Describing of anharmonic effects is complicated because exact treatment as in the harmonic case is not possible and phonons are no longer exact eigensolutions to the equations of motion.
22.
It is possible to use first-principles methods such as density-functional theory to map the anharmonic potential experienced by the atoms in both molecules and solids.
23.
Such an anharmonic overtone might occur if, say, your guitar string is corroded .-- talk ) 20 : 57, 18 February 2007 ( UTC)
24.
Kupiainen continued his investigations into the origins of diffusion and time-irreversibility in various model systems ( such as coupled chaotic mappings and weakly coupled anharmonic oscillations ).
25.
He then solved the same problem by treating the anharmonic potential term as a perturbation to the harmonic oscillator and using the perturbation methods that he and Born had developed.
26.
Those authors had observed long-time nearly recurrent behavior of a one-dimensional chain of anharmonic oscillators, in contrast to the rapid thermalization that had been expected.
27.
Consequently, the action of the modular group on \ lambda ( \ tau ) is that of the anharmonic group, giving the six values of the cross-ratio:
28.
For example, a solid with two identical phonons does not have exactly twice the excitation energy of a solid with just one phonon, because the crystal vibration is slightly anharmonic.
29.
Studying vibrating anharmonic systems using quantum mechanics is a computationally demanding task because anharmonicity not only makes the potential experienced by each oscillator more complicated, but also introduces coupling between the oscillators.
30.
It says in Cross-ratio that " The anharmonic group is the group of order 6 generated by ? ?! 1 / ? and ? ?! 1 " ?.
