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:1806.02554 · Physical review. B./Physical review. B

Models for supercritical motion in a superfluid Fermi liquid

J. A. Kuorelahti, Sami Laine, E. V. Thuneberg

Published Oct 16, 2018• 13 citations
arXivHTMLPDF

Abstract

We study the drag force on objects moving in a Fermi superfluid at velocities on the order of the Landau velocity ${v}_{L}$. The expectation has been that ${v}_{L}$ is the critical velocity beyond which the drag force starts to increase toward its normal-state value. This expectation is challenged by a recent experiment measuring the heat generated by a uniformly moving wire immersed in superfluid $^{3}\mathrm{He}$. We introduce the basis for the calculation of the drag force on a macroscopic object using the Fermi-liquid theory of superfluidity. As a technical tool in the calculations, we propose a boundary condition that describes diffuse reflection of quasiparticles from a surface on a scale that is larger than the superfluid coherence length. We calculate the drag force on steadily moving objects of different sizes. For an object that is small compared to the coherence length, we find a drag force that is in accordance with the expectation. For a macroscopic object, we need to take into account the spatially varying flow field around the object. At low velocities, this arises from ideal flow of the superfluid. At higher velocities, the flow field is modified by excitations that are created when the flow velocity locally exceeds ${v}_{L}$. The flow field causes Andreev reflection of quasiparticles and thus leads to change in the drag force. We calculate multiple limiting cases for a cylinder-shaped object. In the absence of quasiparticle-quasiparticle collisions, we find that the critical velocity is larger than ${v}_{L}$ and the drag force (per cross-sectional area) at $2{v}_{L}$ is reduced by an order of magnitude compared to the case of a small object. In a collision-dominated limit, the flow shows signs of instability at a velocity below ${v}_{L}$.

DOI
10.1103/physrevb.98.144512

Related papers

Dynamics of supersolid state: Normal fluid, superfluid, and supersolid velocities

Wayne M. Saslow

We consider the dynamics of a supersolid state that is based on Leggett's idea of local phase flow around the atomic sites of the solid. This leads to a local microscopic superfluid velocity that is not Galilean and is defined only relative to the solid and a $T=0$ superfluid fraction ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}<1$ (with $\ensuremath{\rho}$ being the macroscopic mass density). Landau's excitation-based argument for superfluids---that at temperature $T=0$ the normal fluid mass density ${\ensuremath{\rho}}_{N}$ is zero---should apply to supersolids. Together these two arguments imply that at low $T$ there is a missing mass density. We attribute this to a supersolid density ${\ensuremath{\rho}}_{L}$, with ${\ensuremath{\rho}}_{L}\ensuremath{\equiv}\ensuremath{\rho}\ensuremath{-}{\ensuremath{\rho}}_{S}\ensuremath{-}{\ensuremath{\rho}}_{N}$ and a momentum-bearing supersolid velocity ${v}_{Li}$. We derive the macroscopic dynamical equations for this system with three momentum-bearing macroscopic velocities $({v}_{Li},{v}_{Ni},{v}_{Si})$ using Onsager's irreversible thermodynamics. For slow spatial variations, ${v}_{Si}$ accelerates along the negative gradient of the chemical potential or mass, like for an ordinary superfluid, and ${v}_{Ni}$ is subject to drag against ${v}_{Li}$ with a characteristic drag time $\ensuremath{\tau}$. There are three contributions to the acceleration of ${v}_{Li}$: drag against ${v}_{Ni}$, along the negative gradient of the chemical potential or mass, and due to the forces of lattice elasticity. For high-frequency motion relative to the drag time $\ensuremath{\tau}$, ${\ensuremath{\rho}}_{L}$ moves independently of ${\ensuremath{\rho}}_{N}$. The normal modes for such a system have a crossover frequency below which the normal fluid velocity ${v}_{Ni}$ is dragged into motion with ${v}_{Li}$ (so the theory reduces to the ${v}_{Si},{v}_{Ni}$ theory of Andreev and Lifshitz) and above which the normal fluid velocity ${v}_{Ni}$ is an independent variable. For an isotropic lattice we study the transverse and longitudinal responses. A frequency-dependent rotational inertia experiment is predicted to show, at frequencies that are low relative to $\ensuremath{\tau}$, that ${\ensuremath{\rho}}_{L}$ and ${\ensuremath{\rho}}_{N}$ move together but that at high frequencies ${\ensuremath{\rho}}_{L}$ moves much more than ${\ensuremath{\rho}}_{N}$.

arXiv:2501.06338•Physical Review A•Aug 12, 2025•1 citation

Critical velocity, vortex shedding, and drag in a unitary Fermi superfluid

Francesco Ancilotto, Luca Salasnich, Flavio Toigo

We study the real-time motion of a microscopic object in a cold Fermi gas at unitary conditions by using an extended Thomas-Fermi density functional approach. We find that the spontaneous creation of singly quantized vortex-antivortex pairs occurs as a critical velocity is exceeded, which leads to a drag between the moving object and the Fermi gas. The resulting force is linear in the velocity for subsonic motion and becomes quadratic for supersonic motion.

