Do these defects actually correspond in a local acceleration of the superfluid or deceleration?

And if superfluid is locally accelerated inside these vortices wouldn't that rise the temperature of the superfluid at these points? Or is it the other way around and the temperature drops even more in these voritices? But would that not mean that the atoms of the superfluid in the quantum vortices get decelarated instead compared to the rest of the undisturbed bulk of the superfluid?

  • $\begingroup$ "Do these defects actually correspond in a local acceleration of the superfluid or deceleration?" what do you mean? $\endgroup$
    – Quillo
    Jun 6, 2022 at 15:11
  • $\begingroup$ @Quillo If atom's total kinetic energy is locally increased or decreased by the vortex? It could be prior to the vortex formation that atoms had a higher total kinetic energy due to high frequency random vibrational motion. I am interested if these vortices are actually increasing or decreasing their initial rest energy of these atoms locally? $\endgroup$
    – Markoul11
    Jun 8, 2022 at 18:06
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    $\begingroup$ They do, but the important thing that is globally minimized is $H-L \Omega$, where $L$ is the (conserved) total angular momentum and $ \Omega$ is the angular velocity of the system (ofc $H$ is the Hamiltonian). These are global quantities. A vortex state is more energetic than a no-vortex state. $\endgroup$
    – Quillo
    Jun 9, 2022 at 8:13
  • $\begingroup$ @Quillo The main reason why I am asking is because I want to learn how these defects (i.e. vortices) in the homogeneous BEC are created? Is it because locally there are spots with atoms with slight higher kinetic energy or lower kinetic energy and the pressure differential with the surrounding superfluid creates these vortices? In other word why is the symmetry and homogeneity breaking at these spots? $\endgroup$
    – Markoul11
    Jun 9, 2022 at 13:06
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    $\begingroup$ In general, to answer your question: no, vortices are not hotter than the rest of the superfluid. They can be there even at T=0 and even at complete thermodynamic equilibrium, where everything is thermalized (provided that the temperature is smaller than the transition temperature). $\endgroup$
    – Quillo
    Jun 9, 2022 at 13:19

1 Answer 1


The vortex is an equilibrium solution to the equations of superfluid hydrodynamics. The temperature is constant in space and time, and the velocity is constant in time, but varies as $1/r$ from the center of the vortex core. The circulation is quantized. There is a singularity at the vortex core. This singularity is regularized in microscopic theories of the superfluid, which show that the core has a size which is comparable to the separation between atoms, and that in the vortex core the superfluid density goes to zero.

In order to make a superfluid vortex the superfluid has to be stirred (or the container has to be spun up), and during the time that the vortex is formed superfluid is accelerated, and some heating takes place.

P.S.: A simple comment, in case this is driving the question. A particle undergoing circular motion is accelerated, but there is no work done on the particle. The same is true for a rotating fluid, in both the normal (rigid motion) and superfluid (vortex motion). In the Euler frame there is no acceleration at all, $\partial_t (\rho\vec{v})=0$. If we follow a fluid element (Lagrangian frame), then there is acceleration (the material derivative is not zero), but there is no work being done.

The difference between normal and superfluid rotation is that the vortex is (meta) stable because the circulation is quantized. In a normal fluid undergoing rotation the motion can decay by ordinary friction with the walls. A superfluid vortex can only disappear by quantum tunneling, or by reconnection of the vortex endpoints.

  • $\begingroup$ Thank for you expert answer. By not "work done" I guees it is meant that there is no energy exhange between the quantum vortex and its surroundings. All the steering kinetic energy put in the artificial rotation of the superhluid is transferred to the quantum vortices formed in the superfluid by this steeting action and then dissipated as heat? Just curious, what is a typical lifetime of these vortices after we stop steering? In seconds, ms or ns in duration? $\endgroup$
    – Markoul11
    Jun 6, 2022 at 9:30
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    $\begingroup$ In principle vortices are (essentially) eternal. In a neutron star, superfluid vortices in neutron matter can likely last millions of years. In a helium vessel a lattice of vortex lines can last for a long time, but indvidual vortex lines are more short-lived, lasting seconds in typical experimental conditions. $\endgroup$
    – Thomas
    Jun 6, 2022 at 13:35

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