Chebyshev polynomial expansion of two-dimensional Landau–Fermi liquid parameters
Dec 6, 201919 pages
Published in:
- J.Phys.A 53 (2020) 22, 225203
- Published: May 18, 2020
e-Print:
- 1912.03427 [cond-mat.str-el]
View in:
Citations per year
0 Citations
Abstract: (IOP)
We study the intrinsic effects of dimensional reduction on the transport equation of a perfectly two-dimensional Landau–Fermi liquid. By employing the orthogonality condition on the 2D analog of the Fourier–Legendre expansion, we find that the equilibrium and non-equilibrium properties of the fermionic system differ from its three-dimensional counterpart, with the latter changing drastically. Specifically, the modified Landau–Silin kinetic equation is heavily dependent on the solution of a non-trivial contour integral specific to the 2D liquid. We find the solution to this integral and its generalizations, effectively reducing the problem of solving for the collective excitations of a collisionless two-dimensional Landau–Fermi liquid to solving for the roots of some high-degree polynomial. This analysis ultimately lays the mathematical foundation for the exploration of atypical behavior in the non-equilibrium properties of two-dimensional fermionic liquids in the context of the Landau quasiparticle paradigm.Note:
- 22 pages, 2 figures
References(0)
Figures(0)
Loading ...