28,071 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
Geometric Phase for Fermionic Quasiparticles Scattering by Disgyration in Superfluids
We consider a Volovik's analog model for description of a topological defects
in a superfluid and we investigate the scattering of quasiparticles in this
background. The analog of the gravitational Aharonov-Bohm in this system is
found. An analysis of this problem employing loop variables is considered and
corroborates for the existence of the Aharonov-Bohm effect in this system. The
results presented here may be used to study the Aharonov-Bohm effect in
superconductors.Comment: 7 pages, to appear in Europhys. Let
The Role of Fermions in Bubble Nucleation
We present a study of the role of fermions in the decay of metastable states
of a scalar field via bubble nucleation. We analyze both one and
three-dimensional systems by using a gradient expansion for the calculation of
the fermionic determinant. The results of the one-dimensional case are compared
to the exact results of previous work.Comment: 15 pages, revtex, 9 figure
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