I was thinking about the Umklapp process, or thinking about it as much as you can think about it if you don’t have a fairly basic background in mechanics, electricity, and magnetism, and atomic physics along with relatively intuitive ideas in quantum physics. The Umklapp process relates to groups of waves that cross each other’s paths: there is little or no interference when the waves are in a linear medium, i.e. one in which the displacement at any point is proportional to the applied force. The waves are said to be harmonic, and the energy of the wave is proportional to the square of its amplitude; the displacement of the medium at any point can be obtained by adding the sums of the amplitudes of the individual waves at that point. If the medium is not exactly linear, on the other hand, the principle of superpositon no longer applies, and the waves are said to be anharmonic. The Umklapp process is a special case of this: if the sum of two oncoming phonons is large enough, their resultant will be a phonon with the same total energy, but travelling in the opposite direction!
The staff at the museum had not been very helpful when I had asked questions, and I knew that Sibylla would not be able to help. I was wondering whether I should try to get into a school. I came into the house and Sibylla sat at the computer with the 12 issues of
He is a monstrous peacock, and He waveth all the night His languid tail above us, lit with myriad spots of light.
She said:
The sun’s rim dips, the stars rush out
At one stride comes the dark.
She asked if I had had a good day. I said I was reading
I said: They are quanta of lattice vibrational energy.
They died as men before their bodies died, said Sibylla.
I said: What?
Never mind, said Sibylla. I believe that the body can survive 30 hours of typing
She was flipping through the book and now she said: Oh, listen to this!
However carefully we prepare a specimen, using extremely high purity materials and very specially controlled methods of crystal growth, one form of defect will always be present—that due to the thermal vibration of the atoms. At any instant in time the atoms are never exactly at their correct lattice sites. At room temperature they are vibrating with approximately simple harmonic motion at around 1013Hz about an origin which is at the geometrical lattice position. Even at very low temperatures the zero-point motion of the atoms is still present.
This is delightful, said Sibylla. If you were at school they would not let you read a book like this, they would keep you from reading it by involving you in sport. And look! It was written in 1976, so that Liberace might have read it in his intellectually malformative years and profited thereby, instead of allowing his mind to solidify, we may say, to the state where the cerebratory atoms spent their time perpetually away from their correct lattice sites. I wish I understood this, said Sibylla, and she flashed a bitter look at
Her face was pinched and grey. Her eyes were burning. The next day I took the heart out and put it in my backpack and left the house.
I took the Circle Line and when it stopped at Farringdon I stayed on. I didn’t want to go to the agent but I was going to have to do it. Sometimes I thought the problem wasn’t really money but then I remembered that someone had saved Sib’s life because it wasn’t worth killing yourself over money.
Someone left an
