Fourier amplitudes conductivity

A measurement of the optical conductivity of PAni samples over the range 2 meV to leV is illustrated in Fig. 9.38. The reflection spectra were obtained using a Fourier transform interferometer and a synchrotron radiation source. The Kramers-Kroiiig transformation, with appropriate extrapolation of the data to zero and high energy, was used to extract the complex frequency-dependent conductivity and its real part, the optical conductivity. The optical conductivity is related to the imaginary component of the electric susceptibility, since the power dissipated by an optical field of amplitude E is given by ... 

Any periodic function (such as the electron density in a crystal which repeats from unit cell to unit cell) can be represented as the sum of cosine (and sine) functions of appropriate amplitudes, phases, and periodicities (frequencies). This theorem was introduced in 1807 by Baron Jean Baptiste Joseph Fourier (1768-1830), a French mathematician and physicist who pioneered, as a result of his interest in a mathematical theory of heat conduction, the representation of periodic functions by trigonometric series. Fourier showed that a continuous periodic function can be described in terms of the simpler component cosine (or sine) functions (a Fourier series). A Fourier analysis is the mathematical process of dissecting a periodic function into its simpler component cosine waves, thus showing how the periodic function might have been been put together. A simple... 

Conduction is a process where heat flows within a body (soUd, liquid, or gas) from a region of high temperature to one of lower temperature. While the basic mechanism of heat conduction is different for metals, non-metals, and fluids, the result is the same—an increase in the vibrational amplitude as heat flows into a body. The basic law of conductive heat transfer is Fourier s equation (1822) ... 

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