ULTRASONIC RESPONSE TO TWO AND FOUR LEVEL QUANTUM SYSTEMS

Abstract
The theory already available for the ultrasonic response to a quantum twolevel system for amorphous materials is discussed and adapted to two and four level systems in crystals. It is given in a simple physical way which helps make clear the distinction between resonance and relaxation. Resonance and no relaxation occurs for small enough static strain, while for large enough strain, the opposite is true. For a TLS, relaxation occurs by a direct process, with a rate linear in temperature in the measurable range. This leads to a Debye response, but the temperature dependence is inverted from that usually found for faster relaxation rates. At low enough temperatures the relaxation strength deviates from the classical 1/T behavior, going to zero as the upper state becomes depopulated, while the resonance strength saturates. At high temperatures, the sum of these approaches the classical value. Relaxation and resonance strengths are given for two and four level systems as a function of temperature and strain for two strain distributions.