Electron lifetime in Luttinger liquids

We investigate the decoherence of the electron wave packet in purely ballistic one-dimensional systems described through the Luttinger liquid (LL). At a finite temperature T and long times t, we show that the electron Green's function for a fixed wave vector close to one Fermi point decays as exp(-t/ τF) -as opposed to the power-law behavior occurring at short times-and the emerging electron lifetime obeys τF -1 T for spinful as well as spinless electrons. For strong interactions, (T τF) 1, reflecting that the electron is not a good Landau quasiparticle in LL's. We justify that fractionalization is the main source of electron decoherence for spinful as well as spinless electrons clarifying the peculiar electron mass renormalization close to the Fermi points. For spinless electrons and weak interactions, our intuition can be enriched through a diagrammatic approach or Fermi golden rule and through a Johnson-Nyquist noise picture. We stress that the electron lifetime (and the fractional quasiparticles) can be revealed from Aharonov-Bohm experiments or momentum resolved tunneling. We aim to compare the results with those of spin-incoherent and chiral LL's.