Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1403.7408 · Physical Review A

Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid

Oleg Valentinovich Lychkovskiy

Published Apr 24, 2015• 23 citations
arXivHTMLPDF

Abstract

We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting, the impurity is injected in the fluid with some initial velocity ${\mathbf{v}}_{0}$, and we are interested in its velocity at infinite time, ${\mathbf{v}}_{\ensuremath{\infty}}$. We derive a rigorous upper bound on $|{\mathbf{v}}_{0}\ensuremath{-}{\mathbf{v}}_{\ensuremath{\infty}}|$ for initial velocities smaller than the generalized critical velocity. In the limit of vanishing impurity-fluid coupling, this bound amounts to ${\mathbf{v}}_{\ensuremath{\infty}}={\mathbf{v}}_{0}$, which can be regarded as a rigorous proof of the Landau criterion of superfluidity. In the case of a finite coupling, the velocity of the impurity can drop, but not to zero; the bound quantifies the maximal possible drop. In the second setting, a small constant force is exerted upon the impurity. We argue that two distinct dynamical regimes exist---backscattering oscillations of the impurity velocity and saturation of the velocity without oscillations. For fluids with ${v}_{c\mathrm{L}}={v}_{s}$ (where ${v}_{c\mathrm{L}}$ and ${v}_{s}$ are the Landau critical velocity and sound velocity, respectively), the latter regime is realized. For fluids with ${v}_{c\mathrm{L}}<{v}_{s}$, both regimes are possible. Which regime is realized in this case depends on the mass of the impurity, a nonequilibrium quantum phase transition occurring at some critical mass. Our results are equally valid in one, two, and three dimensions.

DOI
10.1103/physreva.91.040101

Related papers

Perpetual motion and backscattering oscillations of a mobile impurity in a quantum fluid

Oleg Valentinovich Lychkovskiy

We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting an impurity is injected in a fluid with some initial velocity ${\mathbf v}_0$, and we are interested in its velocity at infinite time, ${\mathbf v}_\infty$. We derive a rigorous upper bound on $|{\mathbf v}_0-{\mathbf v}_\infty|$ for initial velocities smaller than some critical velocity. In the limit of vanishing impurity-fluid coupling this bound can be regarded as a rigorous proof of the Landau criterion of superfluidity. In the case of a finite coupling the velocity of the impurity can drop, but not to zero; the bound quantifies the maximal possible drop. In the second setting a small constant force acts on the impurity. We identify two possible regimes of the impurity dynamics -- backscattering oscillations of the impurity velocity and saturation of the velocity without oscillations. Which regime is realized depends on the spectrum of the fluid and the mass of the impurity. In particular, backscattering oscillations are possible for sufficiently heavy impurities in fluids with a roton feature of the spectrum. We critically discuss a concept of Bloch oscillations of a mobile impurity in a one-dimensional quantum fluid introduced in [Phys. Rev. Lett. 102, 070402 (2009)] and argue that this type of oscillations is absent in the thermodynamic limit.

•Mar 28, 2014•2 citations

Relaxation dynamics of a mobile impurity injected into a one-dimensional Bose gas

Saptarshi Majumdar, Aleksandra Petković

The nonequilibrium dynamics of an impurity immersed with a finite velocity into a one-dimensional system of weakly interacting bosons is studied within the framework of the time-dependent Gross-Pitaevskii equation. We uncover and characterize different regimes of relaxation dynamics. We find that the final impurity velocity remains constant in a large interval of sufficiently big and realistic initial velocities. The underlying physical mechanism is the emission of the dispersive density shock waves that carry away the excess of the initial impurity momentum, while locally the system remains in the same stationary state. In contrast, a heavy impurity with the same coupling constant relaxes differently and the regime of constant final velocity disappears. Furthermore, a fast heavy impurity exhibits damped velocity oscillations in time before reaching a stationary state. This process is accompanied by the oscillations of the local depletion of the boson density around the impurity, until their positions coincide and they continue the motion together. Decreasing the impurity-boson coupling or increasing the strength of repulsion between bosons, the oscillations get amplified. In the case of a heavy impurity with the mass bigger than the critical one, the ground-state energy as a function of momentum exhibits cusps and metastable branches. We show that they manifest themselves by a soliton emission, a considerable slowing down of the relaxation, and a change of the impurity direction of motion with respect to the initial one.

