Inverting Time-Dependent Harmonic Oscillator Potential by a Unitary Transformation and a New Class of Exactly Solvable Oscillators

A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass and imaginary frequency. The latter may be reduced to an ordinary harmonic oscillator by means of another unitary (canonical) transformation. A simple analysis of the resulting system leads to the identification of a previously unknown class of exactly solvable time-dependent oscillators. Furthermore, it is shown how one can apply these results to establish a canonical equivalence between some real and imaginary frequency oscillators. In particular it is shown that a harmonic oscillator whose frequency is constant and whose mass grows linearly in time is canonically equivalent with an oscillator whose frequency changes from being real to imaginary and vice versa repeatedly.Comment: 7 pages, 1 figure include

Algebraic approach in the study of time-dependent nonlinear integrable systems: Case of the singular oscillator

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability of this system is established by evaluating the exact invariant closely related to the Lewis and Riesenfeld invariant for the time-dependent harmonic oscillator. We study extensively the special and interesting case of a kicked quadratic potential from which we derive a new integrable, nonlinear, area preserving, two-dimensional map which may, for instance, be used in numerical algorithms that integrate the Calogero-Sutherland-Moser Hamiltonian. The dynamics, both classical and quantal, is studied via the time-evolution operator which we evaluate using a recent method of integrating the quantum Liouville-Bloch equations \cite{rau}. The results show the exact one-to-one correspondence between the classical and the quantal dynamics. Our analysis also sheds light on the connection between properties of the SU(1,1) algebra and that of simple dynamical systems.Comment: 17 pages, 4 figures, Accepted in PR

New possibilities for the gauging of chiral bosons

We study a new mechanism for the electromagnetic gauging of chiral bosons showing that new possibilities emerge for the interacting theory of chiral scalars. We introduce a chirally coupled gauge field necessary to mod out the degree of freedom that obstructs gauge invariance in a system of two opposite chiral bosons soldering them together.Comment: 11 pages, Latex. Accepted for publication in Physical Review

Spontaneous emission in a planar Fabry-Perot microcavity

Published versio

An analysis of Methylenetetrahydrofolate reductase and Glutathione S-transferase omega-1 genes as modifiers of the cerebral response to ischemia

<p>Abstract</p> <p>Background</p> <p>Cerebral ischemia involves a series of reactions which ultimately influence the final volume of a brain infarction. We hypothesize that polymorphisms in genes encoding proteins involved in these reactions could act as modifiers of the cerebral response to ischemia and impact the resultant stroke volume. The final volume of a cerebral infarct is important as it correlates with the morbidity and mortality associated with non-lacunar ischemic strokes.</p> <p>Methods</p> <p>The proteins encoded by the methylenetetrahydrofolate reductase (<it>MTHFR</it>) and glutathione S-transferase omega-1 (<it>GSTO-1</it>) genes are, through oxidative mechanisms, key participants in the cerebral response to ischemia. On the basis of these biological activities, they were selected as candidate genes for further investigation. We analyzed the C677T polymorphism in the <it>MTHFR </it>gene and the C419A polymorphism in the <it>GSTO-1 </it>gene in 128 patients with non-lacunar ischemic strokes.</p> <p>Results</p> <p>We found no significant association of either the <it>MTHFR </it>(p = 0.72) or <it>GSTO-1 </it>(p = 0.58) polymorphisms with cerebral infarct volume.</p> <p>Conclusion</p> <p>Our study shows no major gene effect of either the <it>MTHFR </it>or <it>GSTO-1 </it>genes as a modifier of ischemic stroke volume. However, given the relatively small sample size, a minor gene effect is not excluded by this investigation.</p

TNFA and IL10 Gene Polymorphisms are not Associated with Periodontitis in Brazilians

IL-10 and TNF-α are cytokines that have complex and opposing roles in the inflammatory responses. G/A polymorphisms at position –1082 of IL10 and –308 of TNFA genes have been reported to influence the expression of IL-10 and TNF-α, respectively. The aim of this study was to investigate the association between the IL10 (-1082) and TNFA (- 308) gene polymorphisms with different clinical forms or severity of periodontitis in a sample of Brazilian individuals. DNA was obtained from oral swabs of 165 Brazilian individuals, which were divided into three groups: individuals with chronic periodontitis, aggressive periodontitis and individuals without clinical evidence of periodontitis. Evaluation of IL10 and TNFA polymorphisms was performed by RFLP analysis. Statistical analysis of data was performed using the χ2 likelihood ratio and Fisher`s exact test. No significant differences in the genotype and allele distribution of either IL10 or TNFA were observed among individuals with different clinical forms or with different degrees of severity of periodontitis. Moreover, combined analysis of IL10 and TNFA polymorphisms did not show any association with periodontal status. As conclusion, the IL10 and TNFA gene promoter polymorphisms investigated are not associated with different clinical forms of periodontitis or with severity of the disease in the Brazilian population polymorphisms