1,445 research outputs found
Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media
Maxwell's equations for propagation of electromagnetic waves in dispersive
and absorptive (passive) media are represented in the form of the Schr\"odinger
equation , where is a linear
differential operator (Hamiltonian) acting on a multi-dimensional vector
composed of the electromagnetic fields and auxiliary matter fields describing
the medium response. In this representation, the initial value problem is
solved by applying the fundamental solution to the initial field
configuration. The Faber polynomial approximation of the fundamental solution
is used to develop a numerical algorithm for propagation of broad band wave
packets in passive media. The action of the Hamiltonian on the wave function
is approximated by the Fourier grid pseudospectral method. The algorithm
is global in time, meaning that the entire propagation can be carried out in
just a few time steps. A typical time step is much larger than that in finite
differencing schemes, . The accuracy and stability
of the algorithm is analyzed. The Faber propagation method is compared with the
Lanczos-Arnoldi propagation method with an example of scattering of broad band
laser pulses on a periodic grating made of a dielectric whose dispersive
properties are described by the Rocard-Powels-Debye model. The Faber algorithm
is shown to be more efficient. The Courant limit for time stepping, , is exceeded at least in 3000 times in the Faber propagation
scheme.Comment: Latex, 17 pages, 4 figures (separate png files); to appear in J.
Comput. Phy
A New Approach to Numerical Quantum Field Theory
In this note we present a new numerical method for solving Lattice Quantum
Field Theory. This Source Galerkin Method is fundamentally different in concept
and application from Monte Carlo based methods which have been the primary mode
of numerical solution in Quantum Field Theory. Source Galerkin is not
probabilistic and treats fermions and bosons in an equivalent manner.Comment: 10 pages, LaTeX, BROWN-HET-908([email protected]),
([email protected]), ([email protected]
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