arXiv:2507.10402•Physical Review A•Nov 25, 2025•2 citations

Perpetual motion of a mobile impurity in a one-dimensional quantum gas

Oleg Valentinovich Lychkovskiy

Consider an impurity particle injected in a degenerate one-dimensional gas of noninteracting fermions (or, equivalently, Tonks-Girardeau bosons) with some initial momentum ${p}_{0}$. We examine the infinite-time value of the momentum of the impurity, ${p}_{\ensuremath{\infty}}$, as a function of ${p}_{0}$. A lower bound on $|{p}_{\ensuremath{\infty}}({p}_{0})|$ is derived under fairly general conditions. The derivation, based on the existence of the lower edge of the spectrum of the host gas, does not resort to any approximations. The existence of such bound implies the perpetual motion of the impurity in a one-dimensional gas of noninteracting fermions or Tonks-Girardeau bosons at zero temperature. The bound admits an especially simple and useful form when the interaction between the impurity and host particles is everywhere repulsive.

arXiv:1308.6260•Physical Review A•Mar 13, 2014•22 citations

Dynamical Quantum Cherenkov Transition of Fast Impurities in Quantum Liquids

Kushal Seetharam, Yulia E. Shchadilova, Fabian Grusdt +2 more

The challenge of understanding the dynamics of a mobile impurity in an interacting quantum many-body medium comes from the necessity of including entanglement between the impurity and excited states of the environment in a wide range of energy scales. In this Letter, we investigate the motion of a finite mass impurity injected into a three-dimensional quantum Bose fluid as it starts shedding Bogoliubov excitations. We uncover a transition in the dynamics as the impurity's velocity crosses a critical value that depends on the strength of the interaction between the impurity and bosons as well as the impurity's recoil energy. We find that in injection experiments, the two regimes differ not only in the character of the impurity velocity abatement but also exhibit qualitative differences in the Loschmidt echo, density ripples excited in the Bose-Einstein condensate, and momentum distribution of scattered bosonic particles. The transition is a manifestation of a dynamical quantum Cherenkov effect and should be experimentally observable with ultracold atoms using Ramsey interferometry, rf spectroscopy, absorption imaging, and time-of-flight imaging.

arXiv:2101.00030•Physical Review Letters•Oct 29, 2021•38 citations

Critical Velocity of a Mobile Impurity in One-Dimensional Quantum Liquids

Michael Schecter, Alex Kamenev, Dimitri M. Gangardt +1 more

We study the notion of superfluid critical velocity in one spatial dimension. It is shown that, for heavy impurities with mass M exceeding a critical mass Mc, the dispersion develops periodic metastable branches resulting in dramatic changes of dynamics in the presence of an external driving force. In contrast to smooth Bloch oscillations for M<Mc, a heavy impurity climbs metastable branches until it reaches a branch termination point or undergoes a random tunneling event, both leading to an abrupt change in velocity and an energy loss. This is predicted to lead to a nonanalytic dependence of the impurity drift velocity on small forces.

arXiv:1110.2788•Physical Review Letters•May 14, 2012•59 citations

Observing dissipationless flow of an impurity in a strongly repulsive quantum fluid