arXiv:1301.5133•Physical Review A•Jan 31, 2013•4 citations

Quantum drag forces below the superfluid critical velocity in dilute gas Bose-Einstein condensates

Chao Feng, Tod M. Wright, Matthew J. Davis

It has been proposed in recent years that an impurity moving in a superfluid will experience drag forces even below the Landau critical velocity [1–3]. Quantum fluctuations that are present in superfluid systems at zero temperature can scatter from impurities present in the fluid. If the impurity is moving, there will be an asymmetric Doppler shift associated with the scattered waves, which will result in a net drag force. This challenges the long-accepted notion of dissipationless flow in superfluids. Analytical estimates of this drag force in superfluid Bose-Einstein condensates using Bogoliubov methods have found a non-zero drag force, resulting from the most sensible choice of boundary conditions in an infinite system. Through stochastic simulations of the 1D Bose gas under the truncated Wigner formalism, we verify the existence of this sub-critical drag force and quantify the drag forces present. We will also determine whether dissipationless flow can be recovered in finite sized systems.

Optics InfoBase Conference Papers•Jan 1, 2011•0 citations

Casimir Friction II: Casimir effect and drag in zero temperature superfluids

David C K Roberts, Yves Pomeau A

We discuss a force arising from zero-temperature quantum fluctuations in a weakly interacting Bose-Einstein condensate (BEC). We argue that there is a drag force on an object moving at speeds well below Landau's critical velocity, and motivate our argument by an analogy to the Casimir force in an electromagnetic vacuum. We sketch the calculation of this force for an object described by a general potential. We comment about the relevance of our results to the stability of superfluid flow, arguing that this effect is consistent with the observation of persistent currents and that this effect introduces new experimental observables. Finally, we describe a new hydryodynamic boundary condition for superfluid flow that takes into account the scattering of quantum fluctuations off a rough surface.

arXiv:cond-mat/0503757•Mar 31, 2005•2 citations

Landau critical velocity for a macroscopic object moving in superfluid B3 : Evidence for gap suppression at a moving surface

C. A. M. Castelijns, K. F. Coates, A. M. Guénault +2 more

We have observed that the motion of a vibrating-wire resonator in superfluid $^{3}\mathit{B}$ at temperatures below ${\mathrm{T}}_{\mathrm{c}}$/8 is associated with a sharp critical velocity, ${\mathrm{v}}_{\mathrm{c}}$, above which very high dissipation sets in. We identify this velocity with the Landau critical velocity for pair breaking. That the observed value of ${\mathrm{v}}_{\mathrm{c}}$ is a factor of 2 lower than the critical velocity expected from the BCS value of the gap we take as evidence that the gap is suppressed by about 50% of its bulk value near a moving boundary.

Physical Review Letters•Jan 6, 1986•145 citations

When superfluids are a drag

David C K Roberts

The article considers the dramatic phenomenon of seemingly frictionless flow of slow-moving superfluids. Specifically the question of whether an object in a superfluid flow experiences any drag force is addressed. A brief account is given of the history of this problem and it is argued that recent advances in ultracold atomic physics can shed much new light on this problem. The article presents the commonly held notion that sufficiently slow-moving superfluids can flow without drag and also discusses research suggesting that scattering quantum fluctuations might cause drag in a superfluid moving at any speed.

