Anharmonicity

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Anharmonicity is the deviation of a system from being a harmonic oscillator [1]. An oscillator that is not oscillating in simple harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmonic oscillator and the anharmonicity can be calculated using perturbation theory. If the anharmonicity is large then other numerical techniques have to be used.

[edit] Anharmonic ratio (cross-ratio)

If A, B, C, D all lie on a straight line then the anharmonic ratio is: [2]

( A, B, C, D) = \frac{AC/AD}{BC/BD}.

In the complex plane the anharmonic ratio is

(z_1,z_2;z_3,z_4) = \frac{(z_1-z_3)(z_2-z_4)}{(z_1-z_4)(z_2-z_3)}.
  • There are six distinct anharmonic ratios depending on the order of which the points are chosen.
  • Anharmonicity plays a role in lattice and molecular vibrations, in quantum oscillations [3], and in Acoustics.

[edit] See also