Milena Horvath, Sudipta Dhar, Elisabeth Wybo +6 more

The frictionless motion of an object through a fluid medium is commonly viewed as a hallmark of superfluidity. According to Landau, kinematic constraints prohibit superfluid behavior in one-dimensional (1D) bosonic systems. Here, using ultracold atoms, we show how a microscopic impurity can propagate through a strongly interacting 1D Bose gas without any friction, at odds with conventional expectations. We inject the impurity with initial velocities ranging from the subsonic to supersonic regime, and subsequently track its dynamics. For supersonic initial velocities, we observe the formation of a shock wave and a remarkably fast relaxation to a stationary regime, on a time scale that increases with decreasing impurity velocity. After reaching the stationary state, the impurity continues its motion through the system with a finite velocity. Our findings demonstrate how quantum effects can conspire to eliminate dissipation of a microscopic object immersed in a quantum fluid, thereby bringing novel insights into the propagation of matter and information in the quantum realm.

cond-mat.quant-gasCross-listedarXiv:2602.12320•Feb 13, 2026•0 citations
We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting, the impurity is injected in the fluid with some initial velocity v0{\mathbf{v}}_{0}v0​, and we are interested in its velocity at infinite time, v\ensuremath∞{\mathbf{v}}_{\ensuremath{\infty}}v\ensuremath∞​. We derive a rigorous upper bound on ∣v0\ensuremath−v\ensuremath∞∣|{\mathbf{v}}_{0}\ensuremath{-}{\mathbf{v}}_{\ensuremath{\infty}}|∣v0​\ensuremath−v\ensuremath∞​∣ for initial velocities smaller than the generalized critical velocity. In the limit of vanishing impurity-fluid coupling, this bound amounts to v\ensuremath∞=v0{\mathbf{v}}_{\ensuremath{\infty}}={\mathbf{v}}_{0}v\ensuremath∞​=v0​, which can be regarded as a rigorous proof of the Landau criterion of superfluidity. In the case of a finite coupling, the velocity of the impurity can drop, but not to zero; the bound quantifies the maximal possible drop. In the second setting, a small constant force is exerted upon the impurity. We argue that two distinct dynamical regimes exist---backscattering oscillations of the impurity velocity and saturation of the velocity without oscillations. For fluids with vcL=vs{v}_{c\mathrm{L}}={v}_{s}vcL​=vs​ (where vcL{v}_{c\mathrm{L}}vcL​ and vs{v}_{s}vs​ are the Landau critical velocity and sound velocity, respectively), the latter regime is realized. For fluids with vcL<vs{v}_{c\mathrm{L}}<{v}_{s}vcL​<vs​, both regimes are possible. Which regime is realized in this case depends on the mass of the impurity, a nonequilibrium quantum phase transition occurring at some critical mass. Our results are equally valid in one, two, and three dimensions.
We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting an impurity is injected in a fluid with some initial velocity v0{\mathbf v}_0v0​, and we are interested in its velocity at infinite time, v∞{\mathbf v}_\inftyv∞​. We derive a rigorous upper bound on ∣v0−v∞∣|{\mathbf v}_0-{\mathbf v}_\infty|∣v0​−v∞​∣ for initial velocities smaller than some critical velocity. In the limit of vanishing impurity-fluid coupling this bound can be regarded as a rigorous proof of the Landau criterion of superfluidity. In the case of a finite coupling the velocity of the impurity can drop, but not to zero; the bound quantifies the maximal possible drop. In the second setting a small constant force acts on the impurity. We identify two possible regimes of the impurity dynamics -- backscattering oscillations of the impurity velocity and saturation of the velocity without oscillations. Which regime is realized depends on the spectrum of the fluid and the mass of the impurity. In particular, backscattering oscillations are possible for sufficiently heavy impurities in fluids with a roton feature of the spectrum. We critically discuss a concept of Bloch oscillations of a mobile impurity in a one-dimensional quantum fluid introduced in [Phys. Rev. Lett. 102, 070402 (2009)] and argue that this type of oscillations is absent in the thermodynamic limit.
