44,252 research outputs found
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 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
- …