UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2024-11-23 17:49
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Conference: Bucharest University Faculty of Physics 2023 Meeting


Section: Theoretical Physics and Applied Mathematics


Title:
Collective modes of Fermi Liquids


Authors:
Bogdan SAVA


Affiliation:
Facultatea de Fizică a Universității din București


E-mail
sava_bog@yahoo.com


Keywords:
Fermi liquids


Abstract:
In this paper, we aim to give a brief description of the Landau model of the Fermi liquid. The way this subject will be approached will be partly microscopic, partly phenomenological. This theory starts from the case of the Fermi gas, a system whose constituents do not interact with each other. What is different, however, from the Fermi gas model, is the fact that, for liquid, the interaction between particles can no longer be neglected. In the first part, we will briefly describe the Fermi gas, studying some of its characteristics, considering that this model is the basis from which we will start. Further, the changes in physical properties when considering an interaction between fermions will be analyzed. This is introduced based on the phenomenological hypothesis, proposed by Landau, that the energy of the system is a functional of the Fermi-Dirac distribution function, which characterizes the quasiparticles of the Fermi liquid. It will allow us to express static and thermodynamic properties such as: effective mass, compressibility modulus, heat capacity, in terms of the Landau parameters, which encode the interaction properties. Next, we will study the transport equation in the Fermi liquid and use it to infer the existence of zero sound, a phenomenon of collective motion of fermions near absolute zero. This sound, which differs from the normal sound, also called the first sound, was predicted in Landau's theory and later verified experimentally. The zero sound was one of the biggest successes of this model. Although fermions theoretically cannot collide with each other at absolute zero temperatures, perturbations can propagate through a different mechanism in the Fermi liquid. This mechanism is characteristic, as we shall see, of the zero sound. By this, this mode is fundamentally different from the first sound, which is based precisely on collisions between particles.


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