The nonequilibrium dynamics of an impurity immersed with a finite velocity into a one-dimensional system of weakly interacting bosons is studied within the framework of the time-dependent Gross-Pitaevskii equation. We uncover and characterize different regimes of relaxation dynamics. We find that the final impurity velocity remains constant in a large interval of sufficiently big and realistic initial velocities. The underlying physical mechanism is the emission of the dispersive density shock waves that carry away the excess of the initial impurity momentum, while locally the system remains in the same stationary state. In contrast, a heavy impurity with the same coupling constant relaxes differently and the regime of constant final velocity disappears. Furthermore, a fast heavy impurity exhibits damped velocity oscillations in time before reaching a stationary state. This process is accompanied by the oscillations of the local depletion of the boson density around the impurity, until their positions coincide and they continue the motion together. Decreasing the impurity-boson coupling or increasing the strength of repulsion between bosons, the oscillations get amplified. In the case of a heavy impurity with the mass bigger than the critical one, the ground-state energy as a function of momentum exhibits cusps and metastable branches. We show that they manifest themselves by a soliton emission, a considerable slowing down of the relaxation, and a change of the impurity direction of motion with respect to the initial one.
Consider an impurity particle injected in a degenerate one-dimensional gas of noninteracting fermions (or, equivalently, Tonks-Girardeau bosons) with some initial momentum p0{p}_{0}p0​. We examine the infinite-time value of the momentum of the impurity, ${p}_{\ensuremath{\infty}}$, as a function of p0{p}_{0}p0​. A lower bound on $|{p}_{\ensuremath{\infty}}({p}_{0})|$ is derived under fairly general conditions. The derivation, based on the existence of the lower edge of the spectrum of the host gas, does not resort to any approximations. The existence of such bound implies the perpetual motion of the impurity in a one-dimensional gas of noninteracting fermions or Tonks-Girardeau bosons at zero temperature. The bound admits an especially simple and useful form when the interaction between the impurity and host particles is everywhere repulsive.
The challenge of understanding the dynamics of a mobile impurity in an interacting quantum many-body medium comes from the necessity of including entanglement between the impurity and excited states of the environment in a wide range of energy scales. In this Letter, we investigate the motion of a finite mass impurity injected into a three-dimensional quantum Bose fluid as it starts shedding Bogoliubov excitations. We uncover a transition in the dynamics as the impurity's velocity crosses a critical value that depends on the strength of the interaction between the impurity and bosons as well as the impurity's recoil energy. We find that in injection experiments, the two regimes differ not only in the character of the impurity velocity abatement but also exhibit qualitative differences in the Loschmidt echo, density ripples excited in the Bose-Einstein condensate, and momentum distribution of scattered bosonic particles. The transition is a manifestation of a dynamical quantum Cherenkov effect and should be experimentally observable with ultracold atoms using Ramsey interferometry, rf spectroscopy, absorption imaging, and time-of-flight imaging.
We study the notion of superfluid critical velocity in one spatial dimension. It is shown that, for heavy impurities with mass M exceeding a critical mass Mc, the dispersion develops periodic metastable branches resulting in dramatic changes of dynamics in the presence of an external driving force. In contrast to smooth Bloch oscillations for M<Mc, a heavy impurity climbs metastable branches until it reaches a branch termination point or undergoes a random tunneling event, both leading to an abrupt change in velocity and an energy loss. This is predicted to lead to a nonanalytic dependence of the impurity drift velocity on small forces.
The frictionless motion of an object through a fluid medium is commonly viewed as a hallmark of superfluidity. According to Landau, kinematic constraints prohibit superfluid behavior in one-dimensional (1D) bosonic systems. Here, using ultracold atoms, we show how a microscopic impurity can propagate through a strongly interacting 1D Bose gas without any friction, at odds with conventional expectations. We inject the impurity with initial velocities ranging from the subsonic to supersonic regime, and subsequently track its dynamics. For supersonic initial velocities, we observe the formation of a shock wave and a remarkably fast relaxation to a stationary regime, on a time scale that increases with decreasing impurity velocity. After reaching the stationary state, the impurity continues its motion through the system with a finite velocity. Our findings demonstrate how quantum effects can conspire to eliminate dissipation of a microscopic object immersed in a quantum fluid, thereby bringing novel insights into the propagation of matter and information in the quantum realm.