We investigate the energy relaxation process produced by thermal baths at zero temperature acting on the boundary atoms of chains of classical anharmonic oscillators. Time–dependent perturbation theory allows us to obtain an explicit solution of the harmonic problem: even in such a simple system nontrivial features emerge from the interplay of the different decay rates of Fourier modes. In part...

We analyze the use of strong static electric and magnetic fields for controlling two intense laser-atom processes: laser-assisted x-ray-atom scattering and highorder harmonic generation. We find that x-rays scattered from atoms in the presence of both a strong laser field and a strong static electric field can be boosted in energy many-fold by absorption of energy from the laser field. The spec...

Introduction A map : M ! N of Riemannian manifolds is harmonic if it extremises the energy functional: Z jdj 2 dvol on every compact subdomain of M. Harmonic maps arise in many diierent contexts in Geometry and Physics (for an overview, see 15,16]) but the setting of concern to us is the following: take M to be 2-dimensional and N to be a Riemannian symmetric space of compact type. In this case...

The theory of phase congruency is that features such as step edges, roofs, and deltas always reach the maximum phase of image harmonic components. We propose a modified algorithm of phase congruency to detect image features based on two-dimensional (2-D) discrete Hilbert transform. Windowing technique is introduced to locate image features in the algorithm. Local energy is obtained by convoluti...

By taking a Klein-Gordon field as the environment of an harmonic oscillator and using a new method for dealing with quantum dissipative systems (minimal coupling method), the quantum dynamics and radiation reaction for a quantum damped harmonic oscillator investigated. Applying perturbation method, some transition probabilities indicating the way energy flows between oscillator, reservoir and q...

The canonical metric on a surface is of nonpositive curvature, so it is natural to study harmonic maps between canonical metrics on a surface in a fixed homotopy class. Through this approach, we establish the LBergman metric on Teichmüller space as the second variation of energy functionals of chosen families of harmonic maps.

Certain solutions to Harper’s equation are discrete analogues of (and approximations to) the Hermite–Gaussian functions. They are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the time-evolution operator of the discrete harmonic oscill...

Three-point functions of analytic (chiral primary) operators in N = 4 Yang-Mills theory in four dimensions are calculated using the harmonic superspace formulation of this theory. In the case of the energy-momentum tensor multiplet anomaly considerations determine the coefficient. Analyticity in N = 2 harmonic superspace is explicitly checked in a two-loop calculation.

An ODE variational calculation shows that an image principle curvature ratio factor, (√ ρ1 ρ2 + √ ρ2 ρ1 ) , can raise the lower bound, 2(Image Area), on energy of a harmonic map of a surface into R. In certain situations, including all radially symmetry harmonic maps, equality is achieved.

Using the fact that harmonic morphisms to a surface have minimal bres, links between the volume-stability of the bres and the energy-stability of the map are found for manifolds without boundary. A stability result for harmonic morphisms from a manifold with boundary to a Riemann surface is also established.