Damping of zero sound in Luttinger liquids |
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Authors: | P Pirooznia P Kopietz |
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Institution: | 1.Institut für Theoretische Physik, Universit?t Frankfurt,Frankfurt,Germany |
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Abstract: | We calculate the damping γq of collective density oscillations
(zero sound) in a
one-dimensional Fermi gas
with dimensionless forward scattering interaction
F and quadratic energy dispersion
k2 / 2 m at zero temperature.
Using standard many-body perturbation theory,
we obtain γq from the expansion
of the
inverse irreducible polarization to first order
in the effective screened (RPA) interaction.
For wave-vectors | q| /kF ≪F (where kF = m vF is the Fermi wave-vector)
we find to leading order γq ∝| q |3 /(vF m2).
On the other hand, for F ≪| q| /kF most of the spectral weight
is carried by the particle-hole continuum, which is
distributed over a frequency interval of the order of q2/m.
We also show that zero sound damping
leads to a finite maximum proportional to
|k - kF | -2 + 2 η
of the charge peak in the single-particle
spectral function, where η is the anomalous
dimension. Our prediction agrees with photoemission data for
the blue bronze K0.3MoO3.
We comment on other recent calculations of γq. |
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Keywords: | 71 10 Pm Fermions in reduced dimensions (anyons composite fermions Luttinger liquid etc ) 71 10 -w Theories and models of many-electron systems |
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