of the biology and pathogenicity of these organisms

Alexithymia and interleukin variations in somatoform disorder

Objective: The aim of the present study was to investigate if somatoform disorders (SFD) are associated with changes in the normal serum levels of important interleukins, and further, to establish if these changes are related to the presence and severity of alexithymia in patients with SFD. Methods: Twenty-four unmedicated patients who met the International Classification of Diseases (ICD-10) diagnostic criteria for SFD completed the psychological questionnaire to assess alexithymia (Toronto Alexithymia Scale), symptom reporting (SCL-90-R) and diagnostic criteria for SFD (Screening for Somatoform Symptoms scale). Serum concentrations of soluble interleukin 2 receptor α (sIL-2 Rα), IL-4, IL-6, IL-10 and IL-12 were determined in patients with SFD and in 9 healthy subjects. Results: In patients with SFD, serum levels of IL-6 (p < 0.001), IL-10 (p = 0.047) and immunoglobulin E (p = 0.045) were significantly increased in comparison with healthy controls. Additionally, a negative correlation was observed between the level of alexithymia ('total' Toronto Alexithymia Scale score) and the serum levels of sIL-2 Rα (r = -0.538) in SFD. Conclusions: Taken together, these results suggest that SFD, with clinically significant alexithymia, are associated with a reduction in Th1-mediated immune function and an increase in the activation of the Th2 immune function, indicated by the augmented serum levels of IL-6 and IL-10 and elevated immunoglobulin E. Copyright © 2007 S. Karger AG