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Additional info for Modern Many Particle Physics
It can be shown that its behavior is approximately T~2. g. ). This regime is referred to as the hydrodynamic or classical regime. In the opposite limit, LOT » 1, the frequency is so high that the system can undergo many oscillation periods without any collision. In this case the collision term can be neglected and the system is said to be in the elastic regime. In this regime, the interaction plays a crucial role. To study these two regimes, it is possible to change the temperature and, consequently, r.
127) Finite Temperature and Quasiparticles 27 where m is the bare quasiparticle mass. 127) implies -=v k -X>, k ,f^v k ,. 128) is a condition which is imposed on /k,k' by translational invariance. 121). 130) enable for the determination of the Landau parameter F(. In order to establish a connection between F£ and a measurable quantity, let us assume that the hydrodynamic regime holds, and let us look for Euler-like equations for the density variations. 131) m —' oe k m kk' where we have used the result ^ k kjl(5n(k, r, t))coil = 0, which results from the current being conserved during collisions.
Starting from N known single-particle functions ip\ ', which are used to determine vEf. 7) are then solved and TV new wavefunctions are determined, by means of which a new potential vEF is built up. 7) are subsequently solved again, and so on, until solutions are obtained which coincide with those used to set up the potential of the previous iterations (self-consistency). The Slater determinant obtained with the solutions of the last iteration is the Hartree-Fock ground state. 7) provide a complete set of solutions