Dynamics and Bloch oscillations of mobile impurities in one-dimensional quantum liquids

M. Schecter, D. M. Gangardt, A. Kamenev

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We study the dynamics of a mobile impurity moving in a one-dimensional quantum liquid. Such an impurity induces a strong, non-linear depletion of the liquid around it. The dispersion relation of the combined object, called depleton, is a periodic function of its momentum with the period 2πn, where n is the mean density of the liquid. In the adiabatic approximation, a constant external force acting on the impurity leads to the Bloch oscillations of the impurity around a fixed position. Dynamically, such oscillations are accompanied by the radiation of energy in the form of phonons. The ensuing energy loss results in the uniform drift of the oscillation center. We derive exact results for the radiation-induced mobility as well as the thermal friction force in terms of the equilibrium dispersion relation of the dressed impurity (depleton). These results show that there is a wide range of external forces where the (drifted) Bloch oscillations exist and may be observed experimentally.

Original languageEnglish (US)
Pages (from-to)639-670
Number of pages32
JournalAnnals of Physics
Issue number3
StatePublished - Mar 2012

Bibliographical note

Funding Information:
We are indebted to L. Glazman, A. Lamacraft, M. Zvonarev, I. Lerner and J.M.F. Gunn for illuminating discussions. We also extend our gratitude to K. Matveev who pointed out an erroneous numerical factor in the thermal friction in the original version. MS and AK were supported by DOE contract DE-FG02-08ER46482 . DMG acknowledges the support by EPSRC Advanced Fellowship EP/D072514/1 . DMG and AK are thankful to Abdus Salam ICTP in Trieste for hospitality at the early stages of this work.


  • 1d quantum liquids
  • Bloch oscillations
  • Mobile impurity
  • Non-equilibrium transport
  • Superfluidity
  • Ultracold atoms


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