Excitation Spectrum of Dilute ^3He-^4He Solution by Model Hamiltonian : Condensed Matter and Statistical Physics
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The Hamiltonian H of the ^3He-^4He mixture is considered to consist of the part of elementary excitations of ^3He and ^4He, H_F and H_B, and the interacting part between their density fluctuations, H_<FB>. We expand each density fluctuation in terms of the creation and annihilation of elementary excitations. By inserting this into H_<FB> and diagonalizing H, we obtain the dispersion relation. Using sum rules, we solve the dispersion relation and obtain the energy spectrum for 5% ^3He concentration. The phonon-roton spectrum is decreased and the energy of the second branch almost unchanges. This result explains the decrease of a single roton energy observed in the fourth sound, oscillating disk and ion mobility experiments. We comment also on the result of the Raman scattering experiment.
- 理論物理学刊行会の論文
- 1991-10-25
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