We derive and analyze the perturbation series for the classical effective potential in quantum statistical mechanics, treated as a toy model for the dimensionally reduced effective action in quantum field theory at finite temperature. The first few terms of the series are computed for the harmonic oscillator and the quartic potential.

Spectral methods using spherical harmonic basis functions have proven to be very eeective in geophysical and astrophysical simulations. It is an unfortunate fact, however , that spurious oscillations, known as the Gibbs phenomenon, contaminate these spectral solutions, particularly in regions where discontinuities or steep gradients occur. They are also apparent in the polar regions even when c...

Converged quantum mechanical vibrational-rotational partition functions and free energies are calculated using realistic potential energy surfaces for several chalcogen dihydrides (H20, D20, H 2S, H2Se) over a wide range of temperatures (600-4000 K). We employ an adaptively optimized Monte Carlo integration scheme for computing vibrational-rotational partition functions by the Fourier path-inte...

We present a perturbation theory to find the response of an anisotropic DNA to the external tension. It is shown that the anisotropy has a nonzero but small contribution to the force-extension curve of the DNA. Thus an anisotropic DNA behaves like an isotropic one with an effective bending constant equal to the harmonic average of its soft and hard bending constants.

We consider a forced harmonic oscillator at resonance with a nonlinear perturbation and obtain a sharp condition for the existence of unbounded motions. Such a condition is extended to the case of a semilinear vibrating string. AMS classification scheme numbers: 34C11, 35L05

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

We explain the use of Feynman diagrams to do perturbation theory in quantum mechanics. Feynman diagrams are a valuable tool for organizing and understanding calculations. We first work several examples for the 1-dimensional harmonic oscillator, and then proceed to justify our calculations.

Abstract Starting from the general, governing equations for a viscous, compressible fluid written in rotating, spherical coordinates, with an associated prescription its thermodynamics, we construct general amplitude perturbation of background state atmosphere. The state, purely zonal flow (wind) is suitably non-dimensionalised and thin-shell parameter introduced; this sole basis upon which asy...

We examine the ability of two-stage free-energy perturbation methods to yield solid-phase free energies using a system of harmonically coupled particles as a reference. We consider two ways to construct a reference system, one based on derivatives of the intermolecular potential of the target system of interest (the conventional choice in lattice dynamics), and the other based on analysis of pa...