= Landau quasiparticle
{c}
{title2=$\xi_p$}
A <Landau quasiparticle> is a <fermionic> excitation connected continuously to a <Fermi gas> particle when interactions preserve the phase. Near an isotropic <Fermi surface>, its energy relative to the <chemical potential> is $\xi_p=\epsilon_p-\mu\simeq v_F(p-p_F)$, with <Fermi momentum> $p_F$ and <Fermi velocity> $v_F$.<The Theory of a Fermi Liquid by Lev Davidovich Landau>[Section 1, pp.921–922]{ref}
The <Pauli exclusion principle> restricts decay. For a three-dimensional normal <Fermi liquid> with regular short-range interactions, a representative low-energy lifetime model is
$$
\frac{\hbar}{\tau_p}=A\frac{\xi_p^2+(\pi k_BT)^2}{E_*},\qquad A>0,
$$
Here $E_*$ is an <energy> scale and $A$ is dimensionless; sharpness requires $\hbar/\tau_p\ll|\xi_p|$ at zero <temperature>.<Renormalization Group Approach to Interacting Fermions by Ramamurti Shankar>[Section VIII, manuscript p.114, quadratic lifetime corrections]{ref}
For an original example, stipulate $A=1$ and $T=0$. At $|\xi_p|/E_*=0.02$, the decay energy is $0.0004E_*$, just $2\%$ of the excitation <energy>; halving $|\xi_p|$ reduces that ratio to $1\%$. Approaching the <Fermi surface> improves the particle description even though the microscopic interaction has not weakened. This quadratic illustration is three-dimensional; low-dimensional corrections require separate analysis.
\Image[/fermi-liquid-quasiparticle-occupation-and-energy.png]
{title=Quasiparticle occupation and energy near a Fermi surface}
{description=Original local models with $E_u=p_F^2/m$, <Fermi-liquid effective mass> $m^*=2m$ and <quasiparticle residue> $Z=0.65$. The finite-<temperature> curve is the <Fermi-Dirac distribution> of <Landau quasiparticles>; the dashed particle distribution is a separate schematic. The shaded energy shell uses $k_BT/E_u=0.015$. These stipulated examples are not a fit to <helium-3>.}
Back to article page