Contemporary Physics•May 1, 2009•3 citations
We study the drag force on objects moving in a Fermi superfluid at velocities on the order of the Landau velocity vL{v}_{L}vL​. The expectation has been that vL{v}_{L}vL​ is the critical velocity beyond which the drag force starts to increase toward its normal-state value. This expectation is challenged by a recent experiment measuring the heat generated by a uniformly moving wire immersed in superfluid 3He^{3}\mathrm{He}3He. We introduce the basis for the calculation of the drag force on a macroscopic object using the Fermi-liquid theory of superfluidity. As a technical tool in the calculations, we propose a boundary condition that describes diffuse reflection of quasiparticles from a surface on a scale that is larger than the superfluid coherence length. We calculate the drag force on steadily moving objects of different sizes. For an object that is small compared to the coherence length, we find a drag force that is in accordance with the expectation. For a macroscopic object, we need to take into account the spatially varying flow field around the object. At low velocities, this arises from ideal flow of the superfluid. At higher velocities, the flow field is modified by excitations that are created when the flow velocity locally exceeds vL{v}_{L}vL​. The flow field causes Andreev reflection of quasiparticles and thus leads to change in the drag force. We calculate multiple limiting cases for a cylinder-shaped object. In the absence of quasiparticle-quasiparticle collisions, we find that the critical velocity is larger than vL{v}_{L}vL​ and the drag force (per cross-sectional area) at 2vL2{v}_{L}2vL​ is reduced by an order of magnitude compared to the case of a small object. In a collision-dominated limit, the flow shows signs of instability at a velocity below vL{v}_{L}vL​.
We consider the dynamics of a supersolid state that is based on Leggett's idea of local phase flow around the atomic sites of the solid. This leads to a local microscopic superfluid velocity that is not Galilean and is defined only relative to the solid and a T=0T=0T=0 superfluid fraction ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}<1$ (with $\ensuremath{\rho}$ being the macroscopic mass density). Landau's excitation-based argument for superfluids---that at temperature T=0T=0T=0 the normal fluid mass density ${\ensuremath{\rho}}_{N}$ is zero---should apply to supersolids. Together these two arguments imply that at low TTT there is a missing mass density. We attribute this to a supersolid density ${\ensuremath{\rho}}_{L}$, with ${\ensuremath{\rho}}_{L}\ensuremath{\equiv}\ensuremath{\rho}\ensuremath{-}{\ensuremath{\rho}}_{S}\ensuremath{-}{\ensuremath{\rho}}_{N}$ and a momentum-bearing supersolid velocity vLi{v}_{Li}vLi​. We derive the macroscopic dynamical equations for this system with three momentum-bearing macroscopic velocities (vLi,vNi,vSi)({v}_{Li},{v}_{Ni},{v}_{Si})(vLi​,vNi​,vSi​) using Onsager's irreversible thermodynamics. For slow spatial variations, vSi{v}_{Si}vSi​ accelerates along the negative gradient of the chemical potential or mass, like for an ordinary superfluid, and vNi{v}_{Ni}vNi​ is subject to drag against vLi{v}_{Li}vLi​ with a characteristic drag time $\ensuremath{\tau}$. There are three contributions to the acceleration of vLi{v}_{Li}vLi​: drag against vNi{v}_{Ni}vNi​, along the negative gradient of the chemical potential or mass, and due to the forces of lattice elasticity. For high-frequency motion relative to the drag time $\ensuremath{\tau}$, ${\ensuremath{\rho}}_{L}$ moves independently of ${\ensuremath{\rho}}_{N}$. The normal modes for such a system have a crossover frequency below which the normal fluid velocity vNi{v}_{Ni}vNi​ is dragged into motion with vLi{v}_{Li}vLi​ (so the theory reduces to the vSi,vNi{v}_{Si},{v}_{Ni}vSi​,vNi​ theory of Andreev and Lifshitz) and above which the normal fluid velocity vNi{v}_{Ni}vNi​ is an independent variable. For an isotropic lattice we study the transverse and longitudinal responses. A frequency-dependent rotational inertia experiment is predicted to show, at frequencies that are low relative to $\ensuremath{\tau}$, that ${\ensuremath{\rho}}_{L}$ and ${\ensuremath{\rho}}_{N}$ move together but that at high frequencies ${\ensuremath{\rho}}_{L}$ moves much more than ${\ensuremath{\rho}}_{N}$.
It has been proposed in recent years that an impurity moving in a superfluid will experience drag forces even below the Landau critical velocity [1–3]. Quantum fluctuations that are present in superfluid systems at zero temperature can scatter from impurities present in the fluid. If the impurity is moving, there will be an asymmetric Doppler shift associated with the scattered waves, which will result in a net drag force. This challenges the long-accepted notion of dissipationless flow in superfluids. Analytical estimates of this drag force in superfluid Bose-Einstein condensates using Bogoliubov methods have found a non-zero drag force, resulting from the most sensible choice of boundary conditions in an infinite system. Through stochastic simulations of the 1D Bose gas under the truncated Wigner formalism, we verify the existence of this sub-critical drag force and quantify the drag forces present. We will also determine whether dissipationless flow can be recovered in finite sized systems.
We discuss a force arising from zero-temperature quantum fluctuations in a weakly interacting Bose-Einstein condensate (BEC). We argue that there is a drag force on an object moving at speeds well below Landau's critical velocity, and motivate our argument by an analogy to the Casimir force in an electromagnetic vacuum. We sketch the calculation of this force for an object described by a general potential. We comment about the relevance of our results to the stability of superfluid flow, arguing that this effect is consistent with the observation of persistent currents and that this effect introduces new experimental observables. Finally, we describe a new hydryodynamic boundary condition for superfluid flow that takes into account the scattering of quantum fluctuations off a rough surface.
We have observed that the motion of a vibrating-wire resonator in superfluid 3B^{3}\mathit{B}3B at temperatures below Tc{\mathrm{T}}_{\mathrm{c}}Tc​/8 is associated with a sharp critical velocity, vc{\mathrm{v}}_{\mathrm{c}}vc​, above which very high dissipation sets in. We identify this velocity with the Landau critical velocity for pair breaking. That the observed value of vc{\mathrm{v}}_{\mathrm{c}}vc​ is a factor of 2 lower than the critical velocity expected from the BCS value of the gap we take as evidence that the gap is suppressed by about 50% of its bulk value near a moving boundary.
The article considers the dramatic phenomenon of seemingly frictionless flow of slow-moving superfluids. Specifically the question of whether an object in a superfluid flow experiences any drag force is addressed. A brief account is given of the history of this problem and it is argued that recent advances in ultracold atomic physics can shed much new light on this problem. The article presents the commonly held notion that sufficiently slow-moving superfluids can flow without drag and also discusses research suggesting that scattering quantum fluctuations might cause drag in a superfluid moving at any speed.