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New Trends in Mathematical and Theoretical Physics
October 3, 2016 17:30, Moscow, MIAN, Gubkina, 8

Dynamics of a mobile impurity in a one-dimensional quantum fluid

Oleg Lychkovskiyab

a International Center for Quantum Optics and Quantum Technologies (the Russian Quantum Center)
b Steklov Mathematical Institute
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MP4 145.1 Mb

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Oleg Lychkovskiy
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Abstract: Consider a mobile impurity particle injected in a one-dimensional quantum fluid with some initial velocity, $v_0$. What will be the relaxation dynamics of the impurity? Numerical and seminumerical studies of finite systems ($N<50$, where $N$ is the number of particles of the fluid) revealed a highly nontrivial dynamics: The impurity's velocity experienced oscillations superimposed on a slowdown; finally the velocity apparently saturated at some non-zero value, $v_f$ [1,2]. These studies, while producing much excitement, left unanswered basic questions on the nature of the effects discovered. It was even unclear whether the the incomplete relaxation was a finite-size effect or an effect present in the thermodynamic limit.
We present a detailed analytical study of the anomalous relaxation dynamics of an impurity particle injected in the one-dimensional quantum fluid [3-7]. In particular, we rigorously prove that the impurity particle of finite mass never stops completely, even in the thermodynamic limit [3,4]. This should be contrasted with the well-known absence of superfluidity in one dimension. These two facts can be reconciled since $v_f$ depends on the mass of the particle and vanishes for the infinite mass, which is equivalent to the absence of superfluid flow through a static constriction. We also find analytical dependence of the final velocity, $v_f$, on the initial velocity, $v_0$, for particular quantum fluids, the one-dimensional Fermi gas and the gas of impenetrable bosons [5-7].

Language: English

  1. C. J. M. Mathy, M. B. Zvonarev, and E. Demler, “Quantum flutter of supersonic particles in one-dimensional quantum liquids”, Nature Physics, 8 (2012), 881–886  crossref  isi  scopus
  2. M. Knap, C. J. M. Mathy, M. Ganahl, M. B. Zvonarev, and E. Demler, “Quantum flutter: Signatures and robustness”, Phys. Rev. Lett., 112 (2014), 015302  crossref  isi  scopus
  3. O. Lychkovskiy, “Perpetual motion of a mobile impurity in a one-dimensional quantum gas”, Phys. Rev. A, 89 (2014), 033619  crossref  isi  scopus
  4. O. Lychkovskiy, “Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid”, (Rapid Communication), Phys. Rev. A, 91 (2015), 040101  crossref  scopus
  5. E. Burovski, V. Cheianov, O. Gamayun, and O. Lychkovskiy, “Momentum relaxation of a mobile impurity in a one-dimensional quantum gas”, (Rapid Communication), Phys. Rev. A, 89 (2014), 041601  crossref  scopus
  6. O. Gamayun, O. Lychkovskiy, V. Cheianov, “Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas”, Phys. Rev. E, 90 (2014), 032132  crossref  isi  scopus
  7. O. Gamayun, E. Burovski, V. Cheianov, O. Lychkovskiy, M. Malcomson, M. Zvonarev, in preparation

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