Fermi液体理论的分数不相容统计
The Fermi liquid theory with fractional exclusion statistics
摘要：
费米液体理论可以很好地描述相互作用粒子系统的热力学性质，当粒子之间的相互作用对系统的总能量的贡献量可能取决于总粒子数，但不取决于温度时。在这种情况下，哈密顿量的理想部分，即没有相互作用能的系统的能量，也提供了系统热力学的良好描述。如果系统的总相互作用能是粒子布居数的复杂函数，是温度依赖的，那么朗道准粒子气体不能准确地描述系统的热力学。本文给出了这个问题的一般解法，其中重新定义了准粒子能量，使得系统的总能量等于准粒子能量之和。这也意味着系统的热力学性质和准粒子气体的热力学性质是相同的。通过选择准粒子能量固定而态密度沿准粒子轴变化的观点，我们将准粒子系统转化为服从分数不相容统计的理想气体。
英文摘要：
The Fermi liquid theory may provide a good description of the thermodynamic properties of an interacting particle system when the interaction between the particles contributes to the total energy of the system with a quantity which may depend on the total particle number, but does not depend on the temperature. In such a situation, the ideal part of the Hamiltonian, i.e. the energy of the system without the interaction energy, also provides a good description of the system's thermodynamics. If the total interaction energy of the system, being a complicated function of the particle populations, is temperature dependent, then the Landau's quasiparticle gas cannot describe accurately the thermodynamics of the system. A general solution to this problem is presented in this paper, in which the quasiparticle energies are redefined in such a way that the total energy of the system is identical to the sum of the energies of the quasiparticles. This implies also that the thermodynamic properties of the system and those of the quasiparticle gas are identical. By choosing a perspective in which the quasiparticle energies are fixed while the density of states along the quasiparticle axis vary, we transform our quasiparticle system into an ideal gas which obey fractional exclusion statistics.
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