Semiclassical Series from Path Integrals

We derive the semiclassical series for the partition function in Quantum Statistical Mechanics (QSM) from its path integral representation. Each term of the series is obtained explicitly from the (real) minima of the classical action. The method yields a simple derivation of the exact result for the harmonic oscillator, and an accurate estimate of ground-state energy and specific heat for a single-well quartic anharmonic oscillator. As QSM can be regarded as finite temperature field theory at a point, we make use of Feynman diagrams to illustrate the non-perturbative character of the series: it contains all powers of $\hbar$ and graphs with any number of loops; the usual perturbative series corresponds to a subset of the diagrams of the semiclassical series. We comment on the application of our results to other potentials, to correlation functions and to field theories in higher dimensions.Comment: 18 pages, 4 figures. References update

Semiclassical Statistical Mechanics

We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on Catastrophe Theory to analyze the pattern of extrema of the corresponding path-integral. We exhibit the propagator in the background of the different extrema and use it to compute the fluctuation determinant and to develop a (nonperturbative) semiclassical expansion which allows for the calculation of correlation functions. We discuss the examples of the single and double-well quartic anharmonic oscillators, and the implications of our results for higher dimensions.Comment: Invited talk at the La Plata meeting on `Trends in Theoretical Physics', La Plata, April, 1997; 14 pages + 5 ps figures. Some cosmetical modifications, and addition of some references which were missing in the previous versio

X-ray powder diffraction of high-absorption materials at the XRD1 beamline off the best conditions: Application to (Gd,Nd)5Si4 compounds

Representative compounds of the new family of magnetic materials Gd5-xNdxSi4 were analyzed by X-ray diffraction at the XRD1 beamline at LNLS. To reduce X-ray absorption, thin layers of the powder samples were mounted outside the capillaries and measured in Debye-Scherrer geometry as usual. The X-ray diffraction analyses and the magnetometry results indicate that the behavior of the magnetic transition temperature as a function of Nd content may be directly related to the average of the four smallest interatomic distances between different rare earth sites of the majority phase of each compound. The quality and consistency of the results show that the XRD1 beamline is able to perform satisfactory X-ray diffraction experiments on high-absorption materials even off the best conditions.Comment: 12 pages, 3 figures, 3 table